2306.09896v1

# Demystifying GPT Self-Repair for Code Generation **Authors**: - Theo X. Olausson (MIT EECS & CSAIL &Jeevana Priya Inala) > Correspondence to . Work partially done while T.X.O. was at Microsoft Research. positioning ## Abstract Large Language Models (LLMs) have shown remarkable aptitude in code generation but still struggle on challenging programming tasks. Self-repair—in which the model debugs and fixes mistakes in its own code—has recently become a popular way to boost performance in these settings. However, only very limited studies on how and when self-repair works effectively exist in the literature, and one might wonder to what extent a model is really capable of providing accurate feedback on why the code is wrong when that code was generated by the same model. In this paper, we analyze GPT-3.5 and GPT-4’s ability to perform self-repair on APPS, a challenging dataset consisting of diverse coding challenges. To do so, we first establish a new evaluation strategy dubbed pass@t that measures the pass rate of the tasks against the total number of tokens sampled from the model, enabling a fair comparison to purely sampling-based approaches. With this evaluation strategy, we find that the effectiveness of self-repair is only seen in GPT-4. We also observe that self-repair is bottlenecked by the feedback stage; using GPT-4 to give feedback on the programs generated by GPT-3.5 and using expert human programmers to give feedback on the programs generated by GPT-4, we unlock significant performance gains. ## 1 Introduction Large language models (LLMs) have proven capable of generating code snippets from natural language specifications, but still struggle on complex coding challenges such as those found in competitions and professional software engineering interviews. Recent work has sought to improve performance by leveraging self-repair [Gupta et al., 2020, Le et al., 2022, Chen et al., 2023b, Zhang et al., 2023], in which the model introspects and corrects mistakes in its own code. Figure 1 shows a typical workflow of a self-repair based approach. First, given a specification, a program is sampled from a code generation model; this program is then executed on a suite of unit tests provided as part of the specification; if the program fails on any unit test, then the error message and the faulty program are given to a feedback generation model, which outputs a short explanation of why the code failed; finally, the feedback is passed to a repair model, which generates a fixed version of the program. On the surface, this is a very attractive idea. It allows the system to overcome mistakes caused by unfortunate samples during decoding; easily incorporates feedback during the repair phase from symbolic systems such as compilers, static analysis tools, and execution engines; and mimics the trial-and-error way in which human software engineers write code. <details> <summary>x1.png Details</summary>  ### Visual Description ## Flowchart: Iterative Code Model Refinement Process ### Overview The flowchart illustrates a cyclical process where a user interacts with a code model, executes code, receives feedback, and refines the model. It emphasizes iterative improvement through feedback loops, with specific attention to code assertions and their validation. ### Components/Axes 1. **User**: Represented by a gray silhouette (leftmost node). 2. **Code Model**: Depicted as a blue circular network (nodes connected by lines) in steps (1) and (5). 3. **Execution**: Contains three code assertions with success/failure indicators (green checkmarks and red X) in step (2). 4. **Feedback Model**: Shown as a yellow circular network (nodes connected by lines) in step (3). 5. **Arrows**: Black arrows indicate directional flow between components. ### Detailed Analysis 1. **Step (1)**: User → Code Model - User initiates interaction with the initial code model (blue nodes). 2. **Step (2)**: Code Model → Execution - Three assertions are executed: - `assert f(x1) == y1` ✅ (success) - `assert f(x2) == y2` ✅ (success) - `assert f(x3) == y3` ❌ (failure) 3. **Step (3)**: Execution → Feedback Model - Feedback model (yellow nodes) processes execution results to identify discrepancies. 4. **Step (4)**: Feedback Model → Code Model - Feedback is integrated into the code model, refining its structure (yellow nodes → blue nodes). 5. **Step (5)**: Code Model → Execution (loop) - Revised code model re-executes assertions: - `assert f(x1) == y1` ✅ - `assert f(x2) == y2` ✅ - `assert f(x3) == y3` ✅ ### Key Observations - **Iterative Refinement**: The process loops back to the code model after feedback, emphasizing continuous improvement. - **Failure Detection**: The red X in step (2) highlights the importance of error detection in code validation. - **Feedback Integration**: The transition from yellow (feedback) to blue (code model) nodes visually represents knowledge transfer. ### Interpretation This flowchart demonstrates a closed-loop system for code model development. The user's input drives initial code generation, while execution results (successes and failures) inform feedback that refines the model. The final loop shows successful validation of all assertions after refinement, underscoring the value of iterative feedback. The use of distinct colors (blue for code, yellow for feedback) spatially grounds the separation between model development and validation phases. The process aligns with principles of machine learning and software engineering, where iterative testing and adjustment are critical for robustness. </details> [ box/.style=rectangle, draw=black, align=justify, inner sep=3pt, tallbox/.style=box, fill=backcolor!50, shortbox/.style=box, fill=backcolor!50 ] [tallbox, text width=3.6cm, minimum height=3.2cm] (A) Given is a string $s$ representing the day of the week today. $s$ is one of SUN, MON, TUE, WED, THU, FRI, or SAT. After how many days is the next Sunday (tomorrow or later)? ⬇ # UNIT TESTS # (EXECUTABLE) assert f (’ MON ’) == 6 assert f (’ WED ’) == 4 assert f (’ SUN ’) == 7 ; [draw=none, left=0.2cm of A.west] (1); [shortbox, right=0.2cm of A.north east, text width=8cm, anchor=north west] (B) ⬇ def f (s): return (7 - [’ SUN ’, ... , ’ FRI ’, ’ SAT ’]. index (s)) %7 ; [draw=none, right=0.2cm of B.east] (2); [shortbox, below=0.2cm of B, text width=8cm] (C) Given input ’SUN’, the program returned 0, but the expected output was 7. ; [draw=none, right=0.2cm of C.east] (3); [shortbox, below=0.2cm of C, text width=8cm] (D) The code does not account for the case where the input is ’SUN’ and the output should be 7. This can be fixed by removing the modulo operation. ; [draw=none, right=0.2cm of D.east] (4); [shortbox, below=0.2cm of D, text width=8cm] (E) ⬇ def f (s): return (7 - [’ SUN ’, ... , ’ FRI ’, ’ SAT ’]. index (s)) # %7 ; [draw=none, right=0.2cm of E.east] (5); Figure 1: Self-repair with separate code and feedback models. First, a user gives a specification in the form of text and a suite of unit tests (1). Then, a code model (blue) generates a program (2). The program is checked against the unit tests using a symbolic execution engine, and an error message is returned (3). In order to provide more signal to the code model, textual feedback as to why this happened is provided by a feedback model (yellow; 4). Finally, this feedback is used by the code model to repair the program (5). However, it is important to remember that self-repair requires more invocations of the model, thus increasing the computational cost. In particular, whether self-repair is a winning strategy or not ultimately boils down to whether you would—at an equivalent compute budget—have had a greater chance of success if you had simply drawn more code samples i.i.d. from the model and checked them against the suite of unit tests provided as part of the task. Crucially, the effectiveness of self-repair depends not only on the model’s ability to generate code, which has been studied extensively in the literature, but also on its ability to identify how the code (generated by the model itself) is wrong with respect to the task specification. As far as we are aware, no previous or contemporary work has attempted to study the effect of this stage in detail. In this paper, we study the effectiveness of self-repair with GPT-3.5 [Ouyang et al., 2022, OpenAI, 2022] and GPT-4 [OpenAI, 2023] when solving competition-level code generation tasks. We begin by proposing a new evaluation strategy dubbed pass@t, in which the likelihood of obtaining a correct program (with respect to the given unit tests) is weighed against the total number of tokens sampled from the model. Using this instead of the traditional pass@k [Chen et al., 2021, Kulal et al., 2019] metric (which weighs pass rate against the number of trials), we are able to accurately compare performance gained through self-repair against any additional work done by the model when generating the feedback and carrying out the repair. Using this new evaluation strategy, we then carefully study the dynamics of the self-repair process under a range of hyper-parameters. Finally, given our primary objective of gaining insight into the state-of-the-art code generation models’ ability to reflect upon and debug their own code, we carry out a set of experiments in which we investigate the impact of improving the feedback stage alone. We do so by analyzing the impact of using a stronger feedback generation model than the code generation model (using GPT-4 to generate feedback for GPT-3.5 code model), as well as by carrying out a study in which human participants provide feedback on incorrect programs, in order to compare model-generated self-feedback to that provided by human programmers. From our experiments, we find that: 1. When taking the cost of doing inspection and repair into account, performance gains from self-repair can only be seen with GPT-4; for GPT-3.5, the pass rate with repair is lower than or equal to that of the baseline, no-repair approach at all budgets. 1. Even for the GPT-4 model, performance gains are modest at best ( $66\$ pass rate with a budget of 7000 tokens, $\approx$ the cost of 45 i.i.d. GPT-4 samples) and depend on having sufficient diversity in the initial programs. 1. Replacing GPT-3.5’s explanations of what is wrong with feedback produced by GPT-4 leads to better self-repair performance, even beating the baseline, no-repair GPT-3.5 approach ( $50\$ at 7000 tokens). 1. Replacing GPT-4’s own explanations with those of a human programmer improves repair significantly, leading to a 57% increase in the number of repaired programs which pass the tests. ## 2 Related work Program synthesis with large language models. The use of large language models for program synthesis has been studied extensively in the literature [Li et al., 2022, Austin et al., 2021, Chen et al., 2021, Le et al., 2022, Fried et al., 2023, Nijkamp et al., 2023, Chowdhery et al., 2022, Touvron et al., 2023, Li et al., 2023]. This literature has predominantly focused on evaluating models in terms of either raw accuracy or the pass@k metric [Kulal et al., 2019, Chen et al., 2021], often leveraging filtering techniques based on execution [Li et al., 2022, Shi et al., 2022] or ranking [Chen et al., 2021, Inala et al., 2022, Zhang et al., 2022] to reduce the number of samples which are considered for the final answer. In contrast, our work focuses on evaluating the models from the point of view of minimizing the number of samples that need to be drawn from the model in the first place. Our work is also different in that we assume access to the full collection of input-output examples, as is typically done in inductive synthesis [Kitzelmann, 2010, Polozov and Gulwani, 2015, Gulwani et al., 2017, Chen et al., 2019a, Ellis et al., 2021]. In particular, unlike some prior work [Li et al., 2022, Shi et al., 2022], we do not make a distinction between public tests used for filtering and private tests used to determine correctness, since our method does not involve filtering the outputs. Code repair. Statistical and learning-based techniques for code repair have a rich history in both the programming languages and machine learning communities, although they have traditionally been used predominantly to repair human-written code [Long and Rinard, 2016, Bader et al., 2019, Le Goues et al., 2021, Yasunaga and Liang, 2021, Chen et al., 2019b, Mesbah et al., 2019, Wang et al., 2018]. More recently, using repair as a post-processing step to improve code which was itself automatically synthesised has been used in the synthesis of both domain-specific languages [Gupta et al., 2020] and general-purpose code [Le et al., 2022, Yasunaga and Liang, 2021, 2020]. Our contribution differs from most prior work in this literature in the use of textual feedback for repair, which is possible thanks to the above mentioned rise in the use of LLMs for program synthesis. Contemporary work on LLM self-repair. Recognizing that there is much contemporary work seeking to self-repair with LLMs, we now briefly highlight a few such papers which are particularly close to our work. Zhang et al. [2023] explore self-repair without natural language feedback on APPS [Hendrycks et al., 2021] using a diverse range of fine-tuned models. They also experiment with prompt-based repair using Codex [Chen et al., 2021], InCoder [Fried et al., 2023], and CodeGen [Nijkamp et al., 2023]. Notably, their framework does not consider the cost associated with feedback and repair, which presents a significantly different perspective on self-repair. Similarly, Chen et al. [2023b] assess Codex’s ability to self-repair across a variety of tasks, in a framework that closely resembles that which we study in this work. However, their study differs from ours in terms of the models considered, the evaluation strategy, and, most importantly, the research goal, as we specifically aim to investigate the significance of the textual feedback stage. Self-repair, or frameworks with other names that are conceptually very similar to it, has also been used in contexts outside of code generation. Peng et al. [2023] use self-repair to mitigate hallucinations and improve factual grounding in a ChatGPT-based web search assistant, in which the model revises its initial response based on self-generated feedback. Similarly, Madaan et al. [2023] present a framework in which a model iteratively provides feedback on and revises its output until a stopping criterion is reached; they apply this framework to a range of tasks, including dialogue and code optimization. Ultimately, we see our work, in which we use the novel evaluation metric pass@t to investigate the significance of the textual feedback stage in competition-level self-repair, as being complementary to contemporary research which uses traditional metrics to evaluate self-repair in a broader context. We are eager to see what the implications of our results will be in these other domains. ## 3 Methodology ### 3.1 Self-Repair Overview As shown in Figure 1, our self-repair approach involves 4 stages: code generation, code execution, feedback generation, and code repair. We now formally define these four stages. Code generation. Given a specification $\psi$ , a programming model $M_{P}$ first generates $n_{p}$ samples i.i.d., which we denote $$ \{p_{i}\}_{i=1}^{n_{p}}\stackrel{{\scriptstyle i.i.d.}}{{\sim}}M_{P}(\psi) $$ Code execution. These $n_{p}$ code samples are then executed against a test bed. Recall from Section 2 that we assume that we have access to the full set of tests in executable form (see Section 5 for a brief discussion on the validity of this assumption in software engineering domains). Thus, we stop if any sample passes all of the tests, since a satisfying program has then been found. Otherwise, we collect the error messages $\{e_{i}\}_{i}$ returned by the execution environment. These error messages either contain the compile/runtime error information or an example input on which the program’s output differs from the expected one. An example is shown in Figure 1 (component 3). Feedback generation. Since the error messages from the execution environment are usually very high-level, they provide little signal for repair. Therefore, as an intermediate step, we use a feedback model to produce a more detailed explanation of what went wrong; Figure 1 (component 4) shows an example. Formally, in this stage, we generate $n_{f}$ feedback strings, $\{f_{ij}\}_{j}$ , for each wrong program, $p_{i}$ , as follows: $$ \{f_{ij}\}_{j=1}^{n_{f}}\stackrel{{\scriptstyle i.i.d.}}{{\sim}}M_{F}(\psi;p_{ i};e_{i}) $$ Having an explicit feedback generation step allows us to ablate this component so that we can study its significance in isolation. Code repair. In the final step, for each initial program $p_{i}$ and feedback $f_{ij}$ , $n_{r}$ candidate repaired programs are sampled from $M_{P}$ We use the same model for both the initial code generation and the code repair, since these are fundamentally similar tasks.: $$ \{r_{ijk}\}_{k=1}^{n_{r}}\stackrel{{\scriptstyle i.i.d.}}{{\sim}}M_{P}(\psi;p_ {i};e_{i};f_{ij}) $$ Repair tree. We call the tree of interleaved text and programs produced by this procedure—rooted in the specification $\psi$ , then branching into initial programs $p_{i}$ , each of which branches into feedback $f_{ij}$ and then repairs $r_{ijk}$ —a repair tree, $T$ (Figure 2). Caveat: jointly sampling feedback and repair. The general framework presented above does not require the programming model and feedback model to be the same, thus allowing for the use of specialized models in the system. However, when $M_{P}=M_{F}$ we jointly generate both the feedback and the repaired program in a single API call, since both GPT-3.5 and GPT-4 have a natural tendency to interleave text and code in their responses. See Appendix E for a detailed look at how the prompt differs between this and the previous setting. Formally, we denote this as $$ \{(f_{ij},r_{ij})\}_{j=1}^{n_{fr}}\stackrel{{\scriptstyle i.i.d.}}{{\sim}}M_{P }(\psi;p_{i};e_{i}) $$ <details> <summary>x2.png Details</summary>  ### Visual Description ## Hierarchical System Architecture Diagram: Code Generation and Feedback Flow ### Overview The diagram illustrates a multi-level hierarchical system architecture with feedback loops and code generation/repair processes. It features a root node (ψ) branching into primary nodes (p₁ to pₙ), which further decompose into functional nodes (f₁₁, f₁ₙ, ..., fₙ₁, fₙₙ), each containing response nodes (r₁₁₁, r₁₁ₙ, ..., rₙₙ₁, rₙₙₙ). Feedback arrows connect response nodes back to their parent functional nodes, while a separate code generation/repair flow operates alongside the hierarchy. ### Components/Axes 1. **Root Node**: ψ (topmost node) 2. **Primary Nodes**: p₁, p₂, ..., pₙ (directly connected to ψ) 3. **Functional Nodes**: - f₁₁, f₁ₙ (under p₁) - fₙ₁, fₙₙ (under pₙ) 4. **Response Nodes**: - r₁₁₁, r₁₁ₙ (under f₁₁) - rₙ₁₁, rₙₙₙ (under fₙₙ) 5. **Flow Arrows**: - **Feedback**: Orange arrows from r-nodes to f-nodes - **Code Generation/Repair**: Blue arrows from f-nodes to a separate process ### Detailed Analysis - **Hierarchical Structure**: - ψ → p₁ → f₁₁ → [r₁₁₁, r₁₁ₙ] - ψ → p₁ → f₁ₙ → [r₁ₙ₁, r₁ₙₙ] - ψ → pₙ → fₙ₁ → [rₙ₁₁, rₙ₁ₙ] - ψ → pₙ → fₙₙ → [rₙₙ₁, rₙₙₙ] - **Feedback Mechanism**: - Response nodes (r) feed back to their parent functional nodes (f) via orange arrows - **Code Generation/Repair Flow**: - Functional nodes (f) connect to a separate process via blue arrows labeled "Code Gen" and "Repair" ### Key Observations 1. **Modular Decomposition**: - Primary nodes (p) split into functional nodes (f) with distinct response nodes (r) - Each f-node contains 2-4 r-nodes (e.g., f₁₁ has r₁₁₁ and r₁₁ₙ) 2. **Feedback Loops**: - All r-nodes have feedback connections to their parent f-nodes - Feedback arrows are consistently orange and positioned below the hierarchy 3. **Code Generation/Repair**: - Blue arrows originate from f-nodes but lack explicit termination points - Positioned to the right of the main hierarchy ### Interpretation This diagram represents a **modular system architecture** with three key characteristics: 1. **Hierarchical Processing**: - ψ represents the system's root, with p-nodes acting as intermediate processors - Functional nodes (f) handle specific tasks, each generating multiple response nodes (r) 2. **Iterative Refinement**: - Feedback loops from r-nodes to f-nodes suggest error correction or performance optimization - The orange feedback arrows imply real-time adjustments to functional node operations 3. **Code-Centric Workflow**: - The blue "Code Gen/Repair" flow indicates a separate code management system - Functional nodes likely interface with this system for code generation and error repair **Notable Patterns**: - Symmetrical structure in p₁/pₙ and f₁₁/fₙₙ nodes suggests parallel processing capabilities - Absence of numerical values implies this is a conceptual architecture rather than a data-driven model - Feedback loops outnumber code generation/repair arrows 4:1, emphasizing real-time adjustment over code management **Technical Implications**: - The architecture could model a code generation pipeline with automated feedback for quality assurance - Response nodes (r) might represent test cases or validation metrics - The dual flow system (feedback vs. code management) suggests separation of concerns between operational adjustments and code-level modifications </details> Figure 2: A repair tree begins with a specification $\psi$ (root node), then grows into initial programs, feedback, and repairs. ### 3.2 pass@t : pass rate vs. token count Since self-repair requires several dependent model invocations of non-uniform cost, this is a setting in which pass@ $k$ —the likelihood of obtaining a correct program in $k$ i.i.d. samples—is not a suitable metric for comparing and evaluating various hyper-parameter choices of self-repair. Instead, we measure the pass rate as a function of the total number of tokens sampled from the model, a metric which we call pass@t. Formally, suppose that you are given a dataset $D=\{\psi_{d}\}_{d}$ and a chosen set of values for the hyper-parameters $(M_{P},M_{F},n_{p},n_{f},n_{r})$ . Let $T_{d}^{i}\sim M(\psi_{d})$ denote a repair tree that is sampled as described in Section 3.1 for the task $\psi_{d}$ ; let $\text{size}(T_{d}^{i})$ denote the total number of program and feedback tokens in the repair tree; and say that $T_{d}^{i}\models\psi_{d}$ is true if, and only if, $T_{d}^{i}$ has at least one leaf program that satisfies the unit tests in the specification $\psi_{d}$ . Then the pass@t metric of this choice of hyper-parameters is defined as the expected pass rate at the number of tokens which you would expect to generate with this choice of hyper-parameters: | | $\displaystyle\texttt{pass@t}\triangleq\mathop{\mathbb{E}}_{\stackrel{{ \scriptstyle\psi_{d}\sim D}}{{T_{d}^{i}\sim M(\psi_{d})}}}\left[T_{d}^{i} \models\psi_{d}\right]\quad\textbf{at}\quad t=\mathop{\mathbb{E}}_{\stackrel{{ \scriptstyle\psi_{d}\sim D}}{{T_{d}^{i}\sim M(\psi_{d})}}}\left[\text{size}(T_ {d}^{i})\right]$ | | | --- | --- | --- | In our experiments, we plot bootstrapped estimates of these two quantities. To obtain these, we first generate a very large repair tree for each task specification, with: $N_{p}\geq n_{p}$ initial program samples; $N_{f}\geq n_{f}$ feedback strings per wrong program; and $N_{r}\geq n_{r}$ repair candidates per feedback string. Given a setting of $(n_{p},n_{f},n_{r})$ , we then sub-sample (with replacement) $N_{t}$ different repair trees from this frozen dataset. Finally, we compute the sample mean and standard deviation of the pass rate and the tree size over these $N_{t}$ trees. Estimating the pass@t in this way greatly reduces the computational cost of our experiments, since we can reuse the same initial dataset to compute the estimates for all of the various choices of $n_{p},n_{f}$ , and $n_{r}$ . We use $N_{p}=50$ for all experiments, and consider $n_{p}\leq 25$ for the self-repair approaches and $n_{p}\leq 50$ for the baseline, no-repair approach. Similarly, for the feedback strings, we use $N_{f}=25$ and $n_{f}\leq 10$ (except for Section 4.2, in which we only consider $n_{f}=1$ and therefore settle for $N_{f}=10$ instead). For the repair candidates, since we do joint sampling of feedback and repair in most of our experiments, we set $N_{r}=n_{r}=1$ . Finally, we use $N_{t}=1000$ for all settings. ## 4 Experiments In this section, we carry out experiments to answer the following research questions: (a) In the context of challenging programming puzzles, is self-repair better than i.i.d. sampling without repair for the models we consider? If so, under what hyper-parameters is self-repair most effective? (b) Would a stronger feedback model boost the model’s repair performance? (c) Would keeping a human in the loop to provide feedback unlock better repair performance even for the strongest model? We evaluate these hypotheses on Python programming challenges from the APPS dataset [Hendrycks et al., 2021]. The APPS dataset contains a diverse range of programming challenges paired with a suite of tests, making it a perfect (and challenging) setting to study self-repair in. To keep our experiments tractable, we evaluate on a subset of the APPS test set, consisting of 300 tasks. These tasks are proportionally sampled in accordance with the frequency of the different difficulty levels in the test set: 180 interview-level questions, 60 competition-level questions, and 60 introductory-level questions (listed in Appendix F). We use GPT-3.5 [Ouyang et al., 2022, OpenAI, 2022] and GPT-4 [OpenAI, 2023] as our models of choice, and implement self-repair using templated string concatenation with one-shot prompting; our prompts are given in Appendix E. When appropriate, we compare against a baseline without repair. This baseline, shown with a black line in the plots, is simply i.i.d. sampling from the corresponding model (e.g., GPT-4 when we explore whether GPT-4 is capable of self-repair). Based on preliminary experiments, we set the decoding temperature to $0.8$ for all the models to encourage diverse samples. <details> <summary>x3.png Details</summary>  ### Visual Description ## Line Graph: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line graph depicting the relationship between the **mean number of tokens generated** (x-axis) and the **mean pass rate** (y-axis). The graph includes multiple data series represented by colored lines and markers, with a shaded confidence interval around the primary trend. The legend on the right maps colors and markers to specific parameter values (`n_p` and `n_fr`). ### Components/Axes - **X-axis**: "Mean number of tokens generated" (range: 0 to 10,000). - **Y-axis**: "Mean pass rate" (range: 0.0 to 1.0). - **Legend**: - **Colors**: - Brown (`n_p = 1`), Orange (`n_p = 2`), Teal (`n_p = 5`), Blue (`n_p = 10`), Dark Blue (`n_p = 25`). - **Markers**: - Circle (`n_fr = 1`), Triangle (`n_fr = 3`), Square (`n_fr = 5`), Diamond (`n_fr = 10`). - **Shaded Area**: Gray, surrounding the dark blue line (`n_p = 25`). ### Detailed Analysis 1. **Primary Trend (`n_p = 25`, Dark Blue Line)**: - A smooth, upward-curving line dominates the graph, starting near (0, 0.2) and ending at (10,000, ~0.5). - The shaded gray area around this line suggests a confidence interval, with the upper bound slightly above 0.5 and the lower bound slightly below 0.5. 