2306.09896v1

# Demystifying GPT Self-Repair for Code Generation **Authors**: - Theo X. Olausson (MIT EECS & CSAIL &Jeevana Priya Inala) > Correspondence totheoxo@mit.edu. Work partially done while T.X.O. was at Microsoft Research. \usetikzlibrary 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 ## Diagram Type: Flowchart ### Overview The flowchart illustrates the process of a user interacting with a code model, followed by execution, feedback, and a final code model update. ### Components/Axes - **User**: Represented by a human figure icon. - **Code Model**: Depicted by a circle with blue nodes connected by lines. - **Execution**: Shown by a rectangle with three assertions. - **Feedback Model**: Illustrated by a circle with yellow nodes connected by lines. - **Code Model**: Depicted again with blue nodes connected by lines. ### Detailed Analysis or ### Content Details 1. **User**: The user initiates the process. 2. **Code Model**: The code model is presented to the user. 3. **Execution**: The code model is executed, and three assertions are made to verify the output. 4. **Feedback Model**: The feedback model is generated based on the execution results. 5. **Code Model**: The code model is updated based on the feedback. ### Key Observations - The process starts with the user interacting with the code model. - The code model is executed, and the output is verified. - Feedback is generated based on the execution results. - The code model is updated based on the feedback. ### Interpretation The flowchart demonstrates the iterative process of code execution and feedback in a machine learning or AI system. The user interacts with the code model, which is then executed and the results are verified. Based on the feedback, the code model is updated, and the process repeats. This cycle is crucial for continuous improvement and refinement of the code model. </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 ; \node [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 ; \node [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. ; \node [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. ; \node [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 ; \node [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 ( $66\%→ 71\%$ pass rate with a budget of 7000 tokens, $≈$ 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 ( $50\%→ 54\%$ 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 ## Decision Tree Diagram ### Overview The image depicts a decision tree diagram, which is a flowchart-like tree structure used to represent a set of decisions and their possible consequences. The diagram is used to illustrate the process of making decisions based on certain criteria or conditions. ### Components/Axes - **Root Node**: The topmost node labeled "ψ" represents the starting point of the decision tree. - **Decision Nodes**: The nodes labeled "p1", "p2", ..., "pn_p" represent the different decision points in the process. - **Branch Nodes**: The nodes labeled "f11", "f1n_f", ..., "fn_p fn_f" represent the different possible outcomes or paths that can be taken from each decision point. - **Leaf Nodes**: The nodes labeled "r111", "r11n_r", ..., "rn_p fn_f" represent the final outcomes or results of the decision-making process. ### Detailed Analysis or ### Content Details The decision tree diagram shows a hierarchical structure with multiple levels of decision points. Each decision point has multiple possible outcomes, represented by the branch nodes. The final outcomes are represented by the leaf nodes. ### Key Observations - The diagram has a total of n decision points, represented by the nodes labeled "p1", "p2", ..., "pn_p". - Each decision point has multiple possible outcomes, represented by the branch nodes. - The final outcomes are represented by the leaf nodes. - The diagram shows a clear flow from the root node to the leaf nodes, indicating the process of decision-making. ### Interpretation The decision tree diagram illustrates the process of decision-making based on certain criteria or conditions. The diagram shows a hierarchical structure with multiple levels of decision points, each with multiple possible outcomes. The final outcomes are represented by the leaf nodes, indicating the end result of the decision-making process. The diagram can be used to analyze the decision-making process and identify the most likely outcomes based on the given criteria or conditions. </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: $N_{p}≥ n_{p}$ initial program samples; $N_{f}≥ n_{f}$ feedback strings per wrong program; and $N_{r}≥ n_{r}$ 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 $n_{p}≤ 25$ for the self-repair approaches and $n_{p}≤ 50$ for the baseline, no-repair approach. Similarly, for the feedback strings, we use $N_{f}=25$ and $n_{f}≤ 10$ (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 ## Heatmap: Mean Passage Rate ### Overview The heatmap illustrates the mean passage rate of different models as the mean number of tokens generated increases. The color intensity represents the rate, with darker shades indicating higher rates. ### Components/Axes - **X-axis**: Mean number of tokens generated, ranging from 0 to 10,000. - **Y-axis**: Mean passage rate, ranging from 0.0 to 1.0. - **Legend**: - **n_p = 1**: Dark orange, circles - **n_p = 2**: Light orange, triangles - **n_p = 5**: Green, squares - **n_p = 10**: Blue, diamonds - **n_p = 25**: Purple, stars ### Detailed Analysis or ### Content Details - **n_p = 1**: The rate is consistently high, peaking around 10,000 tokens. - **n_p = 2**: The rate is slightly lower than n_p = 1, with a peak around 8,000 tokens. - **n_p = 5**: The rate is moderate, with a peak around 6,000 tokens. - **n_p = 10**: The rate is the lowest, with a peak around 4,000 tokens. - **n_p = 25**: The rate is the highest, with a peak around 2,000 tokens. ### Key Observations - The rate increases with the number of tokens generated. - The highest rate is observed with n_p = 25. - The rate decreases as the number of tokens generated increases for all models. ### Interpretation The heatmap suggests that the model with