2. **Secondary Trends (`n_p = 1, 2, 5, 10`)**: - **Brown (`n_p = 1`)**: A dashed line with circle markers, starting near (0, 0.25) and plateauing at ~0.35. - **Orange (`n_p = 2`)**: A dashed line with triangle markers, starting near (0, 0.3) and plateauing at ~0.4. - **Teal (`n_p = 5`)**: A dashed line with square markers, starting near (0, 0.35) and plateauing at ~0.45. - **Blue (`n_p = 10`)**: A dashed line with diamond markers, starting near (0, 0.4) and plateauing at ~0.5. 3. **Data Points**: - **`n_p = 25`**: - At 10,000 tokens, the mean pass rate is ~0.5 (dark blue circle). - **`n_p = 10`**: - At 8,000 tokens, the mean pass rate is ~0.5 (blue diamond). - **`n_p = 5`**: - At 6,000 tokens, the mean pass rate is ~0.45 (teal square). - **`n_p = 2`**: - At 4,000 tokens, the mean pass rate is ~0.4 (orange triangle). - **`n_p = 1`**: - At 2,000 tokens, the mean pass rate is ~0.3 (brown circle). ### Key Observations - **Increasing `n_p` improves pass rate**: Higher `n_p` values (e.g., 25 vs. 1) consistently achieve higher mean pass rates. - **Convergence at high token counts**: All lines plateau near 0.5 at 10,000 tokens, suggesting diminishing returns beyond this point. - **Shaded area variability**: The gray confidence interval around `n_p = 25` indicates lower uncertainty compared to other series. ### Interpretation The graph demonstrates that increasing the number of generated tokens (`n_p`) correlates with higher mean pass rates, particularly for larger `n_p` values. The shaded area around `n_p = 25` suggests this parameter combination is more stable or reliable. The use of distinct markers and colors in the legend ensures clear differentiation between parameter sets. Notably, the pass rate plateaus near 0.5 for all `n_p` values at 10,000 tokens, implying a theoretical upper limit for performance. **Uncertainties**: - Exact values for the shaded area’s bounds are not quantified. - Data points for `n_p = 1, 2, 5, 10` are approximate, with potential variability in their placement. </details> (a) Mean pass rate vs. number of tokens generated. Black line is i.i.d. sampling without repair from GPT-3.5. Note that the error bars are often smaller than the markers; all settings have a standard deviation of less than 1.5 absolute points on the y-axis. Results truncated at $t=10,000$ . <details> <summary>x4.png Details</summary>  ### Visual Description ## Heatmap: Relationship Between Feedback-Repairs and Initial Programs ### Overview The image is a heatmap visualizing the relationship between the number of feedback-repairs (`n_fr`) and the number of initial programs (`n_p`). Values are represented by color intensity (dark brown to black) and numerical labels, with "O.O.B." indicating out-of-bounds or undefined data. --- ### Components/Axes - **X-axis (Horizontal)**: - Label: "Number of initial programs (`n_p`)" - Categories: 1, 2, 5, 10, 25 - **Y-axis (Vertical)**: - Label: "Number of feedback-repairs (`n_fr`)" - Categories: 1, 3, 5, 10 - **Color Legend**: - Dark brown → Black gradient represents increasing values (0.78 to 1.00). - Black cells labeled "O.O.B." denote undefined or non-applicable data. --- ### Detailed Analysis #### Cell Values and Trends 1. **`n_p = 1`**: - `n_fr = 1`: 0.87 (dark brown) - `n_fr = 3`: 0.81 (medium brown) - `n_fr = 5`: 0.80 (dark brown) - `n_fr = 10`: 0.78 (darkest brown) 2. **`n_p = 2`**: - `n_fr = 1`: 0.92 (medium orange) - `n_fr = 3`: 0.87 (medium brown) - `n_fr = 5`: 0.86 (dark brown) - `n_fr = 10`: 0.86 (dark brown) 3. **`n_p = 5`**: - `n_fr = 1`: 0.96 (light orange) - `n_fr = 3`: 0.94 (medium orange) - `n_fr = 5`: 0.95 (light orange) - `n_fr = 10`: O.O.B. (black) 4. **`n_p = 10`**: - `n_fr = 1`: 0.99 (bright yellow) - `n_fr = 3`: 1.00 (brightest yellow) - `n_fr = 5`: O.O.B. (black) - `n_fr = 10`: O.O.B. (black) 5. **`n_p = 25`**: - All `n_fr` values: O.O.B. (black) --- ### Key Observations 1. **Increasing Trends**: - Values generally increase with higher `n_p` and `n_fr` until reaching thresholds (e.g., `n_p = 10`, `n_fr = 3`). - The maximum value (1.00) occurs at `n_p = 10`, `n_fr = 3`. 2. **Thresholds**: - Beyond `n_p = 10`, all values become O.O.B., suggesting a system limit or undefined behavior. - For `n_p = 5`, `n_fr = 10` is O.O.B., indicating a secondary threshold. 3. **Color Consistency**: - Darker colors (brown/black) correlate with lower values, while lighter colors (yellow) indicate higher values. - "O.O.B." entries are uniformly black, confirming their exclusion from the value gradient. --- ### Interpretation - **Optimal Range**: The highest performance (value = 1.00) occurs at `n_p = 10` and `n_fr = 3`, suggesting this combination maximizes the measured metric (e.g., efficiency, success rate). - **Diminishing Returns**: Values plateau or drop slightly at higher `n_fr` for fixed `n_p` (e.g., `n_p = 2`, `n_fr = 5` vs. `n_fr = 10`). - **System Limits**: The O.O.B. entries at `n_p ≥ 10` imply the system cannot handle more than 10 initial programs, or the metric becomes undefined beyond this point. - **Practical Implications**: Resource allocation should prioritize `n_p ≤ 10` and `n_fr ≤ 3` to avoid undefined outcomes. Scaling beyond these limits may require system redesign. --- ### Spatial Grounding - **Legend**: Implied by color gradient (no explicit legend box). - **Text Placement**: Numerical values are centered in cells; "O.O.B." labels are in black text within black cells. - **Axis Alignment**: Categories are evenly spaced along axes, with labels positioned outside the plot area. --- ### Final Notes The heatmap reveals a clear trade-off between scaling initial programs and feedback-repairs. While increasing both improves performance up to a point, exceeding thresholds (`n_p > 10`) leads to system failure or undefined behavior. This highlights the importance of balancing resource allocation within operational limits. </details> (b) Normalized mean pass rate relative to the (interpolated) baseline at an equivalent budget (number of tokens). Cells for which the number of tokens generated exceeds 50 samples from the GPT-3.5 baseline marked O.O.B. (out of bounds). Figure 3: Pass rate versus number of tokens generated for various settings of $n_{p}$ (number of initial programs) and $n_{fr}$ (number of repairs sampled per program). GPT-3.5 is used for all samples, including the baseline. ### 4.1 Self-repair requires strong models and diverse initial samples In this subsection, we consider the setup where $M_{P}=M_{F}\in\{\text{GPT-3.5, GPT-4}\}$ , i.e., where one single model is used for both code/repair generation and feedback generation. To evaluate if self-repair leads to better pass@t than a no-repair, i.i.d. sampling-based baseline approach, we vary $n_{p}$ and $n_{fr}$ —that is, the number of initial i.i.d. base samples and joint feedback, repair samples drawn from $M_{P}$ —in the range $(n_{p},n_{fr})\in\{1,2,5,10,25\}\times\{1,3,5,10\}$ . Recall that when $M_{P}=M_{F}$ , we jointly sample for $n_{fr}$ pairs of feedback strings and repair programs instead of sampling them one after another (Section 3.1). The results are shown in Figure 3 for GPT-3.5 and Figure 4 for GPT-4. In the left-hand subplots, the color of each dot indicates the number of initial samples ( $n_{p}$ ), while its shape indicates the number of feedback-repair samples ( $n_{fr}$ ). In the right hand plots, we show a heat-map with the two hyper-parameters along the axes, where the value in each cell indicates the mean pass rate with self-repair normalized by the mean pass rate of the baseline, no-repair approach when given the same token budget (i.e., pass@t at the same value of t). When the normalized mean pass rate is 1, this means that self-repair has the same pass rate as the no-repair, baseline approach at that same token budget; a higher value ( $\geq 1$ ) means self-repair performs better than the baseline. From the plots, we can see that for the GPT-3.5 model, the pass@t is lower than or equal to the corresponding baseline (black line) for all settings of $n_{p},n_{fr}$ , clearly showing that self-repair is not an effective strategy for GPT-3.5. On the other hand, for GPT-4, there are several values of $n_{p},n_{fr}$ for which the pass rate with self-repair is significantly better than that of the baseline. For example, with $n_{p}=10,n_{fr}=3$ the pass rate increases from 65% to 70%, and with $n_{p}=25,n_{fr}=1$ it increases from 65% to 71%. Our experiments also show a clear trend with respect to the relationship between the hyper-parameters. Given a fixed number of feedback-repairs ( $n_{fr}$ ), increasing the number of initial programs ( $n_{p}$ ) (i.e., moving right along the x-axis on the heat maps) consistently leads to relative performance gains for both models. On the other hand, fixing $n_{p}$ and increasing $n_{fr}$ (i.e., moving up along the y-axis on the heat maps) does not appear to be worth the additional cost incurred, giving very marginal gains at higher budgets and even decreasing performance at lower budgets. This suggests that, given a fixed budget, the most important factor determining whether self-repair will lead to a correct program or not is the diversity of the base samples that are generated up-front, rather than the diversity of the repairs sampled. Having more initial samples increases the likelihood of there being at least one program which is close to the ideal program and, hence, can be successfully repaired. Since $n_{fr}=1$ is the best choice for the hyper-parameter $n_{fr}$ , we next isolate the effect of the number of initial programs, $n_{p}$ , by exploring a denser set of possible values: $(n_{p},n_{fr})\in\{1,2,....,24,25\}\times\{1\}$ . The plots are shown in Figure 6 for both $M_{P}=M_{F}\in\{\text{GPT-3.5},\text{GPT-4}\}$ and the baseline, no-repair approaches. Note that since $n_{fr}$ is fixed, in these plots, there is a direct correlation between $n_{p}$ and the total number of tokens, $t$ . Again, we see that self-repair is not an effective strategy for the GPT-3.5 model, but that it is effective for GPT-4—especially at higher values of $n_{p}$ ( $\geq 5000$ ), where it increases pass rate by over 5 points. <details> <summary>x5.png Details</summary>  ### Visual Description ## Line Graph: Relationship Between Token Generation and Mean Pass Rate ### Overview The image depicts a line graph with a shaded confidence interval, plotting the relationship between the mean number of tokens generated (x-axis) and the mean pass rate (y-axis). Data points in various colors and shapes represent different parameter configurations (np and nfr values). The graph shows a general upward trend in pass rate with increasing token generation, followed by a plateau. ### Components/Axes - **X-axis**: "Mean number of tokens generated" (0 to 10,000, linear scale) - **Y-axis**: "Mean pass rate" (0.0 to 1.0, linear scale) - **Legend**: Located in the bottom-right corner, mapping colors/shapes to parameters: - **np values** (number of parameters): - np=1 (red line) - np=2 (orange line) - np=5 (teal line) - np=10 (blue line) - np=25 (dark blue line) - **nfr values** (number of function rules): - nfr=1 (red circle) - nfr=3 (orange triangle) - nfr=5 (teal square) - nfr=10 (blue triangle) ### Detailed Analysis 1. **Main Line (Black)**: - Starts at ~0.4 (y-axis) when x=0. - Rises steeply to ~0.65 at x=8,000. - Plateaus at ~0.65–0.70 beyond x=8,000. - Shaded area (confidence interval) widens at lower x-values (e.g., 0.55–0.75 at x=8,000) and narrows as x increases. 2. **Data Series**: - **np=1 (Red Line)**: - Data points: (1,000, 0.45), (2,000, 0.55), (4,000, 0.60), (6,000, 0.63), (8,000, 0.65). - **np=2 (Orange Line)**: - Data points: (1,000, 0.50), (2,000, 0.58), (4,000, 0.62), (6,000, 0.65), (8,000, 0.67). - **np=5 (Teal Line)**: - Data points: (2,000, 0.60), (4,000, 0.65), (6,000, 0.68), (8,000, 0.70). - **np=10 (Blue Line)**: - Data points: (4,000, 0.65), (6,000, 0.70), (8,000, 0.72). - **np=25 (Dark Blue Line)**: - Data points: (6,000, 0.70), (8,000, 0.72). - **nfr Values**: - nfr=1 (Red Circles): (1,000, 0.45), (2,000, 0.55), (4,000, 0.60). - nfr=3 (Orange Triangles): (2,000, 0.58), (4,000, 0.62), (6,000, 0.65). - nfr=5 (Teal Squares): (4,000, 0.65), (6,000, 0.68), (8,000, 0.70). - nfr=10 (Blue Triangles): (6,000, 0.70), (8,000, 0.72). ### Key Observations - **Trend**: Pass rate increases with token generation, but the rate of improvement slows after ~8,000 tokens. - **np Impact**: Higher np values achieve higher pass rates (e.g., np=25 reaches 0.72 vs. np=1 at 0.65). - **nfr Impact**: Higher nfr values correlate with higher pass rates for the same np (e.g., nfr=10 at 0.72 vs. nfr=1 at 0.45 for np=1). - **Confidence Interval**: The shaded area suggests greater uncertainty in pass rate estimates at lower token counts. ### Interpretation The data demonstrates a clear positive correlation between token generation and mean pass rate, with diminishing returns at higher token counts. Increasing np (model complexity) and nfr (rule diversity) both improve performance, but np has a more pronounced effect. The confidence interval narrowing at higher token counts indicates more reliable estimates as data volume grows. The plateau at ~0.7 suggests a performance ceiling under the tested conditions. The overlap between np and nfr data points implies that both parameters contribute synergistically to the outcome, though np appears to dominate. </details> (a) Mean pass rate vs. number of tokens generated. Black line is i.i.d. sampling without repair from GPT-4. Note that the error bars are often smaller than the markers; all settings have a standard deviation of less than 1.5 absolute points on the y-axis. Results truncated at $t=10,000$ . <details> <summary>x6.png Details</summary>  ### Visual Description ## Heatmap: Correlation Between Feedback-Repairs and Initial Programs ### Overview The image is a heatmap visualizing the relationship between the number of feedback-repairs (`n_fr`) and the number of initial programs (`n_p`). Values are represented numerically in grid cells, with color gradients transitioning from orange (low values) to green (mid values) to black (high values). Some cells are marked "O.O.B." (Out of Bounds), indicating undefined or non-applicable results. --- ### Components/Axes - **Y-Axis (Vertical)**: "Number of feedback-repairs (`n_fr`)" with values: 1, 3, 5, 10. - **X-Axis (Horizontal)**: "Number of initial programs (`n_p`)" with values: 1, 2, 5, 10, 25. - **Grid Cells**: Each cell contains a numerical value (e.g., 0.90, 1.05) or "O.O.B.". - **Color Gradient**: - Orange (low values, e.g., 0.90–0.99), - Green (mid values, e.g., 1.04–1.08), - Black (high values, e.g., 1.09 or O.O.B.). --- ### Detailed Analysis #### Grid Values | `n_p` \ `n_fr` | 1 | 2 | 5 | 10 | 25 | |----------------|---------|---------|---------|---------|---------| | **1** | 0.98 | 1.01 | 1.04 | 1.06 | 1.09 | | **3** | 0.93 | 0.99 | 1.04 | 1.08 | O.O.B. | | **5** | 0.91 | 0.98 | 1.04 | 1.08 | O.O.B. | | **10** | 0.90 | 0.98 | 1.05 | O.O.B. | O.O.B. | #### Color-Space Correlation - **Orange** dominates the lower-left quadrant (small `n_p` and `n_fr`). - **Green** appears in the mid-range (moderate `n_p` and `n_fr`). - **Black** occupies the upper-right quadrant (large `n_p` and `n_fr`), with "O.O.B." indicating thresholds beyond which results are undefined. --- ### Key Observations 1. **Threshold Effects**: - Values increase monotonically with `n_p` and `n_fr` until reaching ~1.09 (e.g., `n_p=25`, `n_fr=1`). - Beyond `n_p=10` or `n_fr=10`, values transition to "O.O.B.", suggesting system limitations or undefined behavior at scale. 2. **Consistency in Mid-Range**: - For `n_p=5` and `n_fr=3–5`, values stabilize at 1.04, indicating a plateau in the relationship. 3. **Asymmetry in High Values**: - High `n_fr` (e.g., 10) combined with low `n_p` (e.g., 1) yields lower values (0.90) compared to high `n_p` with low `n_fr` (e.g., 1.09). --- ### Interpretation The heatmap demonstrates a **non-linear relationship** between feedback-repairs and initial programs. While increasing either variable generally improves outcomes (higher values), the system exhibits **diminishing returns** and **threshold effects**: - **Positive Correlation**: Up to `n_p=10` and `n_fr=10`, values rise predictably (e.g., 0.90 → 1.09). - **System Saturation**: Beyond these thresholds, results become undefined ("O.O.B."), implying operational limits or resource exhaustion. - **Asymmetry**: High `n_p` with low `n_fr` yields better results than the reverse, suggesting initial programs are more impactful than feedback-repairs in this context. This pattern could reflect a scenario where initial program quality or quantity drives outcomes, while feedback-repairs become less effective or counterproductive at scale. </details> (b) Normalized mean pass rate relative to the (interpolated) baseline at an equivalent budget (number of tokens). Cells for which the number of tokens generated exceeds 50 samples from the GPT-4 baseline marked O.O.B. (out of bounds). Figure 4: Pass rate versus number of tokens generated for various settings of $n_{p}$ (number of initial programs) and $n_{fr}$ (number of repairs per failing program). GPT-4 is used for all samples, including the baseline. ### 4.2 GPT-4 feedback improves GPT-3.5 repair Next, we conduct an experiment in which we evaluate the impact of using a separate, stronger model to generate the feedback. This is to test the hypothesis that self-repair is held back (especially for GPT-3.5) by the model’s inability to introspect and debug its own code. For this experiment, we set $M_{P}$ = GPT-3.5 and $M_{F}$ = GPT-4 and vary the hyper-parameters as $(n_{p},n_{f},n_{r})\in\{1,2,....,24,25\}\times\{1\}\times\{1\}$ , similarly to the previous experiment. Note that since we are now operating in a setting in which the feedback and repair stages must be separated, we have three hyper-parameters— $n_{p},n_{f},n_{r}$ —instead of two— $n_{p},n_{fr}$ (Section 3.1). To keep the computational budget tractable, and since the variance was seen to be very low in the previous experiment, we use $N_{f}=10$ instead of $N_{f}=25$ for this experiment (see Section 3.2). The results for this experiment are shown in Figure 6 (bright blue line). We observe that in terms of absolute performance, $M_{P}=$ GPT-3.5, $M_{F}=$ GPT-4 does break through the performance barrier and becomes marginally more efficient than i.i.d. sampling from GPT-3.5. This suggests that the textual feedback stage itself is of crucial importance, and that improving it relieves the bottleneck in GPT-3.5 self-repair. Figure 5: Mean pass rate for each model when $n_{fr}$ (or $n_{f}$ and $n_{r}$ ) = 1. Shaded region is $\pm 1$ standard deviation. Complete breakdown per difficulty in Appendix A. <details> <summary>x7.png Details</summary>  ### Visual Description ## Line Graph: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line graph comparing the mean pass rate of different model configurations (M_p and M_f) across varying numbers of generated tokens. Five distinct lines represent combinations of GPT-3.5 and GPT-4 models with/without repair mechanisms. The graph emphasizes performance trends as token generation scales from 0 to 10,000. ### Components/Axes - **X-axis**: "Mean number of tokens generated" (0 to 10,000, increments of 2,000). - **Y-axis**: "Mean pass rate" (0.0 to 1.0, increments of 0.2). - **Legend**: Located at the bottom-right, with five entries: 1. Dark blue: `M_p = GPT-4 (no repair)` 2. Teal: `M_p = GPT-4; M_f = GPT-4` 3. Gray: `M_p = GPT-3.5 (no repair)` 4. Orange: `M_p = GPT-3.5; M_f = GPT-3.5` 5. Light blue: `M_p = GPT-3.5; M_f = GPT-4` ### Detailed Analysis 1. **Dark Blue Line (`M_p = GPT-4, no repair`)**: - Starts at ~0.4 (2,000 tokens) and rises to ~0.65 (10,000 tokens). - Steady upward slope with minimal fluctuation. 2. **Teal Line (`M_p = GPT-4; M_f = GPT-4`)**: - Begins at ~0.35 (2,000 tokens) and peaks at ~0.7 (6,000 tokens). - Slight plateau after 6,000 tokens, maintaining ~0.7 pass rate. 3. **Gray Line (`M_p = GPT-3.5, no repair`)**: - Starts at ~0.25 (2,000 tokens) and reaches ~0.5 (10,000 tokens). - Gradual, consistent increase. 4. **Orange Line (`M_p = GPT-3.5; M_f = GPT-3.5`)**: - Begins at ~0.2 (2,000 tokens) and climbs to ~0.55 (10,000 tokens). - Slightly steeper slope than the gray line. 5. **Light Blue Line (`M_p = GPT-3.5; M_f = GPT-4`)**: - Starts at ~0.3 (2,000 tokens) and plateaus at ~0.55 (10,000 tokens). - Minimal growth after 4,000 tokens. ### Key Observations - **GPT-4 Superiority**: Lines using GPT-4 (dark blue, teal) consistently outperform GPT-3.5 variants. - **Repair Mechanism Impact**: - GPT-4 with GPT-4 repair (teal) achieves the highest pass rate (~0.7). - GPT-3.5 with GPT-4 repair (light blue) matches GPT-3.5 with GPT-3.5 repair (orange) at ~0.55. - **Diminishing Returns**: Most lines plateau after ~6,000 tokens, suggesting limited gains from further token generation. ### Interpretation The data demonstrates that: 1. **Model Version Matters**: GPT-4 models (M_p) achieve ~20–30% higher pass rates than GPT-3.5 at equivalent token counts. 2. **Repair Strategy Synergy**: Pairing GPT-4 with GPT-4 repair (teal line) maximizes performance, while mixed configurations (e.g., GPT-3.5 with GPT-4 repair) yield intermediate results. 3. **Scalability Limits**: Performance improvements plateau beyond ~6,000 tokens, indicating diminishing returns for larger token generation. This suggests that optimizing both the primary model (M_p) and repair mechanism (M_f) is critical for high pass rates, with GPT-4 being the dominant factor. The repair mechanism’s effectiveness depends on alignment with the primary model’s capabilities. </details> | Introductory Interview Competition | 42.64% 19.33% 3.67% | 62.21% 45.67% 14.67% | | --- | --- | --- | | Overall | 33.30% | 52.60% | Figure 5: Mean pass rate for each model when $n_{fr}$ (or $n_{f}$ and $n_{r}$ ) = 1. Shaded region is $\pm 1$ standard deviation. Complete breakdown per difficulty in Appendix A. Figure 6: Success rate of repair with GPT-4’s explanations vs. with those of our human participants. ### 4.3 Human feedback significantly improves the success rate of GPT-4 repair For our final experiment, we consider the effect of using an expert human programmer’s feedback when performing repair with stronger models such as GPT-4. The goal of this study is not to do a direct comparison between a human-in-the-loop approach vs. self-repair, since a human-in-the-loop approach imposes more cognitive burden, which we do not study. Instead, our goal is to understand how the model’s ability to identify mistakes in the code compares to that of a human, and how this affects downstream performance in self-repair. We thus conduct both qualitative and quantitative analyses of the impact of human feedback on self-repair. Data collection methodology. We first sample 20 tasks $\{\psi_{i}\}_{i=1}^{20}$ from the APPS test set; to make the data collection process less time-consuming for the participants of the study, we skew the distribution towards easier tasks (14 introductory; 3 interview; 3 competition). For each task $\psi_{i}$ , we then sample two failing GPT-4 completions $p_{i,1},p_{i,2}$ , making for a total of $20\cdot 2=40$ programs to refine. We recruit 16 participants, consisting of 15 graduate students and one professional machine learning engineer. Each participant is provided with five different base programs based on their level of experience with Python and competitive programming. Each program is taken from a distinct task; participants are never showed two different programs belonging to the same task. Participants are then asked to explain, in their own words, what the program is doing wrong. To reduce the cognitive load for participants, each program $p_{i,j}$ is accompanied by the error message $e_{i,j}$ and two feedback strings $f_{i,j,1},f_{i,j,2}$ sampled from GPT-4. We obtain these feedback strings by randomly sampling from the feedback-repair pairs used in the previous experiments and removing the code block. Note that each of the 40 programs will be shown to two different participants, to reduce variance caused by participants’ skill levels and writing style. Participants were told to spend approximately one hour on the study overall, and were compensated with a $15 gift card. This human data collection was approved by our Institutional Review Board (IRB) and carried out exclusively through an online survey. See Appendix B for a complete, concrete copy of the instructions which we provide to our participants. Quantitative Analysis. Having obtained two human-written pieces of feedback $h_{i,j,1},h_{i,j,2}$ for each program $p_{i,j}$ , we sample 25 repaired programs $$ \{r_{l}\}_{l=1}^{25}\stackrel{{\scriptstyle i.i.d.}}{{\sim}}\text{GPT-4}(\psi_ {i};p_{i,j};e_{i,j};f) $$ for $f\in\{h_{i,j,1},h_{i,j,2},f_{i,j,1},f_{i,j,2}\}$ . That is: we ask GPT-4 to generate 25 candidate repairs for each program, conditioned on the specification, the initial program, and a feedback string which is either set to one of GPT-4’s own feedback strings or to one provided by a participant. Finally, we execute all of these candidate repairs against the test bed, and take note of how often they pass. The results are summarized in Table 6, with a complete task-by-task breakdown in Appendix C. We note first of all that the overall success rate is increased by over $1.57\times$ when we replace GPT-4’s own debugging with that of our human participants. Perhaps unsurprisingly, the relative difference increases as the problems get harder, indicating that GPT-4’s ability to produce accurate and useful feedback trails further behind our human participants’ when the task (and code) becomes more complex. Qualitative Analysis. In this section, we qualitatively analyze the difference between the feedback provided by the human participants and the feedback provided by GPT-4. We manually go through all of GPT-4’s and the participants’ feedback and note down whether the feedback: (a) seems, at a cursory glance, to be correct, or if it is obviously inaccurate; (b) explicitly suggests a small change to the code (e.g. "change the condition on line X"); (c) explicitly suggests a large change to the code (e.g. "frame the problem as min-cut instead of shortest-path"); (d) contains blocks of pseudocode or Python (which GPT-4’s feedback never does, per our experiment design); or (e) expresses uncertainty (using phrases such as "unsure", "it appears", etc.). We do not count individual single-line statements/expressions such as “ $x=5$ ” as pseudocode or Python. Examples of each category are shown in Appendix D. We find that - Only 2/80 human-contributed feedback strings include pseudocode or explicit Python; that is, almost all human feedback we obtain is natural language interleaved with occasional single-statement math/code expressions. - GPT-4’s feedback is much more likely to be obviously inaccurate (32/80 vs. 7/80 for human feedback). - GPT-4 is more likely to explicitly suggest small changes (54/80 vs 42/80; 28/48 vs. 38/73 when seemingly correct), while our human participants show a slightly greater tendency to suggest high-level changes (23/80 vs. 18/80 for GPT-4; 21/73 vs. 13/48 when seemingly correct). - Our human participants sometimes express uncertainty (7/80); GPT-4 never does (0/80). This further analysis suggests that the results in Table 6 are not due to artefacts such as our participants providing explicit code blocks which the model simply copies. Instead, the difference in performance appears to be caused by a combination of more accurate feedback, a greater ability to suggest high-level, large-scale changes to the code when needed, and our participants’ ability to express their uncertainty (instead of confidently giving potentially inaccurate feedback). ## 5 Limitations Firstly, to reduce computational cost, we pre-populate and then sub-sample from large repair trees, which introduces statistical bias. We mitigate this by being generous in our uncertainty of the pass@t, using the maximum standard deviation across all points. We also note that this standard deviation, which is obtained at values of $(n_{p},n_{f},n_{r})$ that are small enough that we have very many samples thereof in our pre-populated repair trees, is very low ( $<2\$ pass rate for all models). While these measures do not completely eliminate the risk of bias in our results, not performing this amortization would have required significantly larger amounts of compute. Secondly, we assume access to an executable suite of unit tests for each task. We do not, for example, require the model to extract tests from textual specifications. While this assumption may seem out of place in the era of chat-style assistants like ChatGPT [OpenAI, 2022], it does align well with established software engineering practices like Test-Driven Development [Astels, 2003]. Furthermore, techniques which automatically synthesize test cases given a specification [Li et al., 2022, Chen et al., 2023a] may relieve some of the user burden. Finally, our study on human data did not track how much time the participants took to debug the programs. As a result, we can only evaluate the quality of the feedback (and the impact this has on repair). Further research at the intersection of HCI, AI, and program synthesis is needed to explore when and how human intervention should be leveraged, as well as how programming assistants should be designed to facilitate this style of interaction. ## 6 Broader Impact Any tool that improves the productivity of people writing software will necessarily also increase the productivity of people writing software with malicious intent. It is also important to remember that research on LLMs comes at a very high environmental cost. Although we exclusively use publicly available pre-trained models in this work, and so do not train any models of our own, even inference comes with a significant carbon footprint at scale. At the same time, this work—in which we weigh model performance against the computational cost of obtaining it, and through which we learn more about when and how these models do and do not work—is a step towards more sample-efficient usage paradigms. ## 7 Conclusion In this paper, we investigated the role of textual feedback in self-repair. We presented pass@t, a new evaluation strategy which takes the cost of carrying out repair into account, and then used this metric to show that (1) GPT-3.5 is not capable of carrying out self-repair on challenging coding tasks, and (2) while performance gains are seen in GPT-4, they are modest and rely on achieving sufficient diversity in the initial programs. Furthermore, by ablating the feedback stage we found that (3) substituting GPT-3.5’s feedback with GPT-4’s improved performance, even surpassing GPT-3.5’s baseline. Finally, we carried out an experiment with human participants, in which we found that (4) replacing GPT-4’s self-generated feedback with feedback provided by an experienced programmer increased the number of repaired programs which pass all unit tests by 57%. ## Acknowledgments and Disclosure of Funding T.X. Olausson is supported by the Defense Advanced Research Projects Agency (DARPA) under the ASKEM program, award HR00112220042. T.X. Olausson was also supported through a position at Microsoft Research for part of the time period during which this work was carried out. A. Solar-Lezama is supported by the National Science Foundation (NSF) and Intel Corporation through NSF Grant CCF:2217064. This work benefited greatly from discussion with several colleagues at Microsoft Research. 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The plot suggests a positive correlation between token count and pass rate, with diminishing returns at higher token counts. ### Components/Axes - **X-axis**: "Mean number of tokens generated" (0 to 10,000, linear scale) - **Y-axis**: "Mean pass rate" (0.0 to 1.0, linear scale) - **Legend**: Located in the bottom-left corner, mapping: - **Colors/Symbols**: - Red circles: `n_p = 1`, `n_fr = 1` - Orange triangles: `n_p = 2`, `n_fr = 3` - Teal squares: `n_p = 5`, `n_fr = 5` - Blue triangles: `n_p = 10`, `n_fr = 10` - Dark blue circles: `n_p = 25`, `n_fr = 1` - **Trend Line**: Black curve with shaded gray confidence interval ### Detailed Analysis 1. **Trend Line**: - Starts near (0, 0.5) and rises steeply, plateauing near (6,000, 0.85). - Shaded area (confidence interval) widens slightly between 2,000–4,000 tokens, then narrows. 2. **Data Series**: - **`n_p = 25` (dark blue circles)**: Highest pass rates (0.8–0.9) at 4,000–6,000 tokens. - **`n_p = 10` (blue triangles)**: Pass rates ~0.7–0.85, peaking at 6,000 tokens. - **`n_p = 5` (teal squares)**: Pass rates ~0.6–0.8, plateauing earlier (~4,000 tokens). - **`n_p = 2` (orange triangles)**: Pass rates ~0.5–0.7, with lower variability. - **`n_p = 1` (red circles)**: Pass rates ~0.4–0.6, clustered at lower token counts. 3. **Key Data Points**: - At 2,000 tokens: Pass rates range from 0.55 (n_p=1) to 0.75 (n_p=25). - At 6,000 tokens: All series converge near 0.8–0.85 pass rate. - Beyond 8,000 tokens: Minimal improvement (pass rates stabilize ~0.85–0.9). ### Key Observations - **Diminishing Returns**: Pass rate improvements plateau after ~6,000 tokens, regardless of `n_p`. - **Efficiency Tradeoff**: Higher `n_p` values achieve better pass rates with fewer tokens (e.g., `n_p=25` reaches 0.85 at 4,000 tokens vs. `n_p=1` at 6,000 tokens). - **Symbol Consistency**: All legend mappings align with plotted data (e.g., `n_p=10` = blue triangles). ### Interpretation The data demonstrates that increasing the mean number of tokens generated (`n_p`) improves the mean pass rate, but with diminishing returns beyond ~6,000 tokens. The shaded confidence interval suggests the trend is statistically robust, though variability exists at lower token counts. The legend’s `n_fr` values (e.g., `n_fr=3` for `n_p=2`) may represent experimental conditions or subgroups, but their impact on pass rate is less clear without additional context. The plot implies optimizing `n_p` to balance token efficiency and performance, with `n_p=25` offering the best tradeoff in this dataset. </details> <details> <summary>x9.png Details</summary>  ### Visual Description ## Heatmap: Correlation Between Initial Programs and Feedback-Repairs ### Overview The image is a heatmap visualizing the relationship between the number of initial programs (`n_p`) and feedback-repairs (`n_fr`). Values are represented as numerical coefficients, with darker shades indicating higher values. Some cells are labeled "O.O.B." (likely "Out of Bounds"), suggesting values beyond the observed range. ### Components/Axes - **X-axis (Horizontal)**: "Number of initial programs (`n_p`)" with categories: 1, 2, 5, 10, 25. - **Y-axis (Vertical)**: "Number of feedback-repairs (`n_fr`)" with categories: 1, 3, 5, 10. - **Color Gradient**: Light orange (low values) to dark brown (high values). "O.O.B." cells are black. - **Annotations**: Numerical values in white text within each cell. ### Detailed Analysis #### Data Table Structure | `n_p` \ `n_fr` | 1 | 2 | 5 | 10 | 25 | |----------------|---------|---------|---------|---------|---------| | **1** | 0.92 | 0.97 | 1.00 | 1.01 | 1.01 | | **3** | 0.88 | 0.94 | 0.99 | 1.00 | O.O.B. | | **5** | 0.87 | 0.94 | 0.98 | 1.00 | O.O.B. | | **10** | 0.87 | 0.93 | 0.97 | O.O.B. | O.O.B. | #### Key Observations 1. **Trend Verification**: - Values generally increase with both `n_p` and `n_fr`, suggesting a positive correlation. - For `n_fr = 1`, values rise from 0.92 (at `n_p = 1`) to 1.01 (at `n_p = 10` and `25`). - For `n_fr = 10`, values plateau at 1.00 for `n_p = 5` and `10`, then become "O.O.B." for `n_p = 25`. 2. **Notable Patterns**: - The highest observed value is **1.01** (at `n_p = 10` and `25` for `n_fr = 1`). - "O.O.B." annotations appear exclusively for `n_p = 25` and `n_fr ≥ 10`, indicating a threshold beyond which data is unobserved. 3. **Anomalies**: - The value at `n_p = 1`, `n_fr = 3` (0.88) is lower than adjacent cells, suggesting a potential outlier or measurement error. ### Interpretation - **System Behavior**: The data implies that increasing both initial programs and feedback-repairs generally improves the measured coefficient, but there is a critical threshold (`n_p = 25`, `n_fr ≥ 10`) where the system cannot accommodate further increases. - **Practical Implications**: The "O.O.B." values suggest operational limits, possibly due to resource constraints or system instability at higher scales. - **Peircean Insight**: The plateau at 1.00 for `n_fr = 10` and `n_p ≤ 10` may indicate an optimal balance, while values exceeding this (e.g., 1.01) could represent over-optimization or measurement artifacts. ### Spatial Grounding - **Legend**: Implicit in the color gradient (no explicit legend). Darker shades = higher values. - **Text Placement**: Numerical values are centered in cells; "O.O.B." annotations are in black, matching the darkest cells. ### Component Isolation - **Header**: Axis labels (`n_p`, `n_fr`). - **Main Chart**: Grid of cells with values and "O.O.B." markers. - **Footer**: No additional elements. ### Final Notes The heatmap effectively highlights scalability limits, with values exceeding 1.00 potentially indicating normalized metrics or error margins. The "O.O.B." annotations warrant further investigation into system constraints. </details> <details> <summary>x10.png Details</summary>  ### Visual Description ## Scatter Plot: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a scatter plot showing the relationship between the **mean number of tokens generated** (x-axis) and the **mean pass rate** (y-axis). Data points are grouped by combinations of two parameters: `n_p` (number of participants) and `n_fr` (number of failures). A smooth black trend line indicates the general relationship between tokens generated and pass rate. The plot includes six distinct data series, each represented by unique colors and symbols. --- ### Components/Axes - **X-axis**: "Mean number of tokens generated" (ranges from 0 to 10,000 in increments of 2,000). - **Y-axis**: "Mean pass rate" (ranges from 0.0 to 1.0 in increments of 0.2). - **Legend**: Located in the **top-left corner**, with the following entries: - `n_p = 1` (brown circles) - `n_p = 2` (orange triangles) - `n_p = 5` (green squares) - `n_p = 10` (blue diamonds) - `n_p = 25` (dark blue circles) - `n_fr = 1` (black circles) - `n_fr = 3` (black triangles) - `n_fr = 5` (black squares) - `n_fr = 10` (black diamonds) --- ### Detailed Analysis 1. **Data Series**: - **`n_p = 1` (brown circles)**: - Pass rates range from ~0.22 to ~0.35. - Tokens generated: 2,000–6,000. - **`n_p = 2` (orange triangles)**: - Pass rates range from ~0.3 to ~0.4. - Tokens generated: 2,000–6,000. - **`n_p = 5` (green squares)**: - Pass rates range from ~0.35 to ~0.45. - Tokens generated: 2,000–6,000. - **`n_p = 10` (blue diamonds)**: - Pass rates range from ~0.4 to ~0.5. - Tokens generated: 4,000–8,000. - **`n_p = 25` (dark blue circles)**: - Pass rates range from ~0.45 to ~0.55. - Tokens generated: 6,000–10,000. - **`n_fr = 1` (black circles)**: - Pass rates range from ~0.2 to ~0.5. - Tokens generated: 2,000–10,000. - **`n_fr = 3` (black triangles)**: - Pass rates range from ~0.25 to ~0.4. - Tokens generated: 2,000–6,000. - **`n_fr = 5` (black squares)**: - Pass rates range from ~0.3 to ~0.45. - Tokens generated: 4,000–8,000. - **`n_fr = 10` (black diamonds)**: - Pass rates range from ~0.35 to ~0.5. - Tokens generated: 6,000–10,000. 2. **Trend Line**: - A smooth black line shows a **positive correlation** between tokens generated and pass rate. - At 0 tokens, the trend line starts near 0.2. - At 10,000 tokens, it approaches ~0.6. --- ### Key Observations - **Positive Correlation**: Higher token generation generally corresponds to higher pass rates. - **Impact of `n_p`**: Larger `n_p` values (e.g., 25) achieve higher pass rates at the same token count compared to smaller `n_p` (e.g., 1). - **Impact of `n_fr`**: Higher `n_fr` values (e.g., 10) show lower pass rates than lower `n_fr` (e.g., 1) for the same token count. - **Consistency**: The trend line aligns with all data series, suggesting a universal relationship between tokens and pass rate. --- ### Interpretation The data demonstrates that **increasing the mean number of tokens generated improves the mean pass rate**, with diminishing returns as tokens approach 10,000. The parameter `n_p` (number of participants) has a stronger influence on pass rate than `n_fr` (number of failures), as higher `n_p` values consistently yield better performance. The trend line suggests a **logarithmic or sigmoidal relationship**, where initial gains in pass rate are rapid but slow as tokens increase. This implies that optimizing token generation is critical for improving outcomes, but beyond a certain point, additional tokens yield minimal improvements. **Notable Anomalies**: - No outliers are observed; all data points align with the trend line. - The `n_p = 25` series (dark blue circles) shows the highest pass rates, reinforcing the importance of larger participant groups. </details> <details> <summary>x11.png Details</summary>  ### Visual Description ## Heatmap: Relationship Between Feedback-Repairs and Initial Programs ### Overview The image is a heatmap visualizing the relationship between the number of feedback-repairs (n_fr) and the number of initial programs (n_p). The heatmap uses color gradients (dark brown to yellow) to represent numerical values, with "O.O.B." (likely "Out of Bounds") indicating missing or undefined data in certain regions. ### Components/Axes - **Y-axis (Vertical)**: "Number of feedback-repairs (n_fr)" with labels: 1, 3, 5, 10. - **X-axis (Horizontal)**: "Number of initial programs (n_p)" with labels: 1, 2, 5, 10, 25. - **Color Gradient**: Dark brown (low values) to yellow (high values), with black cells labeled "O.O.B." for undefined data. - **Legend**: Not explicitly shown, but inferred from color intensity (darker = lower values, lighter = higher values). ### Detailed Analysis - **Cell Values**: - **n_p = 1**: - n_fr = 1: 0.84 - n_fr = 3: 0.77 - n_fr = 5: 0.75 - n_fr = 10: 0.73 - **n_p = 2**: - n_fr = 1: 0.89 - n_fr = 3: 0.84 - n_fr = 5: 0.82 - n_fr = 10: 0.82 - **n_p = 5**: - n_fr = 1: 0.93 - n_fr = 3: 0.91 - n_fr = 5: 0.91 - n_fr = 10: 0.91 - **n_p = 10**: - n_fr = 1: 0.97 - n_fr = 3: 0.98 - n_fr = 5: O.O.B. - n_fr = 10: O.O.B. - **n_p = 25**: - All n_fr values: O.O.B. ### Key Observations 1. **Positive Correlation**: Higher n_p and n_fr generally correspond to higher values (e.g., 0.84 → 0.97 as n_p increases from 1 to 10). 2. **Threshold Effects**: Values plateau or become undefined (O.O.B.) for n_p ≥ 10 and n_fr ≥ 5. 3. **Anomalies**: The cell at (n_p=10, n_fr=3) has a high value (0.98), suggesting an outlier or special case. 4. **Missing Data**: The top-right quadrant (n_p ≥ 10, n_fr ≥ 5) is entirely "O.O.B.", indicating no valid data in this region. ### Interpretation The heatmap suggests a **positive relationship** between the number of initial programs (n_p) and feedback-repairs (n_fr), with higher values of both variables leading to increased metrics (e.g., efficiency, success rates). However, the "O.O.B." entries imply that the system or model being analyzed **cannot handle combinations of n_p ≥ 10 and n_fr ≥ 5**, possibly due to: - **Data collection limitations** (e.g., insufficient samples for high n_p/n_fr). - **Model constraints** (e.g., the metric becomes undefined or unstable beyond certain thresholds). - **Practical boundaries** (e.g., the system cannot process more than 10 initial programs or 5 feedback-repairs). The outlier at (n_p=10, n_fr=3) with a value of 0.98 may indicate a unique scenario where high n_p and moderate n_fr yield exceptional results, warranting further investigation. The absence of data in the top-right quadrant highlights a critical gap in the dataset or analysis scope. </details> <details> <summary>x12.png Details</summary>  ### Visual Description ## Line Graph: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line graph depicting the relationship between the **mean pass rate** (y-axis) and the **mean number of tokens generated** (x-axis). Multiple data series are plotted, each corresponding to different combinations of parameters `n_p` (number of participants) and `n_fr` (number of free tokens). The graph includes shaded regions representing confidence intervals and a legend in the top-right corner. --- ### Components/Axes - **X-axis**: "Mean number of tokens generated" (ranges from 0 to 10,000 in increments of 2,000). - **Y-axis**: "Mean pass rate" (ranges from 0.0 to 1.0 in increments of 0.2). - **Legend**: Located in the top-right corner, with the following entries: - `n_p = 1` (red circle) - `n_p = 2` (orange triangle) - `n_p = 5` (green square) - `n_p = 10` (blue diamond) - `n_p = 25` (dark blue line) - `n_fr = 1` (red circle) - `n_fr = 3` (orange triangle) - `n_fr = 5` (green square) - `n_fr = 10` (blue diamond) - **Shaded Regions**: Gray bands around each line, indicating confidence intervals. --- ### Detailed Analysis #### Data Series Trends 1. **`n_p = 1` (red circle)**: - At 2,000 tokens: ~0.05 pass rate. - At 4,000 tokens: ~0.07 pass rate. - At 6,000 tokens: ~0.09 pass rate. - At 8,000 tokens: ~0.11 pass rate. - At 10,000 tokens: ~0.13 pass rate. - **Trend**: Gradual increase with diminishing returns. 2. **`n_p = 2` (orange triangle)**: - At 2,000 tokens: ~0.07 pass rate. - At 4,000 tokens: ~0.09 pass rate. - At 6,000 tokens: ~0.11 pass rate. - At 8,000 tokens: ~0.13 pass rate. - At 10,000 tokens: ~0.15 pass rate. - **Trend**: Slightly steeper than `n_p = 1`. 3. **`n_p = 5` (green square)**: - At 4,000 tokens: ~0.11 pass rate. - At 6,000 tokens: ~0.13 pass rate. - At 8,000 tokens: ~0.15 pass rate. - At 10,000 tokens: ~0.17 pass rate. - **Trend**: Faster growth than lower `n_p` values. 4. **`n_p = 10` (blue diamond)**: - At 6,000 tokens: ~0.15 pass rate. - At 8,000 tokens: ~0.17 pass rate. - At 10,000 tokens: ~0.19 pass rate. - **Trend**: Steeper than `n_p = 5`. 5. **`n_p = 25` (dark blue line)**: - At 8,000 tokens: ~0.18 pass rate. - At 10,000 tokens: ~0.20 pass rate. - **Trend**: Highest pass rate, with minimal increase at higher token counts. 6. **`n_fr = 1` (red circle)**: - Matches `n_p = 1` data points. 7. **`n_fr = 3` (orange triangle)**: - Matches `n_p = 2` data points. 8. **`n_fr = 5` (green square)**: - Matches `n_p = 5` data points. 9. **`n_fr = 10` (blue diamond)**: - Matches `n_p = 10` data points. #### Confidence Intervals - Shaded regions around each line indicate variability. For example: - `n_p = 1` has the widest confidence interval (e.g., ±0.02 at 2,000 tokens). - `n_p = 25` has the narrowest confidence interval (e.g., ±0.01 at 10,000 tokens). --- ### Key Observations 1. **Positive Correlation**: Higher `n_p` values generally correspond to higher mean pass rates. 2. **Diminishing Returns**: Pass rates plateau as the number of tokens increases, especially for lower `n_p` values. 3. **Confidence Intervals**: Larger `n_p` values (e.g., 25) show tighter confidence intervals, suggesting more reliable estimates. 4. **Parameter Relationship**: `n_fr` values are directly tied to `n_p` (e.g., `n_fr = 1` for `n_p = 1`, `n_fr = 10` for `n_p = 10`). --- ### Interpretation The data suggests that increasing the number of participants (`n_p`) improves the mean pass rate, but the effect diminishes as the number of tokens grows. The shaded confidence intervals highlight that higher `n_p` values (e.g., 25) provide more precise estimates, likely due to reduced sampling variability. The direct mapping of `n_fr` to `n_p` implies a designed relationship between free tokens and participant count, possibly to balance resource allocation. The plateau effect at higher token counts indicates a saturation point where additional tokens yield minimal performance gains. </details> <details> <summary>x13.png Details</summary>  ### Visual Description ## Heatmap: Relationship Between Feedback-Repairs and Initial Programs ### Overview The image is a heatmap visualizing the relationship between the number of feedback-repairs (`n_fr`) and the number of initial programs (`n_p`). Values are represented numerically in grid cells, with color gradients (brown to green to black) indicating magnitude. Some cells contain "O.O.B." (likely "Out of Bounds" or "Not Applicable"). ### Components/Axes - **Y-axis (Vertical)**: "Number of feedback-repairs (`n_fr`)" with values: 1, 3, 5, 10. - **X-axis (Horizontal)**: "Number of initial programs (`n_p`)" with values: 1, 2, 5, 10, 25. - **Grid Cells**: Numerical values (e.g., 0.78, 0.93, 1.09) and "O.O.B." markers. - **Color Gradient**: - Brown (low values, ~0.78–0.93) - Green (mid values, ~1.05–1.13) - Black (high values or "O.O.B."). ### Detailed Analysis #### Grid Values | `n_p` \ `n_fr` | 1 | 2 | 5 | 10 | 25 | |----------------|---------|---------|---------|---------|---------| | **1** | 0.87 | 0.93 | 1.05 | 1.13 | O.O.B. | | **3** | 0.81 | 0.91 | 1.08 | O.O.B. | O.O.B. | | **5** | 0.79 | 0.91 | 1.09 | O.O.B. | O.O.B. | | **10** | 0.78 | 0.93 | O.O.B. | O.O.B. | O.O.B. | #### Key Observations 1. **Trend**: - Values increase with higher `n_p` and `n_fr` until reaching "O.O.B.". - For `n_p = 1`, values rise from 0.87 (at `n_fr = 1`) to 1.13 (at `n_fr = 10`). - For `n_p = 2`, values peak at 0.93 (consistent across `n_fr = 1` and `n_fr = 10`). - "O.O.B." dominates for larger `n_p` (e.g., `n_p = 25` is entirely "O.O.B."). 2. **Anomalies**: - `n_p = 10` and `n_fr = 1` has the highest valid value (1.13). - `n_p = 5` and `n_fr = 10` is "O.O.B.", while `n_p = 5` and `n_fr = 5` is 1.09. ### Interpretation The heatmap suggests a nonlinear relationship between initial programs and feedback-repairs. Lower `n_p` values (1–5) show gradual increases in feedback-repair efficiency (values 0.78–1.13), but beyond `n_p = 10`, results become invalid ("O.O.B."). This implies diminishing returns or system instability at higher program counts. The "O.O.B." markers likely indicate thresholds where the system cannot handle additional feedback-repairs or programs. The color gradient reinforces this, with black cells signaling critical limits. </details> Figure 7: GPT-3.5 results from Figure 3 (Section 4.1) per difficulty (row), from top to bottom: introductory, interview, and competition. <details> <summary>x14.png Details</summary>  ### Visual Description ## Line Graph: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image is a line graph comparing the **mean pass rate** (y-axis) to the **mean number of tokens generated** (x-axis) across multiple data series. Each series is differentiated by **np** (number of parameters) and **nfr** (number of function calls), with distinct colors and markers. The graph includes a shaded region around the primary data series, likely representing confidence intervals or variability. ### Components/Axes - **X-axis**: "Mean number of tokens generated" (range: 0 to 10,000). - **Y-axis**: "Mean pass rate" (range: 0.0 to 1.0). - **Legend**: Located in the bottom-left corner, mapping: - **np = 1**: Red line with circular markers. - **np = 2**: Orange line with triangular markers. - **np = 5**: Teal line with square markers. - **np = 10**: Blue line with triangular markers. - **np = 25**: Dark blue line with square markers. - **nfr = 1**: Red line (same as np=1). - **nfr = 3**: Orange line (same as np=2). - **nfr = 5**: Teal line (same as np=5). - **nfr = 10**: Blue line (same as np=10). ### Detailed Analysis 1. **np = 1 (Red, Circles)**: - Starts at ~0.8 pass rate at 2,000 tokens, rising to ~0.95 at 6,000 tokens. - Shaded region spans ~0.75–0.95, indicating variability. 2. **np = 2 (Orange, Triangles)**: - Begins at ~0.85 at 2,000 tokens, reaching ~0.98 at 6,000 tokens. - Shaded region spans ~0.8–0.98. 3. **np = 5 (Teal, Squares)**: - Starts at ~0.9 at 2,000 tokens, peaking at ~0.99 at 6,000 tokens. - Shaded region spans ~0.85–0.99. 4. **np = 10 (Blue, Triangles)**: - Begins at ~0.92 at 2,000 tokens, stabilizing at ~0.995 at 6,000 tokens. - Shaded region spans ~0.9–0.995. 5. **np = 25 (Dark Blue, Squares)**: - Starts at ~0.95 at 2,000 tokens, reaching ~0.998 at 6,000 tokens. - Shaded region spans ~0.93–0.998. 6. **nfr = 10 (Blue, Triangles)**: - A single data point at ~9,000 tokens with a pass rate of ~0.99. ### Key Observations - **Trend**: Higher **np** values correlate with higher mean pass rates. The **np = 25** series achieves the highest performance, while **np = 1** lags behind. - **Convergence**: All series plateau near 1.0 pass rate as tokens increase, suggesting diminishing returns beyond ~6,000 tokens. - **Shaded Regions**: Wider variability for lower **np** values (e.g., np=1 has a broader shaded area than np=25). - **Outlier**: The **nfr = 10** data point (blue triangle) at ~9,000 tokens is isolated, with no other markers in that range. ### Interpretation The graph demonstrates that increasing the number of parameters (**np**) improves the mean pass rate, particularly at lower token counts. However, the performance gains plateau as tokens increase, indicating that beyond a certain threshold (e.g., 6,000 tokens), additional parameters yield minimal improvements. The shaded regions highlight that lower **np** values exhibit greater variability in results, while higher **np** values show more consistent performance. The isolated **nfr = 10** data point suggests a potential anomaly or a specific experimental condition not reflected in other series. This data could inform optimization strategies for balancing computational resources (tokens) and model complexity (parameters) in token generation tasks. </details> <details> <summary>x15.png Details</summary>  ### Visual Description ## Heatmap: Relationship Between Feedback-Repairs and Initial Programs ### Overview The image is a heatmap visualizing the relationship between the number of feedback-repairs (`n_fr`) and the number of initial programs (`n_p`). Values in each cell represent a metric (likely a ratio or efficiency score), with colors transitioning from orange (low values) to dark green (high values). The top-right corner contains "O.O.B." (Out of Bounds) annotations. --- ### Components/Axes - **Y-Axis (Vertical)**: - Label: "Number of feedback-repairs (`n_fr`)" - Scale: Discrete values `[1, 3, 5, 10]` - **X-Axis (Horizontal)**: - Label: "Number of initial programs (`n_p`)" - Scale: Discrete values `[1, 2, 5, 10, 25]` - **Color Legend**: - Implied gradient: Orange (low values) → Dark Green (high values) - No explicit legend present; color intensity correlates with numerical values. --- ### Detailed Analysis #### Cell Values and Trends 1. **`n_fr = 10` (Top Row)**: - `n_p = 1`: `0.98` (orange) - `n_p = 2`: `1.01` (light orange) - `n_p = 5`: `1.02` (medium orange) - `n_p = 10`: `1.03` (light green) - `n_p = 25`: `O.O.B.` (black) 2. **`n_fr = 5` (Second Row)**: - `n_p = 1`: `1.00` (orange) - `n_p = 2`: `1.02` (light orange) - `n_p = 5`: `1.03` (light green) - `n_p = 10`: `1.03` (light green) - `n_p = 25`: `O.O.B.` (black) 3. **`n_fr = 3` (Third Row)**: - `n_p = 1`: `1.02` (light orange) - `n_p = 2`: `1.03` (light green) - `n_p = 5`: `1.04` (medium green) - `n_p = 10`: `1.04` (medium green) - `n_p = 25`: `1.04` (medium green) 4. **`n_fr = 1` (Bottom Row)**: - `n_p = 1`: `1.05` (dark green) - `n_p = 2`: `1.04` (medium green) - `n_p = 5`: `1.04` (medium green) - `n_p = 10`: `1.04` (medium green) - `n_p = 25`: `1.04` (medium green) #### Color Consistency Check - Values increase from orange to dark green as numbers rise. - `O.O.B.` cells (black) are isolated in the top-right corner, confirming they represent undefined/non-applicable data. --- ### Key Observations 1. **General Trend**: - Values increase with higher `n_p` and `n_fr`, suggesting a positive correlation between initial programs and feedback-repairs. - The metric plateaus at `1.04` for `n_fr ≥ 3` and `n_p ≥ 5`. 2. **Anomalies**: - `O.O.B.` values at `n_p = 25` for `n_fr = 5` and `10` indicate a threshold where the metric becomes undefined. - The lowest value (`0.98`) occurs at `n_fr = 10`, `n_p = 1`, suggesting inefficiency at low `n_p` with high `n_fr`. 3. **Color Gradient**: - Darker green dominates the lower-left quadrant (`n_fr = 1`, `n_p = 1`), while lighter shades appear in the upper-right quadrant. --- ### Interpretation - **Relationship**: The heatmap implies that increasing `n_p` generally improves the metric (e.g., efficiency, success rate), but only up to a point. Beyond `n_p = 10`, the metric stabilizes or becomes undefined (`O.O.B.`). - **Thresholds**: - `n_p = 25` triggers `O.O.B.` for `n_fr ≥ 5`, suggesting system limitations or data collection constraints at extreme scales. - `n_fr = 1` consistently yields the highest values (`1.05` at `n_p = 1`), possibly indicating optimal performance with minimal feedback-repairs. - **Practical Implications**: - Organizations should balance `n_p` and `n_fr` to maximize the metric. Exceeding `n_p = 10` may not yield benefits and could introduce instability. - The `O.O.B.` values highlight the need for further investigation into why the metric fails at high `n_p`. --- ### Spatial Grounding - **Legend**: Implied via color gradient; no explicit legend present. - **Text Placement**: - Axis labels are left-aligned (y-axis) and bottom-aligned (x-axis). - `O.O.B.` annotations are centered in the top-right cells. - **Color Matching**: - Dark green corresponds to `1.04–1.05`, light green to `1.02–1.03`, and orange to `0.98–1.01`. --- ### Final Notes The heatmap provides actionable insights into optimizing `n_p` and `n_fr` but leaves open questions about the cause of `O.O.B.` values. Further analysis of system constraints or data collection methods at high `n_p` is warranted. </details> <details> <summary>x16.png Details</summary>  ### Visual Description ## Line Graph: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image depicts a line graph with a shaded confidence interval, showing the relationship between the mean number of tokens generated (x-axis) and the mean pass rate (y-axis). Data points are represented by distinct markers and colors, with a legend indicating parameters `n_p` (number of participants) and `n_fr` (number of failures). The graph includes five data series, each corresponding to a specific `n_p` value, with markers for `n_fr` values. --- ### Components/Axes - **X-axis**: "Mean number of tokens generated" (0 to 10,000, increments of 2,000). - **Y-axis**: "Mean pass rate" (0.0 to 1.0, increments of 0.2). - **Legend**: Located in the bottom-right corner, with: - **Colors**: Red (`n_p = 1`), Orange (`n_p = 2`), Green (`n_p = 5`), Blue (`n_p = 10`), Dark Blue (`n_p = 25`). - **Markers**: Circle (`n_fr = 1`), Triangle (`n_fr = 3`), Square (`n_fr = 5`), Diamond (`n_fr = 10`). - **Shaded Area**: Represents the confidence interval around each line. --- ### Detailed Analysis 1. **Data Series Trends**: - **`n_p = 1` (Red)**: Starts at ~0.45 (2,000 tokens), rises to ~0.6 (4,000 tokens), then plateaus. Confidence interval widens at lower token counts. - **`n_p = 2` (Orange)**: Similar trend to `n_p = 1`, but slightly higher pass rates (~0.55 at 2,000 tokens, ~0.65 at 4,000 tokens). - **`n_p = 5` (Green)**: Higher pass rates (~0.6 at 2,000 tokens, ~0.7 at 4,000 tokens). Confidence interval narrows compared to smaller `n_p`. - **`n_p = 10` (Blue)**: Pass rate ~0.65 at 2,000 tokens, ~0.75 at 4,000 tokens. Confidence interval tighter than smaller `n_p`. - **`n_p = 25` (Dark Blue)**: Highest pass rate (~0.75 at 8,000 tokens). Confidence interval narrowest, indicating least variability. 2. **Markers**: - **`n_fr = 1` (Circle)**: All series show circles at lower token counts (e.g., ~0.45 for `n_p = 1` at 2,000 tokens). - **`n_fr = 3` (Triangle)**: Appears at mid-token counts (e.g., ~0.6 for `n_p = 2` at 4,000 tokens). - **`n_fr = 5` (Square)**: Higher token counts (e.g., ~0.7 for `n_p = 5` at 6,000 tokens). - **`n_fr = 10` (Diamond)**: Highest token counts (e.g., ~0.75 for `n_p = 25` at 8,000 tokens). 3. **Shaded Area**: - Represents variability in pass rates. Wider intervals at lower token counts (e.g., `n_p = 1` at 2,000 tokens) and narrower intervals at higher token counts (e.g., `n_p = 25` at 8,000 tokens). --- ### Key Observations - **Positive Correlation**: Higher `n_p` values generally correspond to higher mean pass rates, especially at lower token counts. - **Diminishing Returns**: Pass rate improvements plateau as token counts increase (e.g., `n_p = 25` reaches ~0.75 by 8,000 tokens, with minimal gains beyond). - **Confidence Intervals**: Larger `n_p` values (e.g., 25) show tighter confidence intervals, suggesting more reliable results. - **Convergence**: All series converge toward similar pass rates (~0.7–0.75) at 8,000+ tokens, indicating diminishing impact of `n_p` at high token counts. --- ### Interpretation The data suggests that increasing the number of participants (`n_p`) improves the mean pass rate, particularly when the mean number of tokens generated is limited. The shaded confidence intervals indicate that higher `n_p` values (e.g., 25) yield more consistent results, as their intervals are narrower. However, beyond ~8,000 tokens, the pass rate plateaus across all `n_p` values, implying that additional tokens provide diminishing returns. The markers for `n_fr` values align with specific token thresholds, suggesting that failure rates (`n_fr`) correlate with token generation milestones. This could inform resource allocation strategies, prioritizing higher `n_p` for critical tasks with limited tokens. </details> <details> <summary>x17.png Details</summary>  ### Visual Description ## Heatmap: Relationship Between Feedback-Repairs and Initial Programs ### Overview The image is a heatmap visualizing the relationship between the number of feedback-repairs (`n_fr`) and the number of initial programs (`n_p`). Values are represented numerically in cells, with color gradients transitioning from orange (low values) to green (mid values) to black (high values). The top-right corner contains "O.O.B." (likely "Out of Bounds") annotations. --- ### Components/Axes - **Y-Axis (Vertical)**: - Label: "Number of feedback-repairs (`n_fr`)" - Categories: 1, 3, 5, 10 (increasing downward) - **X-Axis (Horizontal)**: - Label: "Number of initial programs (`n_p`)" - Categories: 1, 2, 5, 10, 25 (increasing rightward) - **Color Gradient**: - Orange → Green → Black (increasing value intensity) - No explicit legend, but color correlates with numerical values. --- ### Detailed Analysis #### Data Table Reconstruction | `n_fr` \ `n_p` | 1 | 2 | 5 | 10 | 25 | |----------------|-------|-------|-------|-------|-------| | 1 | 0.96 | 0.99 | 1.03 | 1.05 | 1.09 | | 3 | 0.91 | 0.97 | 1.04 | 1.08 | O.O.B.| | 5 | 0.89 | 0.96 | 1.04 | 1.09 | O.O.B.| | 10 | 0.88 | 0.97 | 1.06 | O.O.B.| O.O.B.| #### Key Observations 1. **Trend**: - Values generally increase with higher `n_p` and `n_fr`, peaking at `n_p = 25` and `n_fr = 1` (1.09). - "O.O.B." annotations appear exclusively in the top-right quadrant (`n_p ≥ 10`, `n_fr ≥ 3`), suggesting a threshold beyond which values become undefined or invalid. 2. **Color Consistency**: - Orange cells (e.g., 0.88–0.99) dominate the bottom-left. - Green cells (1.03–1.09) occupy the mid-range. - Black cells (O.O.B.) are confined to the extreme top-right. --- ### Interpretation - **Relationship**: The heatmap suggests a positive correlation between `n_p` and `n_fr` up to a critical threshold. Beyond `n_p = 10` and `n_fr ≥ 3`, the system transitions to "O.O.B.", implying diminishing returns or operational failure. - **Anomalies**: The value at `n_fr = 10`, `n_p = 1` (0.88) is the lowest, contradicting the general upward trend. This may indicate inefficiency at high feedback-repair rates with minimal initial programs. - **Practical Implications**: Balancing `n_p` and `n_fr` is critical. Exceeding thresholds risks system instability, as reflected by "O.O.B." entries. --- ### Spatial Grounding & Verification - **Legend**: Implied via color gradient (no explicit legend). - **Trend Verification**: - For `n_fr = 1`, values rise monotonically with `n_p` (0.96 → 1.09). - For `n_p = 25`, values drop to "O.O.B." as `n_fr` increases, confirming threshold behavior. - **Component Isolation**: - Header: Axis labels and categories. - Main Chart: Heatmap cells with numerical/color data. - Footer: "O.O.B." annotations. --- ### Final Notes The heatmap highlights a trade-off between scaling initial programs and feedback-repairs. Values beyond the "O.O.B." threshold likely represent unsustainable or erroneous states, requiring further investigation into system constraints. </details> <details> <summary>x18.png Details</summary>  ### Visual Description ## Line Graph: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The image depicts a line graph comparing the relationship between the mean number of tokens generated (x-axis) and the mean pass rate (y-axis) across different experimental conditions. The graph includes multiple data series represented by colored lines and markers, with a shaded confidence interval around a central trend line. ### Components/Axes - **X-axis**: "Mean number of tokens generated" (0 to 10,000, logarithmic scale) - **Y-axis**: "Mean pass rate" (0.0 to 1.0) - **Legend**: Located in the top-right corner, mapping colors/markers to experimental conditions: - Red circles: `n_p = 1`, `n_fr = 1` - Orange triangles: `n_p = 2`, `n_fr = 3` - Teal squares: `n_p = 5`, `n_fr = 5` - Blue triangles: `n_p = 10`, `n_fr = 10` - Dark blue circles: `n_p = 25`, `n_fr = 10` - Dashed black line: Central trend line (no legend label) ### Detailed Analysis 1. **Data Series Trends**: - **Red circles (`n_p = 1`, `n_fr = 1`)**: - Starts at ~0.2 at 1,000 tokens, rises to ~0.4 at 10,000 tokens. - Error bars: ±0.02–0.05. - **Orange triangles (`n_p = 2`, `n_fr = 3`)**: - Begins at ~0.25 at 2,000 tokens, plateaus near ~0.35 at 6,000 tokens. - Error bars: ±0.03–0.07. - **Teal squares (`n_p = 5`, `n_fr = 5`)**: - Starts at ~0.3 at 3,000 tokens, reaches ~0.45 at 8,000 tokens. - Error bars: ±0.04–0.08. - **Blue triangles (`n_p = 10`, `n_fr = 10`)**: - Begins at ~0.35 at 4,000 tokens, peaks at ~0.5 at 8,000 tokens. - Error bars: ±0.05–0.10. - **Dark blue circles (`n_p = 25`, `n_fr = 10`)**: - Starts at ~0.4 at 5,000 tokens, stabilizes near ~0.55 at 10,000 tokens. - Error bars: ±0.06–0.12. - **Dashed black line**: Smoothly increases from ~0.1 at 1,000 tokens to ~0.5 at 10,000 tokens, representing an aggregate trend. 2. **Error Bars**: - Larger error bars for lower `n_p` values (e.g., red circles) compared to higher `n_p` values (e.g., dark blue circles). - Error bars shrink as token count increases, suggesting reduced variability in larger datasets. 3. **Legend Placement**: - Top-right corner, with color-marker pairs aligned vertically. - Text labels explicitly state `n_p` and `n_fr` values for each series. ### Key Observations - **Positive Correlation**: Higher `n_p` values consistently yield higher mean pass rates, especially at larger token counts. - **Diminishing Returns**: The rate of improvement in pass rate slows as token counts exceed ~6,000 tokens. - **Error Variability**: Lower `n_p` conditions (e.g., `n_p = 1`) exhibit greater uncertainty in measurements. - **Trend Line Alignment**: The dashed black line closely follows the trajectory of higher `n_p` series (e.g., `n_p = 25`), suggesting it represents an optimal or aggregated performance baseline. ### Interpretation The data demonstrates that increasing the mean number of tokens generated (`n_p`) improves the mean pass rate, with higher `n_p` values achieving better performance. This trend is most pronounced for conditions with higher `n_fr` (e.g., `n_fr = 10`), where larger `n_p` compensates for increased failure rates. The shaded confidence interval around the trend line indicates that the observed relationship is statistically significant, with variability decreasing as token counts grow. The results imply that token generation efficiency is critical for system performance, with diminishing returns at scale. Outliers (e.g., `n_p = 2` plateauing at ~0.35) suggest potential saturation effects or experimental constraints at lower `n_p` values. </details> <details> <summary>x19.png Details</summary>  ### Visual Description ## Heatmap: Feedback-Repair Ratio vs Initial Programs ### Overview The image is a heatmap visualizing the relationship between the number of initial programs (`n_p`) and the number of feedback-repairs (`n_fr`). Values are represented numerically in cells, with color gradients ranging from dark brown (low values) to black (high values). Some cells contain "O.O.B." (likely indicating "Out of Bounds" or undefined values). ### Components/Axes - **X-axis (Horizontal)**: "Number of initial programs (`n_p`)" with categories: 1, 2, 5, 10, 25. - **Y-axis (Vertical)**: "Number of feedback-repairs (`n_fr`)" with categories: 1, 3, 5, 10. - **Color Gradient**: Dark brown (low values) to black (high values), with no explicit legend but implied by shading. - **Embedded Text**: Numerical values (e.g., 0.81, 1.19) and "O.O.B." in specific cells. ### Detailed Analysis - **Data Structure**: - Rows correspond to `n_fr` (1, 3, 5, 10). - Columns correspond to `n_p` (1, 2, 5, 10, 25). - Values increase diagonally from bottom-left (1.01) to top-right (1.19), with "O.O.B." dominating the upper-right quadrant. - **Key Values**: - **Low `n_p` (1–2)**: Values range from 0.81 (n_p=1, n_fr=10) to 0.97 (n_p=2, n_fr=1–5). - **Mid `n_p` (5)**: Values jump to 1.10 (n_fr=3–5) and 1.13 (n_fr=10). - **High `n_p` (10–25)**: Values reach 1.16 (n_p=10, n_fr=3) and 1.19 (n_p=25, n_fr=1), with "O.O.B." for most combinations. ### Key Observations 1. **Trend**: Feedback-repair ratios generally increase with higher `n_p` and lower `n_fr`. 2. **Anomalies**: - "O.O.B." appears for `n_p ≥ 5` and `n_fr ≥ 5`, suggesting undefined or non-applicable values beyond these thresholds. - The highest value (1.19) occurs at `n_p=25` and `n_fr=1`, indicating extreme sensitivity to initial programs when feedback-repairs are minimal. 3. **Color Correlation**: Darker shades (black) align with higher numerical values, confirming the gradient’s consistency. ### Interpretation The heatmap suggests that increasing the number of initial programs (`n_p`) correlates with higher feedback-repair ratios, particularly when feedback-repairs (`n_fr`) are low. However, beyond `n_p=5` and `n_fr=5`, the system may become unstable or undefined ("O.O.B."), implying a practical limit to scaling. The sharpest increase occurs at `n_p=25` with minimal feedback-repairs, highlighting a potential risk of over-initialization without adequate repair mechanisms. This could inform resource allocation strategies to balance program initialization and repair capacity. </details> Figure 8: GPT-4 results from Figure 4 (Section 4.1) per difficulty (row), from top to bottom: introductory, interview, and competition. <details> <summary>x20.png Details</summary>  ### Visual Description ## Line Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The chart compares the performance of different GPT model configurations in terms of mean pass rate across varying numbers of tokens generated. Five data series are plotted, differentiated by primary model (M_P) and repair model (M_F) versions. All lines exhibit sigmoidal growth patterns with plateau phases. ### Components/Axes - **X-axis**: Mean number of tokens generated (0–10,000 tokens) - **Y-axis**: Mean pass rate (0.0–1.0) - **Legend**: Positioned in the bottom-left corner, with five entries: 1. Dark blue: M_P = GPT-4 (no repair) 2. Teal: M_P = GPT-4; M_F = GPT-4 3. Gray: M_P = GPT-3.5 (no repair) 4. Orange: M_P = GPT-3.5; M_F = GPT-3.5 5. Light blue: M_P = GPT-3.5; M_F = GPT-4 ### Detailed Analysis 1. **Dark Blue Line (GPT-4 no repair)**: - Starts at ~0.55 pass rate at 1,000 tokens - Reaches plateau at ~0.92 pass rate by 4,000 tokens - Maintains stable performance through 10,000 tokens 2. **Teal Line (GPT-4 with GPT-4 repair)**: - Begins at ~0.60 pass rate at 1,000 tokens - Plateaus at ~0.88 pass rate by 3,000 tokens - Shows slight decline to ~0.86 at 6,000 tokens 3. **Gray Line (GPT-3.5 no repair)**: - Initial pass rate ~0.50 at 1,000 tokens - Reaches ~0.80 pass rate by 4,000 tokens - Stabilizes at ~0.82 through 10,000 tokens 4. **Orange Line (GPT-3.5 with GPT-3.5 repair)**: - Starts at ~0.55 pass rate at 1,000 tokens - Peaks at ~0.78 pass rate by 4,000 tokens - Declines to ~0.75 at 6,000 tokens 5. **Light Blue Line (GPT-3.5 with GPT-4 repair)**: - Initial pass rate ~0.62 at 1,000 tokens - Reaches ~0.80 pass rate by 4,000 tokens - Maintains ~0.81 through 10,000 tokens ### Key Observations - GPT-4 models consistently outperform GPT-3.5 across all configurations - Repair operations reduce performance compared to no-repair scenarios - Using GPT-4 for repair (light blue) improves GPT-3.5's performance by ~0.19 pass rate - All models show diminishing returns after ~4,000 tokens generated - GPT-4 no-repair achieves highest performance (0.92 pass rate) ### Interpretation The data demonstrates that model version significantly impacts performance, with GPT-4 consistently outperforming GPT-3.5. Repair operations introduce performance degradation, but using a higher version model for repair (GPT-4) mitigates this effect. The no-repair configurations achieve the highest pass rates, suggesting that repair mechanisms may introduce inefficiencies. The plateau phases indicate that increasing token generation beyond ~4,000 tokens provides minimal performance gains. This suggests optimal resource allocation should focus on GPT-4 models with careful consideration of repair strategy tradeoffs. </details> <details> <summary>x21.png Details</summary>  ### Visual Description ## Line Chart: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The chart illustrates the relationship between the mean number of tokens generated and the mean pass rate for different configurations of GPT models. Five distinct data series are plotted, each representing a unique combination of primary (M_P) and repair (M_F) models. The y-axis represents the mean pass rate (0.0–1.0), while the x-axis shows the mean number of tokens generated (0–10,000). ### Components/Axes - **X-axis**: "Mean number of tokens generated" (0–10,000, linear scale). - **Y-axis**: "Mean pass rate" (0.0–1.0, linear scale). - **Legend**: Located in the bottom-right corner, with five entries: 1. **Dark blue**: M_P = GPT-4 (no repair) 2. **Teal**: M_P = GPT-4; M_F = GPT-4 3. **Gray**: M_P = GPT-3.5 (no repair) 4. **Orange**: M_P = GPT-3.5; M_F = GPT-3.5 5. **Light blue**: M_P = GPT-3.5; M_F = GPT-4 ### Detailed Analysis 1. **Dark blue (M_P = GPT-4, no repair)**: - Starts at ~0.4 at 2,000 tokens. - Rises sharply to ~0.65 at 6,000 tokens. - Plateaus at ~0.65 beyond 6,000 tokens. - **Trend**: Steady increase followed by stabilization. 2. **Teal (M_P = GPT-4; M_F = GPT-4)**: - Begins at ~0.5 at 2,000 tokens. - Peaks at ~0.7 at 6,000 tokens. - Drops to ~0.55 at 8,000 tokens. - **Trend**: Initial improvement, followed by a decline. 3. **Gray (M_P = GPT-3.5, no repair)**: - Starts at ~0.3 at 2,000 tokens. - Gradually increases to ~0.55 at 8,000 tokens. - **Trend**: Slow, linear growth. 4. **Orange (M_P = GPT-3.5; M_F = GPT-3.5)**: - Begins at ~0.3 at 2,000 tokens. - Rises to ~0.5 at 8,000 tokens. - **Trend**: Moderate, linear increase. 5. **Light blue (M_P = GPT-3.5; M_F = GPT-4)**: - Starts at ~0.35 at 2,000 tokens. - Reaches ~0.55 at 10,000 tokens. - **Trend**: Steady, linear improvement. ### Key Observations - **GPT-4 superiority**: Configurations using GPT-4 (dark blue, teal) consistently outperform GPT-3.5 variants. - **Repair mechanism impact**: - For GPT-4, the repair model (M_F = GPT-4) initially improves performance but later causes a decline (teal line). - For GPT-3.5, pairing with GPT-4 as M_F (light blue) significantly boosts pass rates compared to GPT-3.5 alone (orange line). - **Threshold effects**: The teal line’s drop after 6,000 tokens suggests potential overfitting or diminishing returns when both models are GPT-4. ### Interpretation The data demonstrates that GPT-4 models achieve higher pass rates across all token ranges. However, the repair mechanism’s effectiveness depends on the primary model: - **GPT-4**: Using GPT-4 as both M_P and M_F yields peak performance but risks overfitting, as seen in the teal line’s decline. - **GPT-3.5**: Pairing with GPT-4 as M_F (light blue) maximizes performance, highlighting the value of hybrid configurations. The gray and orange lines (GPT-3.5 variants) show that standalone GPT-3.5 models underperform compared to GPT-4. Notably, the teal line’s post-6,000-token drop warrants further investigation—it may indicate a flaw in the repair process when both models are identical high-capacity systems. This suggests that repair mechanisms might need to be tailored to the primary model’s capabilities to avoid unintended consequences. </details> <details> <summary>x22.png Details</summary>  ### Visual Description ## Line Graph: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The graph compares the performance of different GPT model configurations (GPT-4 and GPT-3.5) across two scenarios: "no repair" and "with repair" (denoted as _M_P_ and _M_F_). Performance is measured as "Mean pass rate" against the "Mean number of tokens generated" (x-axis). Five data series are plotted, with shaded regions indicating uncertainty. ### Components/Axes - **X-axis**: "Mean number of tokens generated" (0 to 10,000, logarithmic scale). - **Y-axis**: "Mean pass rate" (0.0 to 1.0, linear scale). - **Legend**: Located in the top-right corner, with five entries: 1. Dark blue: _M_P_ = GPT-4 (no repair) 2. Teal: _M_P_ = GPT-4; _M_F_ = GPT-4 (repair) 3. Gray: _M_P_ = GPT-3.5 (no repair) 4. Orange: _M_P_ = GPT-3.5; _M_F_ = GPT-3.5 (repair) 5. Light blue: _M_P_ = GPT-3.5; _M_F_ = GPT-4 (repair) ### Detailed Analysis 1. **Dark Blue Line (GPT-4, no repair)**: - Starts at ~0.1 pass rate at 1,000 tokens. - Rises steadily to ~0.4 pass rate at 10,000 tokens. - Shaded region widens slightly, indicating moderate uncertainty. 2. **Teal Line (GPT-4 with repair)**: - Begins at ~0.05 pass rate at 1,000 tokens. - Reaches ~0.5 pass rate at 10,000 tokens. - Shaded region is the widest, suggesting higher variability. 3. **Gray Line (GPT-3.5, no repair)**: - Starts at ~0.02 pass rate at 1,000 tokens. - Ends at ~0.15 pass rate at 10,000 tokens. - Shaded region is narrow, indicating low uncertainty. 4. **Orange Line (GPT-3.5 with repair)**: - Begins at ~0.01 pass rate at 1,000 tokens. - Ends at ~0.18 pass rate at 10,000 tokens. - Shaded region is moderately wide. 5. **Light Blue Line (GPT-3.5 with GPT-4 repair)**: - Starts at ~0.03 pass rate at 1,000 tokens. - Ends at ~0.22 pass rate at 10,000 tokens. - Shaded region is the narrowest, indicating high confidence. ### Key Observations - **GPT-4 superiority**: All GPT-4 configurations outperform GPT-3.5 variants, especially at higher token counts. - **Repair impact**: Repair mechanisms improve pass rates for both models, with GPT-4 showing the largest gains. - **Uncertainty patterns**: GPT-4 models exhibit wider shaded regions, suggesting greater variability in performance across trials. - **Efficiency trade-off**: GPT-3.5 with GPT-4 repair achieves ~20% pass rate at 10,000 tokens but requires more tokens than GPT-4 alone. ### Interpretation The data demonstrates that GPT-4 models consistently achieve higher pass rates than GPT-3.5, with repair mechanisms amplifying performance gains. The shaded regions imply that GPT-4's results are less predictable, possibly due to architectural complexity or training data differences. The light blue line (hybrid repair) suggests that combining GPT-3.5 with GPT-4 repair offers a cost-effective middle ground, though it underperforms pure GPT-4 configurations. These trends highlight the trade-offs between model size, repair strategies, and computational efficiency in NLP systems. </details> Figure 9: Results from Figure 6 (Section 4.2) per difficulty (row), from top to bottom: introductory, interview, and competition. ## Appendix B Human Experiment: Study Instructions For our study on human data, participants were given a slide deck with instructions. The following ten images show the instructions, which include an example of a task shown to a participant: <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/1.jpg Details</summary>  ### Visual Description ## Screenshot: Task List for Python Debugging Challenge ### Overview The image displays a structured task list for a Python debugging challenge. It outlines setup requirements, task objectives, and submission guidelines. The text is presented in a hierarchical bullet-point format with emphasis on specific instructions. ### Components/Axes - **Headings**: - "Tasks" (main title) - "Setup" - "Task" - "Task format" - **Subpoints**: - Circular bullet points (`○`) for nested instructions - Bold text for key terms (e.g., "Debug five incorrect Python programs") - Blue hyperlinks for critical actions (e.g., "explain what the program is doing wrong") ### Detailed Analysis 1. **Setup**: - Requires a laptop or desktop computer (explicitly excludes phones). - No additional technical specifications provided. 2. **Task**: - Objective: Debug **five** incorrect Python programs. - Each program represents an incorrect attempt to solve a coding challenge. - Answers must **explain what the program is doing wrong** (hyperlinked text). - Time expectation: ~10 minutes per task. 3. **Task Format**: - Each task is hosted on a **separate website**. - Answers must be submitted via a **Google form embedded in each page**. - Explicit statement: "**No other data is being collected**" (hyperlinked). ### Key Observations - **Emphasis on Explanation**: The task prioritizes understanding over rote correction, requiring users to articulate errors. - **Time Constraints**: ~10 minutes per task suggests a focus on efficiency or assessment of problem-solving speed. - **Data Privacy Note**: The explicit mention of no additional data collection may address user concerns about privacy or compliance. ### Interpretation This task list appears to be part of a structured assessment or training module for Python debugging skills. The requirement to explain errors (rather than just fix them) implies an emphasis on pedagogical understanding. The use of Google Forms for submission suggests integration with an existing platform, while the exclusion of phones indicates a controlled environment for task completion. The ~10-minute timeframe per task may reflect either a realistic estimate for experienced users or a deliberate constraint to simulate real-world debugging pressures. The absence of data collection beyond form submissions highlights a focus on task-specific outcomes rather than broader analytics. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/2.jpg Details</summary>  ### Visual Description ## Screenshot: Webpage Instructions for Code Error Analysis ### Overview The image shows a webpage with instructions for analyzing a programming problem. It emphasizes explaining errors in a program's logic, providing examples of feedback, and clarifying data privacy and tool usage policies. ### Components/Axes - **Title**: "Your Answer" (top-left, bold) - **Main Sections**: 1. **Instructions**: Bullet points guiding response structure. 2. **Example Answers**: Two code critique examples. 3. **Notes**: Data privacy and tool usage disclaimers. ### Detailed Analysis #### Instructions - Users must **briefly explain what the program is doing wrong**. - Optional: Suggest alternative approaches. - Feedback can be: - **Precise**: "The formula used to calculate X on line 5 is wrong, it should be..." - **High-level**: "The program is treating the task as a min-cut graph problem, but it actually shortest-path... It could be rewritten using Dijkstra's algorithm..." #### Example Answers 1. **Issue 1**: - Problem: Code incorrectly validates palindromes starting/ending with zeros (e.g., `010`, `00`). - Fix: Adjust validation to exclude such cases. 2. **Issue 2**: - Problem: Code ignores indirect subordinates when finding the k-th officer in a command spreading sequence. - Fix: Traverse the tree of officers and reconstruct the command sequence before identifying the k-th element. #### Notes - **Data Privacy**: "We are not collecting any data about how you use the website. Only your submitted answer is recorded." - **Tool Usage**: "Feel free to use external tools: pen and paper, a Python IDE, etc!" ### Key Observations - The instructions prioritize **specificity** in error analysis (e.g., line numbers, algorithmic misapplications). - Examples highlight **common pitfalls** in code logic (e.g., edge cases in palindrome validation, graph algorithm misuse). - The disclaimers address **user concerns** about data tracking and tool flexibility. ### Interpretation This webpage is designed to guide users in providing **structured, actionable feedback** on programming errors. By emphasizing precision (e.g., line numbers, algorithmic corrections) and offering examples, it ensures critiques are both technical and practical. The inclusion of data privacy assurances and tool flexibility suggests the platform values user autonomy and transparency. The examples demonstrate how to balance high-level conceptual errors (e.g., misapplying graph algorithms) with granular code-level fixes (e.g., palindrome validation rules), catering to both novice and experienced developers. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/3.jpg Details</summary>  ### Visual Description ## Text Element: "Example" ### Overview The image contains a single textual element: the word "Example" centered on a plain white background. No additional graphical, numerical, or structural elements are present. ### Components/Axes - **Text Content**: "Example" (blue font, centered) - **Background**: Solid white (no gradients, patterns, or overlays) - **No axes, legends, or data series detected** ### Detailed Analysis - **Text Properties**: - Font: Sans-serif (likely Arial or similar) - Color: Blue (#0000FF or similar) - Position: Exact center of the image (spatial grounding: no offset) - Size: Medium (relative to standard screen resolutions; no scale reference) - **No numerical values, categories, or hierarchical structures present** ### Key Observations 1. The word "Example" is the sole focus, with no contextual or decorative elements. 2. The blue color suggests a design choice for emphasis or thematic consistency (e.g., hyperlink-like styling). 3. No interactive elements (e.g., buttons, links) or metadata (e.g., timestamps, identifiers) are visible. ### Interpretation This image likely serves as a placeholder or illustrative example in a technical or design context. The simplicity implies it could represent: - A template for minimalist UI/UX mockups. - A generic example in educational materials (e.g., "Example of text styling"). - A test image for layout alignment or color calibration. The absence of additional data or complexity suggests intentional minimalism, prioritizing clarity over detail. The blue text may indicate interactivity (e.g., a clickable link) in a digital context, though no such functionality is visually confirmed. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/4.jpg Details</summary>  ### Visual Description ```markdown ## Problem Specification Document ### Overview This document specifies a programming problem involving vote counting for a school election. The task requires processing a list of votes to determine the winning candidate(s) based on majority rules, with specific handling for ties and invalid inputs. ### Components/Axes - **Specification Section**: Describes the election scenario and rules. - **Input-Output Section**: Defines input format (list of votes) and output requirements (winning candidate or "Runoff!"). - **Examples Section**: Provides sample inputs and expected outputs. - **Remarks Section**: Notes about input/output handling through stdin/stdout. ### Detailed Analysis #### Specification The problem describes a school election where: - A controversial new dress code proposal is voted on by students. - The proposal passes if a majority votes "yes"; otherwise, it fails after 4 hours. - If the proposal passes, a winner must be determined to fund a football facility. - The program must count votes for candidates and output the winner(s). #### Input-Output - **Input**: A list of votes (strings) representing candidate names. - **Output**: - The candidate(s) with the highest vote count. - If multiple candidates tie for the highest votes, output "Runoff!". - If no candidate has a simple majority, output "Runoff!". #### Examples 1. **Example 1**: - Input: `["Penny Progrock", "Penny Progrock", "Penny Progrock", "Marty Graham", "Joseph Ivers", "Joseph Ivers", "Joseph Ivers", "Joseph Ivers", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie Froggitt", "Connie 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Incorrect Program"** with a code snippet and explanatory text. The code is written in Python and appears to implement a voting system to determine a winner based on candidate votes. The task includes instructions for debugging the program and notes about input/output handling. ### Components/Axes - **Title**: "2. Incorrect Program" (top-left, bold black text). - **Code Block**: - **Header**: "Incorrect Program" (bold black text on a light gray background). - **Code Content**: - Imports: `from collections import defaultdict`. - Variable Initialization: - `votes = defaultdict(int)`. - `candidate = input()`. - Loop: `while candidates[input()] != -1` (collects candidate votes). - Voting Logic: - `total_votes = sum(votes.values())`. - `max_votes = max(votes.values())`. - Conditional: `if len(candidates) == 1 and max_votes > total_votes // 2:`. - Output: `print(candidate)`. - Else: `print("Runoff!")`. - **Explanatory Text** (right side): - Instructions: "Next, you will be shown the incorrect program." - Tip: "If you are struggling with debugging the program, **try running it on your machine!**" (blue hyperlink). - Note: "The programs handle inputs through `input()`, and outputs through `print()`." ### Detailed Analysis 1. **Code Structure**: - The code uses `defaultdict` to track votes for candidates. - A loop collects candidate names and their vote counts until `-1` is entered. - It calculates total votes and identifies the candidate with the most votes. - If a candidate has more than half the total votes, they win; otherwise, a runoff is declared. 2. **Potential Issues in Code**: - **Variable Mismatch**: The loop condition `while candidates[input()] != -1` may cause errors because `candidates` is not initialized before use. - **Logic Flaw**: The condition `if len(candidates) == 1 and max_votes > total_votes // 2` is redundant. If there’s only one candidate, `max_votes` will always equal `total_votes`, making the condition always false. - **Input Handling**: The code does not validate inputs (e.g., non-integer votes). 3. **Explanatory Text**: - The task emphasizes debugging the provided code. - The blue hyperlink suggests practical experimentation as a debugging strategy. - Input/output conventions (`input()`/`print()`) are explicitly stated. ### Key Observations - The code’s logic for determining a winner is flawed due to uninitialized variables and redundant conditions. - The task’s instructions and notes are designed to guide users toward identifying and fixing these issues. - The blue hyperlink ("try running it on your machine!") is a critical clue for debugging. ### Interpretation This task simulates a real-world debugging scenario where a voting system’s code contains subtle errors. The primary issues are: 1. **Uninitialized Variables**: The `candidates` dictionary is used before being defined, leading to a `NameError`. 2. **Logical Redundancy**: The condition for declaring a winner is logically inconsistent, as a single candidate cannot have more than half the votes if they are the only one. 3. **Input Validation**: The code assumes valid integer inputs but lacks error handling for invalid data. The task’s design encourages users to: - Identify syntax and runtime errors. - Analyze the flow of data (e.g., how votes are aggregated). - Test edge cases (e.g., single candidate, tie votes). The blue hyperlink reinforces the importance of empirical testing in debugging, aligning with the note about input/output conventions. The code’s flaws likely stem from oversight in variable initialization and logical conditions, common pitfalls in iterative programming tasks. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/6.jpg Details</summary>  ### Visual Description ## Screenshot: Error Message Interface ### Overview The image shows a technical error message interface from a Python program. It contains two primary sections: (1) a detailed error report with input/output data and (2) an explanatory text block describing the error components. The interface appears to be part of a testing or debugging environment. ### Components/Axes **Left Section (Error Report):** - **Header**: Bold "Error" label - **Tip**: Instructional text about executing code and piping input - **Input List**: - Penny Franklin - Marti Graham - Connie Froggatt - Joseph Ivers - Connie Froggatt - Penny Franklin - Connie Froggatt - Bruce Stanger - Connie Froggatt - Barbara Skinner - Barbara Skinner - **Program Output**: "Runtime!!" - **Expected Output**: "Connie Froggatt" **Right Section (Explanation):** - **Header**: "The error message shows you the test that the program failed on." - **Bullet Points**: 1. "An example input" 2. "The program's incorrect output" 3. "The expected output" - **Tip**: "try copy-pasting the input to a file and piping it to the program." ### Detailed Analysis **Input List Analysis**: - 11 total entries with 4 unique names - Connie Froggatt appears 4 times (37.3% of entries) - Barbara Skinner appears twice consecutively - Joseph Ivers appears once (unique entry) **Output Comparison**: - Program Output: "Runtime!!" (error indicator) - Expected Output: "Connie Froggatt" (correct result) **Textual Patterns**: - Repeated emphasis on Connie Froggatt in both input and expected output - Instructional language in both sections (technical guidance) - Consistent use of bold formatting for key terms ### Key Observations 1. The error message contains a recursive reference to itself in the tip text 2. Input list contains duplicate entries with potential data quality issues 3. Output format mismatch: "Runtime!!" vs. name string 4. Explanatory text uses imperative language ("try copy-pasting") 5. Interface lacks visual indicators for error severity (e.g., red color) ### Interpretation This error message demonstrates a failure in input processing logic. The repeated occurrence of Connie Froggatt in the input list suggests either: 1. A test case designed to validate duplicate handling 2. A data entry error in the test dataset 3. An intentional stress test for the program's input validation The "Runtime!!" output indicates an unhandled exception occurred during execution, while the expected output shows the program should return a name string. The explanatory text confirms this is a test failure scenario, with the interface designed to help developers debug by providing: - Sample input for reproduction - Actual vs. expected output comparison - Execution method guidance (file piping) The interface follows a common pattern in debugging tools by separating raw error data from explanatory guidance, though it lacks visual prioritization of critical information (e.g., highlighting the Runtime error). </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/7.jpg Details</summary>  ### Visual Description ## Screenshot: Model Explanations Section ### Overview The image shows a technical documentation page titled "4. Model Explanations" with two example explanations of code issues. A disclaimer notes that these explanations are generated by the model and may be incorrect, advising users to treat them as suggestions rather than definitive answers. ### Components/Axes - **Title**: "4. Model Explanations" (top-left) - **Main Content Box**: White rectangular box containing: - Header: "Model Explanations" - Two labeled explanations: - **Explanation 1** - **Explanation 2** - **Disclaimer Text**: Right-aligned text block below the main content box. ### Content Details #### Explanation 1 - **Text**: "The concise explanation of the issue is: The code checks if the maximum votes are strictly greater than half of the total votes to determine if there's a majority. However, it should check if the maximum votes are greater than or equal to half of the total votes." #### Explanation 2 - **Text**: "The following is a concise explanation of the issue: The code checks for a simple majority by comparing 'max_votes' to 'total_votes / 2', which returns the floor division result. This means that if 'max_votes' is equal to half of the 'total_votes', it will not be considered a simple majority. Instead, the condition should check if 'max_votes' is strictly greater than half of the 'total_votes'." #### Disclaimer Text - **Text**: "To help you get started with the debugging, each page lists two example explanations. These explanations are generated by the model itself. They might be completely wrong. You don't have to use them. Think of these like CoPilot suggestions." ### Key Observations 1. **Contradictory Logic**: Explanation 1 identifies a flaw in a majority-checking condition (strict `>` vs. inclusive `>=`). 2. **Floor Division Issue**: Explanation 2 highlights a problem with integer division in Python (e.g., `5/2 = 2` in floor division). 3. **Model Limitations**: The disclaimer explicitly warns that explanations may be incorrect, emphasizing the need for human verification. ### Interpretation The document illustrates how an AI model generates explanations for code issues but acknowledges potential inaccuracies. The examples reveal: - **Logical Flaws**: The model misinterprets majority conditions and integer division behavior. - **Risk of Overreliance**: The disclaimer cautions against treating model outputs as infallible, mirroring real-world challenges with AI-assisted debugging tools like CoPilot. - **Educational Value**: The examples serve as teaching moments for developers to critically evaluate automated suggestions. The text emphasizes the importance of human oversight when using AI-generated explanations, particularly in technical contexts where precision is critical. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/8.jpg Details</summary>  ### Visual Description ## Screenshot: Answer Form Interface ### Overview The image depicts a user interface for submitting an explanation of a program error. The form includes a redacted section for anonymity, input fields, and instructions for users. Key elements include a Google sign-in prompt, required field indicators, and submission guidelines. ### Components/Axes - **Title**: "5. Answer Form" (top-left) - **Redacted Section**: Black box with text "REDACTED FOR ANONYMITY" (center-left) - **Sign-in Prompt**: "Sign in to Google to save your progress. Learn more" (blue text, below redacted section) - **Required Field Indicator**: Red asterisk (*) next to "Your Explanation" (bottom-left) - **Text Area**: Labeled "Your Explanation" with placeholder "Your answer" (below required indicator) - **Buttons**: - "Submit" (purple button, bottom-left) - "Clear form" (purple text, bottom-right) - **Instructions**: Right-aligned text block explaining form requirements (see below) ### Content Details #### Left Panel (Form) 1. **Redacted Section**: - Black box with white text: "REDACTED FOR ANONYMITY" - Position: Center-left, above sign-in prompt 2. **Sign-in Prompt**: - Text: "Sign in to Google to save your progress. Learn more" - Position: Directly below redacted section 3. **Required Field**: - Red asterisk (*) next to "Your Explanation" - Position: Bottom-left, above text area 4. **Text Area**: - Label: "Your Explanation" - Placeholder: "Your answer" - Position: Below required indicator 5. **Buttons**: - "Submit" (purple button, bottom-left) - "Clear form" (purple text, bottom-right) #### Right Panel (Instructions) - **Header**: "Finally, each page contains an embedded Google Form. No login is required." - **Key Instruction**: - Blue text: "Submit your explanation of what the program is doing wrong." - **Answer Format Guidance**: - Text: "Your answer must be self-contained; it should **not** be of the form 'Just like the first model explanation describes, the issue with the code is that ...'" - Position: Bottom of right panel ### Key Observations 1. **Anonymity**: The redacted section ensures user privacy. 2. **Required Field**: The red asterisk (*) explicitly marks "Your Explanation" as mandatory. 3. **Submission Constraints**: Users must provide a self-contained explanation, avoiding generic responses. 4. **Google Integration**: The form is embedded in a page with no login required, but signing in saves progress. ### Interpretation The form is designed for users to report program errors anonymously while ensuring detailed, self-contained explanations. The redaction emphasizes privacy, and the instructions discourage vague answers by requiring specific code-related analysis. The Google sign-in option balances convenience with data persistence, though it is optional. The color coding (red for required fields, purple for buttons) aids usability by highlighting critical elements. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/9.jpg Details</summary>  ### Visual Description ## Screenshot: Study Tips Document ### Overview The image is a screenshot of a text-based document titled "Study Tips," providing guidance for task completion. It includes a gratitude message, bullet-pointed advice, and a closing note. Key elements are emphasized in blue text, likely indicating hyperlinks or important notes. ### Components/Axes - **Title**: "Study Tips" (bold, top-left) - **Introductory Message**: "We are very grateful for your help! 😊" (black text, below title) - **Bullet Points**: Five main tips with sub-points (black and blue text) - **Closing Note**: "Have a question? Ask [REDACTED] before moving on with the study! 😊" (blue text, bottom) ### Detailed Analysis #### Main Bullet Points 1. **Understand the Task First** - Programs contain subtle logic errors, not just compiler errors. - *Blue text*: "Make sure you understand the task first!" 2. **Clear Explanations** - Use proper grammar and punctuation. - *Blue text*: "Try to write clear and concise explanations..." 3. **Model Explanations** - Use or omit model explanations, but ensure answers are self-contained. - *Blue text*: "Feel free to use (or not use) the model explanations..." 4. **Time Allocation** - Tasks vary in difficulty; allocate time as needed. - *Blue text*: "The tasks vary in difficulty. Feel free to allocate your time..." 5. **External Tools** - Use pen/paper, whiteboards, Python IDEs, or online searches. - Sub-points: - "Use pen and paper or a whiteboard..." - "Use a Python IDE to execute and debug..." - "Search online for help." - *Blue text*: "Feel free to use external tools:" #### Closing Note - *Blue text*: "Have a question? Ask [REDACTED] before moving on with the study! 😊" ### Key Observations - **Emphasis on Clarity**: Blue text highlights critical instructions (e.g., understanding tasks, using tools). - **Emojis**: Two smiley faces (😊) add a friendly tone. - **Redaction**: A black rectangle obscures a name/URL in the closing note. - **Structure**: Hierarchical bullet points with sub-points for detailed guidance. ### Interpretation The document prioritizes **task comprehension** and **methodical problem-solving**. It acknowledges the complexity of programming tasks (subtle logic errors) and encourages adaptability (time allocation, tool usage). The redaction suggests sensitive information (e.g., a contact name or URL) was intentionally hidden. The use of emojis and blue text creates a user-friendly, approachable tone, likely aimed at learners or collaborators needing structured guidance. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/10.jpg Details</summary>  ### Visual Description ## FAQ Section: Website Interaction and Study Objectives ### Overview The image displays a FAQ section from a website, structured as a list of three questions with corresponding answers. The text is formatted with bold headers for questions, bullet points for answers, and specific terms highlighted in blue. ### Components/Axes - **Structure**: - Three main questions, each marked with a bolded bullet point (•). - Answers are indented under each question, prefixed with a circle (•) and formatted in italics. - Key terms (e.g., "human feedback") are highlighted in blue, suggesting hyperlinks or emphasis. ### Detailed Analysis 1. **Question 1**: - **Text**: "Are you collecting data as I visit the website?" - **Answer**: - "No - none at all. Only your final answers are recorded." - **Formatting**: "No" is bolded in blue; the rest of the answer is in plain text. 2. **Question 2**: - **Text**: "What is the point of the study?" - **Answer**: - "To investigate how much better the models are at fixing code when given human feedback, instead of having to debug the code themselves." - **Formatting**: "human feedback" is highlighted in blue. 3. **Question 3**: - **Text**: "Are you evaluating how useful the model explanations were to me?" - **Answer**: - "No - they are just there to help you get started with the debugging. We only care about your final answer." - **Formatting**: "No" is bolded in blue; the rest of the answer is in plain text. ### Key Observations - The study explicitly states that **no data is collected during website visits**, only final answers are recorded. - The primary goal of the study is to **improve code-fixing models** by leveraging human feedback, rather than relying on models to debug code independently. - Model explanations are **not evaluated** for usefulness; their sole purpose is to assist users in initiating the debugging process. ### Interpretation The FAQ clarifies that the study prioritizes **outcome-focused data collection** (final answers) over process-oriented metrics (e.g., user interaction with model explanations). By emphasizing human feedback as a tool to enhance model performance, the study aims to reduce the cognitive load on users during debugging. The exclusion of evaluation for model explanations suggests a focus on efficiency rather than user experience with intermediate steps. The use of blue highlights for terms like "human feedback" and "No" likely serves to draw attention to critical aspects of the study’s methodology and objectives. --- **Note**: The image contains no charts, diagrams, or numerical data. All information is textual and structured as a FAQ. </details> Figure 10: ## Appendix C Human Experiment (Quantitative Analysis): Results Per Task In the table below, we give a complete breakdown of the quantitative results presented in Section 4.3. Note that each program is associated with four different pieces of feedback: two sampled from GPT-4, and two given by our human participants. Each cell is the number of repair candidates (out of 25) that passed all the unit tests. See Section 4.3 for details, as well as Appendix B for the instructions given to participants. | 2106 | interview | A | 7 | 10 | 10 | 0 | | --- | --- | --- | --- | --- | --- | --- | | B | 0 | 2 | 20 | 16 | | | | 2673 | interview | A | 4 | 7 | 17 | 24 | | B | 3 | 25 | 25 | 25 | | | | 2923 | interview | A | 0 | 0 | 0 | 0 | | B | 0 | 0 | 0 | 0 | | | | 3070 | competition | A | 0 | 0 | 0 | 0 | | B | 3 | 0 | 5 | 0 | | | | 3286 | competition | A | 2 | 6 | 10 | 25 | | B | 0 | 0 | 0 | 4 | | | | 3754 | competition | A | 0 | 0 | 0 | 0 | | B | 0 | 0 | 0 | 0 | | | | 4182 | introductory | A | 25 | 25 | 25 | 24 | | B | 25 | 0 | 25 | 25 | | | | 4195 | introductory | A | 25 | 3 | 24 | 23 | | B | 23 | 25 | 25 | 25 | | | | 4281 | introductory | A | 0 | 4 | 0 | 0 | | B | 0 | 0 | 0 | 0 | | | | 4333 | introductory | A | 25 | 0 | 25 | 0 | | B | 23 | 24 | 24 | 25 | | | | 4347 | introductory | A | 0 | 0 | 7 | 25 | | B | 0 | 0 | 25 | 25 | | | | 4426 | introductory | A | 25 | 25 | 25 | 25 | | B | 25 | 25 | 25 | 25 | | | | 4450 | introductory | A | 0 | 0 | 0 | 0 | | B | 24 | 0 | 22 | 24 | | | | 4507 | introductory | A | 0 | 0 | 0 | 0 | | B | 0 | 0 | 1 | 0 | | | | 4514 | introductory | A | 15 | 21 | 1 | 16 | | B | 0 | 0 | 25 | 0 | | | | 4704 | introductory | A | 0 | 25 | 0 | 25 | | B | 25 | 25 | 24 | 23 | | | | 4741 | introductory | A | 25 | 25 | 25 | 25 | | B | 25 | 25 | 25 | 25 | | | | 4855 | introductory | A | 0 | 1 | 17 | 25 | | B | 0 | 2 | 3 | 23 | | | | 4873 | introductory | A | 0 | 0 | 0 | 0 | | B | 0 | 0 | 0 | 18 | | | | 4952 | introductory | A | 0 | 0 | 2 | 25 | | B | 24 | 8 | 24 | 21 | | | ## Appendix D Human Experiment (Qualitative Analysis): Examples In this appendix, we give examples of each category used to classify the responses in the qualitative analysis of Section 4.3. For each category, we give one example from the human participants and one from GPT-4 (when possible). Each example contains: the textual specification of the task; the incorrect program; the error message (in the format it was shown to participants); the feedback in question; and a short comment motivating its classification. ### D.1 Category (a): obviously incorrect feedback #### D.1.1 GPT-4: Example ⬇ ### SPECIFICATION The recent schoolboard elections were hotly contested: a proposal to swap school start times for elementary and high school students, a controversial new dress code proposal that bans athletic clothes in school, and a proposal to raise real - estate taxes to pay for a new football practice facility, and the list goes on and on. It is now hours after the polls have closed and a winner has yet to emerge! In their desperation, the election officials turn to you and ask you to write a program to count the vote! ----- Input ----- The input consists of a single test case, which is a list of votes cast. Each line in the input contains the name of a candidate for whom a vote was cast. A name may consist of multiple words, separated by spaces. Words contain letters or hyphens, but no other punctuation characters. There will be at least votes on the list. The list of votes ends with a single line containing the characters ***. This line should not be counted. There can be up to valid votes. ----- Output ----- If a candidate obtained a simple or absolute majority of all votes cast (that is, more than any other candidate), output the name of this candidate! If no candidate obtained a simple majority, output: " Runoff!" (don ’ t forget to include the exclamation mark!) ----- Examples ----- Sample Input: Penny Franklin Marti Graham Connie Froggatt Joseph Ivers Connie Froggatt Penny Franklin Connie Froggatt Bruce Stanger Connie Froggatt Barbara Skinner Barbara Skinner *** Sample Output: Connie Froggatt ### INCORRECT PROGRAM from collections import defaultdict votes = defaultdict (int) candidate = input () while candidate != "***": votes [candidate] += 1 candidate = input () total_votes = sum (votes. values ()) max_votes = max (votes. values ()) winner = [name for name, count in votes. items () if count == max_votes] if len (winner) == 1 and max_votes > total_votes // 2: print (winner [0]) else: print (" Runoff!") ### ERROR MESSAGE === Input === Penny Franklin Marti Graham Connie Froggatt Joseph Ivers Connie Froggatt Penny Franklin Connie Froggatt Bruce Stanger Connie Froggatt Barbara Skinner Barbara Skinner *** === Program Output === Runoff! === Expected Output === Connie Froggatt ### FEEDBACK The concise explanation of the issue is: The code checks if the maximum votes are strictly greater than half of the total votes to determine if there ’ s a majority. However, it should check if the maximum votes are greater than or equal to half of the total votes. ### COMMENT The issue with the code is not that the ">" should have been a ">=", but rather that it is not allowing for a simple majority. #### D.1.2 Human: Example ⬇ ### SPECIFICATION Snuke and Raccoon have a heap of N cards. The i - th card from the top has the integer a_i written on it. They will share these cards. First, Snuke will take some number of cards from the top of the heap, then Raccoon will take all the remaining cards. Here, both Snuke and Raccoon have to take at least one card. Let the sum of the integers on Snuke ’ s cards and Raccoon ’ s cards be x and y, respectively. They would like to minimize | x - y |. Find the minimum possible value of | x - y |. ----- Constraints ----- - 2 \ leq N \ leq 2 \ times 10^5 - -10^{9} \ leq a_i \ leq 10^{9} - a_i is an integer. ----- Input ----- Input is given from Standard Input in the following format: N a_1 a_2 ... a_ {N} ----- Output ----- Print the answer. ----- Sample Input ----- 6 1 2 3 4 5 6 ----- Sample Output ----- 1 If Snuke takes four cards from the top, and Raccoon takes the remaining two cards, x =10, y =11, and thus | x - y |=1. This is the minimum possible value. ### INCORRECT PROGRAM def main (): n = int (input ()) a = list (map (int, input (). split ())) Snuke_sum = 0 Raccoon_sum = sum (a) min_diff = abs (Raccoon_sum) for i in range (n -1): Snuke_sum += a [i] Raccoon_sum -= a [i] diff = abs (Snuke_sum - Raccoon_sum) min_diff = min (min_diff, diff) print (min_diff) main () ### ERROR MESSAGE === Input === 2 10 -10 === Program Output === 0 === Expected Output === 20 ### FEEDBACK The code initializes the result ‘ min_diff ‘ to ‘ abs (Raccoon_sum)‘ corresponding to the case where Raccoon takes all the cards, however this is incorrect because of the constraint " Snuke and Raccoon have to take at least one card ". Instead just setting ‘ min_diff ‘ to negative infinity initially would fix it. ### COMMENT This human participant was on the right track, but note that setting ‘ min_diff ‘ to * negative * infinity would cause it to never be updated inside of the for loop, and so the program would in fact always return negative infinity. ### D.2 Category (b): feedback explicitly suggests a minor change to the code #### D.2.1 GPT-4: Example ⬇ ### SPECIFICATION There is a square in the xy - plane. The coordinates of its four vertices are (x_1, y_1),(x_2, y_2),(x_3, y_3) and (x_4, y_4) in counter - clockwise order. (Assume that the positive x - axis points right, and the positive y - axis points up.) Takahashi remembers (x_1, y_1) and (x_2, y_2), but he has forgot (x_3, y_3) and (x_4, y_4). Given x_1, x_2, y_1, y_2, restore x_3, y_3, x_4, y_4. It can be shown that x_3, y_3, x_4 and y_4 uniquely exist and have integer values. ----- Constraints ----- - | x_1 |,| y_1 |,| x_2 |,| y_2 | \ leq 100 - (x_1, y_1) != (x_2, y_2) - All values in input are integers. ----- Input ----- Input is given from Standard Input in the following format: x_1 y_1 x_2 y_2 ----- Output ----- Print x_3, y_3, x_4 and y_4 as integers, in this order. ----- Sample Input ----- 0 0 0 1 ----- Sample Output ----- -1 1 -1 0 (0,0),(0,1),(-1,1),(-1,0) is the four vertices of a square in counter - clockwise order. Note that (x_3, y_3)=(1,1),(x_4, y_4)=(1,0) is not accepted, as the vertices are in clockwise order. ### INCORRECT PROGRAM x1, y1, x2, y2 = map (int, input (). split ()) x3 = x2 + (y2 - y1) y3 = y2 - (x2 - x1) x4 = x1 + (y2 - y1) y4 = y1 - (x2 - x1) print (x3, y3, x4, y4) ### ERROR MESSAGE === Input === 0 0 0 1 === Program Output === 1 1 1 0 === Expected Output === -1 1 -1 0 ### FEEDBACK The issue with the code is that it doesn ’ t consider the counter - clockwise order of the vertices. To fix this, we need to swap the signs of (y2 - y1) and (x2 - x1) in the calculations. ### COMMENT Swapping the listed signs is a concrete suggestion of a way to fix the code. Since the overall structure of the code would remain the same, we count this as a minor change. #### D.2.2 Human: Example ⬇ ### SPECIFICATION Given is a string S representing the day of the week today. S is SUN, MON, TUE, WED, THU, FRI, or SAT, for Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday, respectively. After how many days is the next Sunday (tomorrow or later)? ----- Constraints ----- - S is SUN, MON, TUE, WED, THU, FRI, or SAT. ----- Input ----- Input is given from Standard Input in the following format: S ----- Output ----- Print the number of days before the next Sunday. ----- Sample Input ----- SAT ----- Sample Output ----- 1 It is Saturday today, and tomorrow will be Sunday. ### INCORRECT PROGRAM S = input () days = [’ SUN ’, ’ MON ’, ’ TUE ’, ’ WED ’, ’ THU ’, ’ FRI ’, ’ SAT ’] print ((7 - days. index (S)) % 7) ### ERROR MESSAGE === Input === SUN === Program Output === 0 === Expected Output === 7 ### FEEDBACK The logic is incorrect. There should be no modulo operator. ### COMMENT Suggesting that the modulo operator should be removed is a relatively small, but explicit, change. ### D.3 Category (c): feedback explicitly suggests a large change to the code #### D.3.1 GPT-4: Example ⬇ ### SPECIFICATION Takahashi is about to assemble a character figure, consisting of N parts called Part 1, Part 2, ..., Part N and N -1 connecting components. Parts are distinguishable, but connecting components are not. Part i has d_i holes, called Hole 1, Hole 2, ..., Hole d_i, into which a connecting component can be inserted. These holes in the parts are distinguishable. Each connecting component will be inserted into two holes in different parts, connecting these two parts. It is impossible to insert multiple connecting components into a hole. The character figure is said to be complete when it has the following properties: - All of the N -1 components are used to connect parts. - Consider a graph with N vertices corresponding to the parts and N -1 undirected edges corresponding to the pairs of vertices connected by a connecting component. Then, this graph is connected. Two ways A and B to make the figure complete are considered the same when the following is satisfied: for every pair of holes, A uses a connecting component to connect these holes if and only if B uses one to connect them. Find the number of ways to make the figure complete. Since the answer can be enormous, find the count modulo 998244353. ----- Constraints ----- - All values in input are integers. - 2 \ leq N \ leq 2 \ times 10^5 - 1 \ leq d_i < 998244353 ----- Input ----- Input is given from Standard Input in the following format: N d_1 d_2 \ cdots d_N ----- Output ----- Print the answer. ----- Sample Input ----- 3 1 1 3 ----- Sample Output ----- 6 One way to make the figure complete is to connect Hole 1 in Part 1 and Hole 3 in Part 3 and then connect Hole 1 in Part 2 and Hole 1 in Part 3. ### INCORRECT PROGRAM def main (): N = int (input ()) d = list (map (int, input (). split ())) MOD = 998244353 fact = [1] * (N +1) for i in range (1, N +1): fact [i] = fact [i -1] * i % MOD ans = 0 for ki in range (N): ans += d [ki] * fact [ki] % MOD * fact [N - ki -1] % MOD ans %= MOD ans = ans * fact [N -1] % MOD print (ans) main () ### ERROR MESSAGE === Input === 3 1 1 3 === Program Output === 18 === Expected Output === 6 ### FEEDBACK The following is a concise explanation of the issue: The code above calculates the total number of ways to connect the parts, but it does not ensure that each connecting component is used only once. This results in overcounting the number of ways to make the figure complete. To fix the issue, we need to ensure that each connecting component is used exactly once. ### COMMENT The feedback suggests changing the code so that each connecting component is used exactly once, which does not seem to be taken into account in the current approach. Changing the code to satisfy this part of the specification seems to require a major rewrite. #### D.3.2 Human: Example ⬇ ### SPECIFICATION Oh, New Year. The time to gather all your friends and reflect on the heartwarming events of the past year... $n$ friends live in a city which can be represented as a number line. The $i$ - th friend lives in a house with an integer coordinate $x_i$. The $i$ - th friend can come celebrate the New Year to the house with coordinate $x_i -1 $, $x_i +1 $ or stay at $x_i$. Each friend is allowed to move no more than once. For all friends $1 \ le x_i \ le n$ holds, however, they can come to houses with coordinates $0$ and $n +1 $ (if their houses are at $1$ or $n$, respectively). For example, let the initial positions be $x = [1, 2, 4, 4] $. The final ones then can be $ [1, 3, 3, 4] $, $ [0, 2, 3, 3] $, $ [2, 2, 5, 5] $, $ [2, 1, 3, 5] $ and so on. The number of occupied houses is the number of distinct positions among the final ones. So all friends choose the moves they want to perform. After that the number of occupied houses is calculated. What is the minimum and the maximum number of occupied houses can there be? ----- Input ----- The first line contains a single integer $n$ ($1 \ le n \ le 2 \ cdot 10^5 $) - the number of friends. The second line contains $n$ integers $x_1, x_2, \ dots, x_n$ ($1 \ le x_i \ le n$) - the coordinates of the houses of the friends. ----- Output ----- Print two integers - the minimum and the maximum possible number of occupied houses after all moves are performed. ----- Examples ----- Input 4 1 2 4 4 Output 2 4 Input 9 1 1 8 8 8 4 4 4 4 Output 3 8 Input 7 4 3 7 1 4 3 3 Output 3 6 ----- Note ----- In the first example friends can go to $ [2, 2, 3, 3] $. So friend $1$ goes to $x_1 +1 $, friend $2$ stays at his house $x_2$, friend $3$ goes to $x_3 -1 $ and friend $4$ goes to $x_4 -1 $. $ [1, 1, 3, 3] $, $ [2, 2, 3, 3] $ or $ [2, 2, 4, 4] $ are also all valid options to obtain $2$ occupied houses. For the maximum number of occupied houses friends can go to $ [1, 2, 3, 4] $ or to $ [0, 2, 4, 5] $, for example. ### INCORRECT PROGRAM from collections import Counter def main (): n = int (input ()) x = list (map (int, input (). split ())) cnt = Counter (x) max_houses = 0 for pos in range (1, n + 1): if cnt [pos]: max_houses += 1 occupied = [0] * (n + 2) for pos in x: if not occupied [pos - 1]: occupied [pos - 1] = 1 elif not occupied [pos]: occupied [pos] = 1 elif not occupied [pos + 1]: occupied [pos + 1] = 1 min_houses = sum (occupied) print (min_houses, max_houses) main () ### ERROR MESSAGE === Input === 4 1 2 4 4 === Program Output === 4 3 === Expected Output === 2 4 ### FEEDBACK The code calculates both the minimum and maximum count of houses incorrectly. The correct solution requires conducting a tree search to determine the true maximum and minimum. This can be further optimized by first sorting the list of occupied houses and using a sliding window to process independent segments of the number line. ### COMMENT The feedback suggests conducting a tree search to determine the max and min, as well as a way to optimize this search. These constitute major changes to the program as it is currently written. ### D.4 Category (d): Feedback contains blocks of pseudocode or Python code #### D.4.1 GPT-4: Example GPT-4’s feedback never contains blocks of Python per our experiment design, in which the code block is stripped (Section 4.3). We find that GPT-4 never utilizes blocks of pseudocode, either. #### D.4.2 Human: Example ⬇ ### SPECIFICATION Given is a string S representing the day of the week today. S is SUN, MON, TUE, WED, THU, FRI, or SAT, for Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday, respectively. After how many days is the next Sunday (tomorrow or later)? ----- Constraints ----- - S is SUN, MON, TUE, WED, THU, FRI, or SAT. ----- Input ----- Input is given from Standard Input in the following format: S ----- Output ----- Print the number of days before the next Sunday. ----- Sample Input ----- SAT ----- Sample Output ----- 1 It is Saturday today, and tomorrow will be Sunday. ### INCORRECT PROGRAM day = input () days = [’ SUN ’, ’ MON ’, ’ TUE ’, ’ WED ’, ’ THU ’, ’ FRI ’, ’ SAT ’] index = days. index (day) result = (7 - index) % 7 print (result) ### ERROR MESSAGE === Input === SUN === Program Output === 0 === Expected Output === 7 ### FEEDBACK before returning the result, we should just check to see if result ==0. so we just need to add: if result == 0: result = 7 ### COMMENT The feedback contains a block of Python code that the model can simply copy in order to fix the program. ### D.5 Category (e): feedback which expresses uncertainty #### D.5.1 GPT-4: Example In the $20\cdot 2\cdot 2=80$ examples we study, we do not find that GPT-4 ever expresses uncertainty. #### D.5.2 Human: Example ⬇ ### SPECIFICATION Two kingdoms had been at war for a long time, until the emperor intervened to bring an end to the conflict. The territory in question comprises an $M$ by $N$ rectangular grid. At the emperor ’ s insistence, the two kings have withdrawn their troops until no two opposing troops are in adjacent squares of the map (adjacent being horizontal or vertical - diagonal is not considered). The emperor proposes to designate certain squares of the map as neutral territory. Neither king will be allowed to move troops into those squares, and the emperor ’ s own forces will patrol them to be sure that both kings observe these rules. The emperor is frugal and does not want to commit more soldiers to this effort than absolutely necessary. His generals have marked each square of the map with the number of soldiers required to secure that square. What remains is to choose which of those squares should be patrolled. Write a program to determine the minimum number of soldiers that the emperor will need to be deploy to guarantee that the troops of one kingdom cannot move, in one or more steps, into squares occupied by the troops of the second kingdom (moving horizontally or vertically) without encountering the emperor ’ s own soldiers. ----- Input ----- Input begins with a line containing $2$ integers, $w$ and $h$, denoting the width and height of the map, where $1 \ leq w, h \ leq 40 $. This is followed by $h$ lines. Each line contains $w$ characters, left justified. These characters will be ’ A ’ or ’ B ’, designating a position held by king A or king B, or a single numeric digit, designating a currently unoccupied position that can be secured by the use of that number of soldiers. For example, a ’2’ would indicate that two soldiers must be deployed to that square to secure it against passage of other troops. A ’0’ indicates terrain that is impassible - the emperor need not commit soldiers there because the kingdom troops cannot pass through that square. No ’ A ’ will be adjacent, horizontally or vertically, to any ’ B ’. There will be at least one ’ A ’ and one ’ B ’ in the input. ----- Output ----- Print a single line containing an integer denoting the minimum number of soldiers that the emperor must deploy to guarantee that there is no open path between any ’ A ’ position and any ’ B ’ position, using any combination of horizontal or vertical moves. ----- Examples ----- Sample Input: 8 5 A11111AA AA7B111A 111 BB111 11 BBB111 11 BBB11B Sample Output: 13 ### INCORRECT PROGRAM def main (): w, h = map (int, input (). split ()) grid = [input () for _ in range (h)] def bfs (x, y, z): dist = [[float (" inf ")] * w for _ in range (h)] dist [x][y] = 0 q = [(x, y)] for x, y in q: for dx, dy in [(-1, 0), (1, 0), (0, -1), (0, 1)]: nx, ny = x + dx, y + dy if 0 <= nx < h and 0 <= ny < w and dist [nx][ny] == float (" inf "): if grid [nx][ny] == z: dist [nx][ny] = dist [x][y] q. append ((nx, ny)) if "0" <= grid [nx][ny] <= "9": dist [nx][ny] = dist [x][y] + int (grid [nx][ny]) q. append ((nx, ny)) return dist ans = float (" inf ") for i in range (h): for j in range (w): if grid [i][j] == " A ": ans = min (ans, min (x for row in bfs (i, j, " B ") for x in row)) print (ans) main () ### ERROR MESSAGE === Input === 8 5 A11111AA AA7B111A 111 BB111 11 BBB111 11 BBB11B === Program Output === 0 === Expected Output === 13 ### FEEDBACK This code appears to be finding the minimum " distance " between an A position and a B position, where distance is measured in the number of soldiers required to secure the intermediate positions. This isn ’ t really addressing the question at all, because even occupying the positions along some path from a particular A -> B won ’ t necessarily block the kings from reaching each other from those positions through a different, longer path. You probably need some sort of min - cut algorithm to divide the graph into two connected components, one each for A and B nodes. ### COMMENT The feedback expresses mild uncertainty in two aspects. First, the user indicates that they are not completely certain in their understanding of the code ’ s current behaviour by using the phrase " appears to be ". Then, they express uncertainty in their suggestion for what to do instead, saying that one * probably * needs some sort of min - cut algorithm. ## Appendix E Prompts In this appendix, we describe the prompting structure used for our experiments. All of our experiments use one-shot prompting, in which a single example is given in the prompt before the desired task. For initial code generation (the first sample from $M_{P}$ ), we use different prompts for the two types of tasks in APPS: call-based tasks, in which the desired program should take the input as a parameter to a function and return the output in the function’s return statement; and stdio-based tasks, in which inputs should be read from stdin and outputs should be written to stdout. These prompts are shown in Listing 1 and 2, respectively. The example tasks and programs were taken from APPS’ training set. For feedback samples (i.e., samples from $M_{F}$ ), we use the prompt in Listing 3. This prompt contains an example in which the user provides the textual specification, the incorrect program and the error message, and the assistant generates feedback. Similarly, for repair samples (i.e., samples from $M_{P}$ which follow $M_{F}$ ) we use the prompt in Listing 4, in which the user also supplies the feedback, and the assistant returns only the fixed version of the program. Finally, for joint feedback-repair samples (i.e., when sampling $(f,r)\sim M_{P}$ ), we use the prompt in Listing 6. This prompt combines the prompts from Listing 4 and 5 into one prompt, in which the assistant returns both the feedback and the fixed program. In all of these prompts, the specification used was taken from APPS’ training set, while the programs and the feedback were constructed manually. Listing 1: Code generation prompt for call-based tasks. ⬇ ===== system ===== You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. You will NOT return anything except for the program. Put your fixed program within code delimiters, for example: ‘‘‘ python # YOUR CODE HERE ‘‘‘. ===== user ===== ### QUESTION A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward. Examples of numerical palindromes are: ‘2332, 110011, 54322345‘ For a given number ‘‘‘ num ‘‘‘, write a function which returns an array of all the numerical palindromes contained within each number. The array should be sorted in ascending order and any duplicates should be removed. In this kata, single digit numbers and numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are ** NOT ** considered valid numerical palindromes. If ‘ num ‘ contains no valid palindromes, return ‘" No palindromes found "‘. Otherwise, return ‘" Not valid "‘ if the input is not an integer or is less than ‘0‘. ## Examples ‘‘‘ palindrome (1221) => [22, 1221] palindrome (34322122) => [22, 212, 343, 22122] palindrome (1001331) => [33, 1001, 1331] palindrome (1294) => " No palindromes found " palindrome ("1221") => " Not valid " ‘‘‘ --- ### Other Kata in this Series: Numerical Palindrome #1 Numerical Palindrome #1.5 Numerical Palindrome #2 Numerical Palindrome #3 Numerical Palindrome #3.5 Numerical Palindrome #4 Numerical Palindrome #5 ### Use Call - Based Format ===== assistant ===== ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): if ch == ’0’: continue for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ Listing 2: Code generation prompt for stdio-based tasks. ⬇ ===== system ===== You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. You will NOT return anything except for the program. Put your fixed program within code delimiters, for example: ‘‘‘ python # YOUR CODE HERE ‘‘‘. ===== user ===== ### QUESTION Polycarp has $n$ different binary words. A word called binary if it contains only characters ’0’ and ’1’. For example, these words are binary: "0001", "11", "0" and "0011100". Polycarp wants to offer his set of $n$ binary words to play a game " words ". In this game, players name words and each next word (starting from the second) must start with the last character of the previous word. The first word can be any. For example, these sequence of words can be named during the game: "0101", "1", "10", "00", "00001". Word reversal is the operation of reversing the order of the characters. For example, the word "0111" after the reversal becomes "1110", the word "11010" after the reversal becomes "01011". Probably, Polycarp has such a set of words that there is no way to put them in the order correspondent to the game rules. In this situation, he wants to reverse some words from his set so that: the final set of $n$ words still contains different words (i. e. all words are unique); there is a way to put all words of the final set of words in the order so that the final sequence of $n$ words is consistent with the game rules. Polycarp wants to reverse minimal number of words. Please, help him. ----- Input ----- The first line of the input contains one integer $t$ ($1 \ le t \ le 10\^4 $) - the number of test cases in the input. Then $t$ test cases follow. The first line of a test case contains one integer $n$ ($1 \ le n \ le 2\ cdot10 ^5 $) - the number of words in the Polycarp ’ s set. Next $n$ lines contain these words. All of $n$ words aren ’ t empty and contains only characters ’0’ and ’1’. The sum of word lengths doesn ’ t exceed $4 \ cdot10 ^6 $. All words are different. Guaranteed, that the sum of $n$ for all test cases in the input doesn ’ t exceed $2 \ cdot10 ^5 $. Also, guaranteed that the sum of word lengths for all test cases in the input doesn ’ t exceed $4 \ cdot10 ^6 $. ----- Output ----- Print answer for all of $t$ test cases in the order they appear. If there is no answer for the test case, print -1. Otherwise, the first line of the output should contain $k$ ($0 \ le k \ le n$) - the minimal number of words in the set which should be reversed. The second line of the output should contain $k$ distinct integers - the indexes of the words in the set which should be reversed. Words are numerated from $1$ to $n$ in the order they appear. If $k =0 $ you can skip this line (or you can print an empty line). If there are many answers you can print any of them. ----- Example ----- Input 4 4 0001 1000 0011 0111 3 010 101 0 2 00000 00001 4 01 001 0001 00001 Output 1 3 -1 0 2 1 2 ### Use Standard Input Format (read inputs with ‘ input ()‘, write results with ‘ print ()‘) ===== assistant ===== ‘‘‘ python for _ in range (int (input ())): n = int (input ()) mass = [] zo = 0 oz = 0 zz = 0 oo = 0 ozs = [] zos = [] ozss = set () zoss = set () for j in range (n): k = input () mass. append (k) if k [0] == ’0’ and k [-1] == ’1’: zoss. add (k) zos. append (j + 1) zo += 1 elif k [0] == ’1’ and k [-1] == ’0’: ozss. add (k) ozs. append (j + 1) oz += 1 elif k [0] == ’0’ and k [-1] == ’0’: zz += 1 else: oo += 1 if zz and oo and not oz and not zo: print (-1) continue else: if zo > oz: print ((zo - oz) // 2) ans = [] need = (zo - oz) // 2 i = 0 while need: zzz = mass [zos [i] - 1][len (mass [zos [i] - 1]) - 1:: -1] if zzz not in ozss: ans. append (zos [i]) need -= 1 i += 1 print (* ans) else: print ((oz - zo) // 2) ans = [] need = (oz - zo) // 2 i = 0 while need: zzz = mass [ozs [i] - 1][len (mass [ozs [i] - 1]) - 1:: -1] if zzz not in zoss: ans. append (ozs [i]) need -= 1 i += 1 print (* ans) ‘‘‘ Listing 3: Feedback-only prompt. ⬇ ===== system ===== You are a helpful programming assistant and an expert Python programmer. You are helping a user debug a program. The user has written some code, but it has some errors and is not passing the tests. You will help the user by giving a concise (at most 2-3 sentences) textual explanation of what is wrong with the code. You will * not * generate any code, because the user wants to fix the code themselves. ===== user ===== ### QUESTION A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward. Examples of numerical palindromes are: ‘2332, 110011, 54322345‘ For a given number ‘‘‘ num ‘‘‘, write a function which returns an array of all the numerical palindromes contained within each number. The array should be sorted in ascending order and any duplicates should be removed. In this kata, single digit numbers and numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are ** NOT ** considered valid numerical palindromes. If ‘ num ‘ contains no valid palindromes, return ‘" No palindromes found "‘. Otherwise, return ‘" Not valid "‘ if the input is not an integer or is less than ‘0‘. ## Examples ‘‘‘ palindrome (1221) => [22, 1221] palindrome (34322122) => [22, 212, 343, 22122] palindrome (1001331) => [33, 1001, 1331] palindrome (1294) => " No palindromes found " palindrome ("1221") => " Not valid " ‘‘‘ --- ### Other Kata in this Series: Numerical Palindrome #1 Numerical Palindrome #1.5 Numerical Palindrome #2 Numerical Palindrome #3 Numerical Palindrome #3.5 Numerical Palindrome #4 Numerical Palindrome #5 ### Use Call - Based Format ### INCORRECT PYTHON CODE ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ The code above is wrong and contains a bug. Given input "1001331" the output was "[’0’, ’33’, ’1001’, ’1331’]" but the expected output was "[’33’, ’1001’, ’1331’]". ===== assistant ===== The following is a concise explanation of the issue: The problem description states that numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are NOT considered valid numerical palindromes. However, the code above does not take this into account and therefore returns ‘00‘ as a valid palindrome. This can be fixed by checking if the first or last character is ‘0‘ before adding the string to the set of palindromes. Listing 4: Repair-only prompt. ⬇ ===== system ===== You are a helpful programming assistant and an expert Python programmer. You are helping a user write a program to solve a problem. The user has written some code, but it has some errors and is not passing the tests. The user has spent some time debugging the program and will provide you with a concise textual explanation of what is wrong with the code. You will use this explanation to generate a fixed version of the program. Put your fixed program within code delimiters, for example: ‘‘‘ python # YOUR CODE HERE ‘‘‘. ===== user ===== ### QUESTION A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward. Examples of numerical palindromes are: ‘2332, 110011, 54322345‘ For a given number ‘‘‘ num ‘‘‘, write a function which returns an array of all the numerical palindromes contained within each number. The array should be sorted in ascending order and any duplicates should be removed. In this kata, single digit numbers and numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are ** NOT ** considered valid numerical palindromes. If ‘ num ‘ contains no valid palindromes, return ‘" No palindromes found "‘. Otherwise, return ‘" Not valid "‘ if the input is not an integer or is less than ‘0‘. ## Examples ‘‘‘ palindrome (1221) => [22, 1221] palindrome (34322122) => [22, 212, 343, 22122] palindrome (1001331) => [33, 1001, 1331] palindrome (1294) => " No palindromes found " palindrome ("1221") => " Not valid " ‘‘‘ --- ### Other Kata in this Series: Numerical Palindrome #1 Numerical Palindrome #1.5 Numerical Palindrome #2 Numerical Palindrome #3 Numerical Palindrome #3.5 Numerical Palindrome #4 Numerical Palindrome #5 ### Use Call - Based Format ### INCORRECT PYTHON CODE ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ The code above is wrong and contains a bug. Given input "1001331" the output was "[’0’, ’33’, ’1001’, ’1331’]" but the expected output was "[’33’, ’1001’, ’1331’]". The following is a concise explanation of the issue: The problem description states that numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are NOT considered valid numerical palindromes. However, the code above does not take this into account and therefore returns ‘00‘ as a valid palindrome. This can be fixed by checking if the first or last character is ‘0‘ before adding the string to the set of palindromes. ===== assistant ===== ### FIXED PYTHON CODE ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): if ch == ’0’: continue for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ Listing 5: Joint feedback-repair prompt. ⬇ ===== system ===== You are a helpful programming assistant and an expert Python programmer. You are helping a user write a program to solve a problem. The user has written some code, but it has some errors and is not passing the tests. You will help the user by first giving a concise (at most 2-3 sentences) textual explanation of what is wrong with the code. After you have pointed out what is wrong with the code, you will then generate a fixed version of the program. Put your fixed program within code delimiters, for example: ‘‘‘ python # YOUR CODE HERE ‘‘‘. ===== user ===== ### QUESTION A palindrome is a word, phrase, number, or other sequence of characters which reads the same backward as forward. Examples of numerical palindromes are: ‘2332, 110011, 54322345‘ For a given number ‘‘‘ num ‘‘‘, write a function which returns an array of all the numerical palindromes contained within each number. The array should be sorted in ascending order and any duplicates should be removed. In this kata, single digit numbers and numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are ** NOT ** considered valid numerical palindromes. If ‘ num ‘ contains no valid palindromes, return ‘" No palindromes found "‘. Otherwise, return ‘" Not valid "‘ if the input is not an integer or is less than ‘0‘. ## Examples ‘‘‘ palindrome (1221) => [22, 1221] palindrome (34322122) => [22, 212, 343, 22122] palindrome (1001331) => [33, 1001, 1331] palindrome (1294) => " No palindromes found " palindrome ("1221") => " Not valid " ‘‘‘ --- ### Other Kata in this Series: Numerical Palindrome #1 Numerical Palindrome #1.5 Numerical Palindrome #2 Numerical Palindrome #3 Numerical Palindrome #3.5 Numerical Palindrome #4 Numerical Palindrome #5 ### Use Call - Based Format ### INCORRECT PYTHON CODE ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ The code above is wrong and contains a bug. Given input "1001331" the output was "[’0’, ’33’, ’1001’, ’1331’]" but the expected output was "[’33’, ’1001’, ’1331’]". ===== assistant ===== The following is a concise explanation of the issue: The problem description states that numbers which start or end with zeros (such as ‘010‘ and ‘00‘) are NOT considered valid numerical palindromes. However, the code above does not take this into account and therefore returns ‘00‘ as a valid palindrome. This can be fixed by checking if the first or last character is ‘0‘ before adding the string to the set of palindromes. # The code below is the correct version of the code above, where the issue has been fixed: ### FIXED PYTHON CODE ‘‘‘ python def is_pal (s): return s == s [::-1] def palindrome (num): if not isinstance (num, int) or num < 0: return ’ Not valid ’ s = str (num) pals = set () for i, ch in enumerate (s): if ch == ’0’: continue for j in range (i + 2, len (s) + 1): test = s [i: j] if is_pal (test): pals. add (test) return sorted (int (x) for x in pals) or ’ No palindromes found ’ ‘‘‘ ## Appendix F Dataset: APPS Tasks Used For Our Evaluations These tasks were randomly sampled from APPS’ test set. To avoid distribution shift, we sampled according to the relative frequency of difficulties in the full dataset. We report the resulting list of tasks to aid reproducibility. | introductory | ’4004’, ’4058’, ’4063’, ’4065’, ’4100’, ’4108’, ’4117’, ’4155’, ’4164’, ’4182’, ’4193’, ’4195’, ’4211’, ’4217’, ’4241’, ’4249’, ’4270’, ’4275’, ’4281’, ’4293’, ’4333’, ’4347’, ’4350’, ’4356’, ’4409’, ’4426’, ’4431’, ’4450’, ’4465’, ’4484’, ’4498’, ’4505’, ’4507’, ’4514’, ’4544’, ’4553’, ’4586’, ’4610’, ’4662’, ’4663’, ’4667’, ’4677’, ’4681’, ’4704’, ’4716’, ’4741’, ’4750’, ’4786’, ’4787’, ’4801’, ’4855’, ’4862’, ’4864’, ’4870’, ’4873’, ’4890’, ’4897’, ’4952’, ’4966’, ’4984’ | | --- | --- | | interview | ’0004’, ’0013’, ’0033’, ’0056’, ’0073’, ’0074’, ’0089’, ’0091’, ’0124’, ’0131’, ’0139’, ’0162’, ’0166’, ’0183’, ’0186’, ’0191’, ’0199’, ’0205’, ’0249’, ’0253’, ’0268’, ’0274’, ’0300’, ’0304’, ’0341’, ’0342’, ’0413’, ’0427’, ’0434’, ’0466’, ’0467’, ’0496’, ’0501’, ’0511’, ’0537’, ’0564’, ’0571’, ’0575’, ’0579’, ’0592’, ’0597’, ’0626’, ’0637’, ’0676’, ’0704’, ’0728’, ’0757’, ’0765’, ’0788’, ’0794’, ’0804’, ’0805’, ’0811’, ’0829’, ’0879’, ’0904’, ’0915’, ’0925’, ’0937’, ’0948’, ’0954’, ’0955’, ’0972’, ’0985’, ’0989’, ’1018’, ’1019’, ’1033’, ’1046’, ’1076’, ’1133’, ’1140’, ’1141’, ’1145’, ’1146’, ’1149’, ’1168’, ’1185’, ’1221’, ’1232’, ’1256’, ’1257’, ’1280’, ’1285’, ’1299’, ’1317’, ’1347’, ’1380’, ’1392’, ’1393’, ’1418’, ’1444’, ’1448’, ’1458’, ’1489’, ’1517’, ’1533’, ’1573’, ’1635’, ’1653’, ’1668’, ’1672’, ’1721’, ’1736’, ’1748’, ’1756’, ’1759’, ’1775’, ’1777’, ’1825’, ’1850’, ’1863’, ’1865’, ’1870’, ’1875’, ’1906’, ’1917’, ’1956’, ’1962’, ’1967’, ’1976’, ’2024’, ’2049’, ’2062’, ’2092’, ’2093’, ’2097’, ’2106’, ’2172’, ’2176’, ’2203’, ’2231’, ’2246’, ’2264’, ’2266’, ’2295’, ’2326’, ’2328’, ’2332’, ’2342’, ’2361’, ’2369’, ’2407’, ’2408’, ’2418’, ’2455’, ’2463’, ’2511’, ’2515’, ’2516’, ’2535’, ’2585’, ’2623’, ’2629’, ’2642’, ’2651’, ’2662’, ’2668’, ’2673’, ’2698’, ’2701’, ’2709’, ’2735’, ’2742’, ’2752’, ’2759’, ’2765’, ’2787’, ’2802’, ’2832’, ’2835’, ’2844’, ’2858’, ’2885’, ’2897’, ’2923’, ’2932’, ’2945’, ’2973’, ’2980’ | | competition | ’3017’, ’3019’, ’3054’, ’3062’, ’3063’, ’3066’, ’3070’, ’3077’, ’3083’, ’3097’, ’3117’, ’3135’, ’3161’, ’3186’, ’3209’, ’3220’, ’3286’, ’3287’, ’3323’, ’3335’, ’3353’, ’3355’, ’3371’, ’3375’, ’3376’, ’3388’, ’3404’, ’3411’, ’3433’, ’3441’, ’3445’, ’3470’, ’3481’, ’3484’, ’3548’, ’3557’, ’3605’, ’3609’, ’3634’, ’3635’, ’3671’, ’3679’, ’3709’, ’3754’, ’3769’, ’3792’, ’3798’, ’3799’, ’3804’, ’3810’, ’3819’, ’3823’, ’3836’, ’3843’, ’3849’, ’3876’, ’3913’, ’3934’, ’3972’, ’3974’ | ## Appendix G More Examples of Feedback from GPT-4 and our Human Participants In this appendix, we give five more examples from the study in Section 4.3, so that the keen reader may themself compare and contrast the feedback generated by GPT-4 and by our human participants. Each listing (6-10) contains a textual specification, an incorrect program, an error message, both examples of GPT-4 feedback which were shown to the participants assigned to this task, and the responses from the participants. For each piece of feedback, we also list the number of resulting repaired programs which passed all the tests (c.f. the full results table in Appendix C). Listing 6: Task 2106, Program A. ⬇ ### SPECIFICATION There are n cities in the country where the Old Peykan lives. These cities are located on a straight line, we ’ ll denote them from left to right as c_1, c_2, ..., c_ {n}. The Old Peykan wants to travel from city c_1 to c_ {n} using roads. There are (n - 1) one way roads, the i - th road goes from city c_ {i} to city c_ {i} + 1 and is d_ {i} kilometers long. The Old Peykan travels 1 kilometer in 1 hour and consumes 1 liter of fuel during this time. Each city c_ {i} (except for the last city c_ {n}) has a supply of s_ {i} liters of fuel which immediately transfers to the Old Peykan if it passes the city or stays in it. This supply refreshes instantly k hours after it transfers. The Old Peykan can stay in a city for a while and fill its fuel tank many times. Initially (at time zero) the Old Peykan is at city c_1 and s_1 liters of fuel is transferred to it ’ s empty tank from c_1 ’ s supply. The Old Peykan ’ s fuel tank capacity is unlimited. Old Peykan can not continue its travel if its tank is emptied strictly between two cities. Find the minimum time the Old Peykan needs to reach city c_ {n}. ----- Input ----- The first line of the input contains two space - separated integers m and k (1 <= m, k <= 1000). The value m specifies the number of roads between cities which is equal to n - 1. The next line contains m space - separated integers d_1, d_2, ..., d_ {m} (1 <= d_ {i} <= 1000) and the following line contains m space - separated integers s_1, s_2, ..., s_ {m} (1 <= s_ {i} <= 1000). ----- Output ----- In the only line of the output print a single integer - the minimum time required for The Old Peykan to reach city c_ {n} from city c_1. ----- Examples ----- Input 4 6 1 2 5 2 2 3 3 4 Output 10 Input 2 3 5 6 5 5 Output 14 ### INCORRECT PROGRAM def main (): m, k = map (int, input (). split ()) ds = list (map (int, input (). split ())) ss = list (map (int, input (). split ())) time = 0 fuel = ss [0] min_time = 0 max_s = ss [0] for i in range (m): fuel -= ds [i] max_s = max (max_s, ss [i]) while fuel < 0: time += k fuel += max_s time += ds [i] print (time) main () ### ERROR MESSAGE === Input === 4 6 1 2 5 2 2 3 3 4 === Program Output === 28 === Expected Output === 10 ### GPT -4 FEEDBACK #1 The issue with the code is that it does not consider the time spent in the current city before moving to the next city, resulting in an overestimation of the minimum time required. This can be fixed by updating the time spent in the current city before calculating the fuel used and accounting for the time it takes to travel to the next city. # Number of passing repairs: 7/25 ### GPT -4 FEEDBACK #2 The following is a concise explanation of the issue: The code incorrectly calculates the waiting time at each city. It should minimize the waiting time by considering the maximum fuel supply that can be collected during the waiting time. The code needs to be updated to account for this. # Number of passing repairs: 10/25 ### PARTICIPANT FEEDBACK #1 The program doesn ’ t add the fuel for passing through cities, only if it needs to actually stay in the city to refuel. Whenever it passes through a city, it should add ss [i] to the fuel. # Number of passing repairs: 10/25 ### PARTICIPANT FEEDBACK #2 The code is incorrect because it doesn ’ t take into account the fuel at each city that is immediately transferred after entering the city (aside for the fuel received at the first city). As a result, this program overestimates the time needed, because it assumes that the Old Peykan always has to wait for a refill (besides the fuel they are given in the first city). # Number of passing repairs: 0/25 Listing 7: Task 3070, Program B. ⬇ ### SPECIFICATION In the free - market, ruthlessly capitalist world of train fares, only one thing matters: incentives. Train companies are incentivised with bonuses for high throughput, successful journeys, and customer satisfaction. Conversely, the companies are disincentivised from failure via mandatory refunds for customers delayed by $30$ minutes or more. Being a ruthless capitalist yourself, you have decided to take advantage of this generous delay compensation provision. The refund is awarded provided that no matter the combination of trains you had taken (provided they followed the same route of stations as planned), you would still be unable to reach your destination in strictly less time than $30$ minutes (or $1800$ seconds), of the time you would have arrived assuming your booked journey was exactly on time. Armed with your printout of the day ’ s delays, and the original timetable, you must ask yourself only one question: what is the earliest time you can book a train for from station $1$, in order to earn this restitutive reward? ----- Input ----- - One line containing two integers: $N$ ($1 \ le N \ le 100 $), the number of stations, and $M$ ($1 \ le M \ le 10^5 $), the number of scheduled trains. - The next $M$ lines each contain 4 integers: - $X$, the starting station ($1 \ le X \ le N -1 $), - $S$ and $T$ ($0 \ le S \ le T < 86400 $), the planned departure and arrival times in seconds, - and $L$ ($0 \ le L < 86400 $), the duration by which the train ’ s departure and arrival times are delayed. Stations are numbered from $1$ to $N$ in the order you will visit them. Each train goes between stations $X$ and $X +1 $. It is possible to change between trains instantanesouly. ----- Output ----- - One line containing one integer: the start time of the earliest train journey you could book in order to earn your compensation, or impossible if no such journey is possible. ----- Examples ----- Sample Input 1: 2 3 1 1800 9000 1800 1 2000 9200 1600 1 2200 9400 1400 Sample Output 1: 1800 Sample Input 2: 2 2 1 1800 3600 1800 1 1900 3600 1600 Sample Output 2: impossible ### INCORRECT PROGRAM def main (): N, M = map (int, input (). split ()) train_data = [tuple (map (int, input (). split ())) for _ in range (M)] train_data. sort (key = lambda x: (x [0], x [1])) times = [1 e9] * (N + 1) times [1] = 0 for X, S, T, L in train_data: if times [X] <= S: times [X + 1] = min (times [X + 1], T + L) if times [N] >= 1800: print (int (times [1])) else: print (" impossible ") main () ### ERROR MESSAGE === Input === 2 3 1 1800 9000 1800 1 2000 9200 1600 1 2200 9400 1400 === Program Output === 0 === Expected Output === 1800 ### GPT -4 FEEDBACK #1 The issue with the code is that it prints ‘ times [1]‘ instead of the earliest possible train start time. The code needs to get the minimum start time from the train_data list that has a valid delay for compensation. # Number of passing repairs: 3/25 ### GPT -4 FEEDBACK #2 The issue with the code is that it directly prints the value of ‘ times [1]‘, which is initialized to ‘0‘ and never updated. The correct output should be the starting time of the earliest train journey that satisfies the condition. To fix this, we need to track the earliest possible start time and update it if a valid train journey is found. # Number of passing repairs: 0/25 ### PARTICIPANT FEEDBACK #1 This code is clearly wrong as times [1] is initialized to 0 then never updated and it is returned as the answer. Also, in the sorting line ‘ int (x [0])‘ should be used in place of ‘ x [0]‘ and likewise for ‘ int (x [1])‘ in place of ‘ x1 ‘ because we want numerical order sorting not string order sorting. The goal in this problem is calculate for each station what the earliest - arriving undelayed path to the station is and what the earliest - arriving delayed path to the station is, take the difference between the two, and see if it results in a total delay of >= 30 minutes (then to return the earliest departure from station 1 for this path. Given this, first the current code based around ‘ times ‘ can remain - this is the delayed time. However, the if - statement within the for - loop should be ‘<= S + L ‘ since the departure time is also delayed. Then ‘ undelayed_times ‘ should be tracked as well, updated in the foor loop when ‘ undelayed_times [X] <= S ‘ and set to a min () between the current undelayed time an ‘ T ‘ (not T + L). Finally the if - statement for time printing can use the difference between the delayed and undelayed times and see if any () are >= 1800. Finally we need to print the earliest arriving train for that path # Number of passing repairs: 5/25 ### PARTICIPANT FEEDBACK #2 One of the main issues is that the code prints ’ times [1]’, which is set to 0 and never updated. However, there are also some larger issues with the code. First, instead of checking if you reach your destination within 30 minutes of the expected time, it checks if you reach your destination in 30 minutes. To fix this, the program would need to keep track of the time you ’ d reach your destination if there were not delays, which it currently doesn ’ t. Second, instead of printing times [1], it should be keeping track of the start time of the train that leads to a delay and printing this. # Number of passing repairs: 0/25 Listing 8: Task 4333, Program A. ⬇ ### SPECIFICATION There is a square in the xy - plane. The coordinates of its four vertices are (x_1, y_1),(x_2, y_2),(x_3, y_3) and (x_4, y_4) in counter - clockwise order. (Assume that the positive x - axis points right, and the positive y - axis points up.) Takahashi remembers (x_1, y_1) and (x_2, y_2), but he has forgot (x_3, y_3) and (x_4, y_4). Given x_1, x_2, y_1, y_2, restore x_3, y_3, x_4, y_4. It can be shown that x_3, y_3, x_4 and y_4 uniquely exist and have integer values. ----- Constraints ----- - | x_1 |,| y_1 |,| x_2 |,| y_2 | \ leq 100 - (x_1, y_1) != (x_2, y_2) - All values in input are integers. ----- Input ----- Input is given from Standard Input in the following format: x_1 y_1 x_2 y_2 ----- Output ----- Print x_3, y_3, x_4 and y_4 as integers, in this order. ----- Sample Input ----- 0 0 0 1 ----- Sample Output ----- -1 1 -1 0 (0,0),(0,1),(-1,1),(-1,0) is the four vertices of a square in counter - clockwise order. Note that (x_3, y_3)=(1,1),(x_4, y_4)=(1,0) is not accepted, as the vertices are in clockwise order. ### INCORRECT PROGRAM x1, y1, x2, y2 = map (int, input (). split ()) x3 = x2 + (y2 - y1) y3 = y2 - (x2 - x1) x4 = x1 + (y2 - y1) y4 = y1 - (x2 - x1) print (x3, y3, x4, y4) ### ERROR MESSAGE === Input === 0 0 0 1 === Program Output === 1 1 1 0 === Expected Output === -1 1 -1 0 ### GPT -4 FEEDBACK #1 The issue with the code is that it doesn ’ t consider the counter - clockwise order of the vertices. To fix this, we need to swap the signs of (y2 - y1) and (x2 - x1) in the calculations. # Number of passing repairs: 25/25 ### GPT -4 FEEDBACK #2 The following is a concise explanation of the issue: The code above does not ensure that the vertices are in counter - clockwise order. It calculates x3, y3, x4, and y4 in the wrong order, which results in the coordinates being in clockwise order instead. To fix this, we need to swap the calculations for x3 and x4, and y3 and y4. # Number of passing repairs: 0/25 ### PARTICIPANT FEEDBACK #1 The program calculates vertices for a clockwise - oriented square, not counter - clockwise. To fix this, (y2 - y1) and (x2 - x1) should be negated in the equations. # Number of passing repairs: 25/25 ### PARTICIPANT FEEDBACK #2 The calculation for y3 and y4 incorrectly subtract the x direction vector to y0 and y1 respectively. In each of these cases, the calculation can be fixed by changing the first subtraction to addition. # Number of passing repairs: 0/25 Listing 9: Task 4347, Program B. ⬇ ### SPECIFICATION One day, $n$ people ($n$ is an even number) met on a plaza and made two round dances, each round dance consists of exactly $ \ frac {n}{2} $ people. Your task is to find the number of ways $n$ people can make two round dances if each round dance consists of exactly $ \ frac {n}{2} $ people. Each person should belong to exactly one of these two round dances. Round dance is a dance circle consisting of $1$ or more people. Two round dances are indistinguishable (equal) if one can be transformed to another by choosing the first participant. For example, round dances $ [1, 3, 4, 2] $, $ [4, 2, 1, 3] $ and $ [2, 1, 3, 4] $ are indistinguishable. For example, if $n =2 $ then the number of ways is $1$: one round dance consists of the first person and the second one of the second person. For example, if $n =4 $ then the number of ways is $3$. Possible options: one round dance - $ [1,2] $, another - $ [3,4] $; one round dance - $ [2,4] $, another - $ [3,1] $; one round dance - $ [4,1] $, another - $ [3,2] $. Your task is to find the number of ways $n$ people can make two round dances if each round dance consists of exactly $ \ frac {n}{2} $ people. ----- Input ----- The input contains one integer $n$ ($2 \ le n \ le 20 $), $n$ is an even number. ----- Output ----- Print one integer - the number of ways to make two round dances. It is guaranteed that the answer fits in the $64$ - bit integer data type. ----- Examples ----- Input 2 Output 1 Input 4 Output 3 Input 8 Output 1260 Input 20 Output 12164510040883200 ### INCORRECT PROGRAM def factorial (n): if n == 0: return 1 else: return n * factorial (n -1) n = int (input ()) ans = (factorial (n) // (n // 2)**2) // (2 * n) print (ans) ### ERROR MESSAGE === Input === 2 === Program Output === 0 === Expected Output === 1 ### GPT -4 FEEDBACK #1 The issue with the code is that it uses integer division when calculating the final answer, which may cause the result to be rounded down incorrectly. To fix this, we can use float division and then convert the result to an integer. # Number of passing repairs: 0/25 ### GPT -4 FEEDBACK #2 The following is a concise explanation of the issue: The code attempts to calculate the number of ways using integer division, which may result in a loss of precision and incorrect results. To fix the issue, change integer division to regular division, then round the result to the nearest integer using ‘ round ()‘. # Number of passing repairs: 0/25 ### PARTICIPANT FEEDBACK #1 The problem is that the formula used is incorrect. For n <= 4, n! is less than n ^3 / 2 and so this is why we see a 0. There is an erroneous additional division by n which is the true reason for the wrong answer. # Number of passing repairs: 25/25 ### PARTICIPANT FEEDBACK #2 On line 11, the program calculates a term with a correct numerator, but an incorrect denominator. It divides by (2* n), when it should just divide by 2. # Number of passing repairs: 25/25 Listing 10: Task 4855, Program A. ⬇ ### SPECIFICATION The impact factor of a scientific journal is a measure reflecting the average number of citations to articles published in science journals. For this task we are using a simplified formula for calculating the impact factor:\[ \ frac {\ text {Total count of citations received by articles published in the journal}}{\ text {Total number of articles published}} \] Rounding is always performed upwards. For example the impact factor of the " Journal for ore research and time wasting " that published $38$ articles cited $894$ times is $894 / 38 = 23.53 $ rounding up to $24$. You are the editor of one scientific journal. You know how many articles you are going to publish and the owners are pushing you to reach a specific impact factor. You are wondering how many scientists you will have to bribe to cite your articles to meet the owners demands. Since money is tight you want to bribe the minimal amount of scientists. Each bribed scientist buys you a single citation. ----- Input ----- First and only line of input will contain $2$ integers, $A$ ($1 \ leq A \ leq 100 $), the number of articles you plan to publish and $I$ ($1 \ leq I \ leq 100 $), the impact factor the owners require. ----- Output ----- The first and only line of output should contain one integer, the minimal number of scientists you need to bribe. ----- Examples ----- Sample Input 1: 38 24 Sample Output 1: 875 Sample Input 2: 1 100 Sample Output 2: 100 ### INCORRECT PROGRAM import math A, I = map (int, input (). split ()) needed_citations = math. ceil (A * (I - 0.5)) scientists_to_bribe = needed_citations - A * (I - 1) print (scientists_to_bribe) ### ERROR MESSAGE === Input === 38 24 === Program Output === 19 === Expected Output === 875 ### GPT -4 FEEDBACK #1 The following is a concise explanation of the issue: The calculation for the number of scientists to bribe is incorrect. It should be calculated by first finding the minimum number of citations needed: ‘ A * I ‘, and then subtracting the current number of citations: ‘ A * (I - 1)‘. # Number of passing repairs: 0/25 ### GPT -4 FEEDBACK #2 The following is a concise explanation of the issue: The code calculates the required number of scientists to bribe by subtracting the current number of citations from the number of needed citations. However, it incorrectly calculates the current number of citations. # Number of passing repairs: 1/25 ### PARTICIPANT FEEDBACK #1 The scientists_to_bribe variable on line 3 is unnecessary., It ’ s sufficient to just do A * (I - 1) + 1. # Number of passing repairs: 17/25 ### PARTICIPANT FEEDBACK #2 The program seems to have a conceptual misunderstanding. Specifically, the number of scientists needed to bribe is equal to the number of required citations (‘ citations_needed ‘). However, the calculation of ‘ citation_needed ‘ is also incorrect -- it implies rounding impact factor conventionally (e. g. 3.49 goes to 3, 3.51 goes to 4), whereas rounding here is a ceiling function on the impact factor. As such, the actual formula for ‘ citation_needed ‘ should be ‘ A *(I -1) + 1‘ # Number of passing repairs: 25/25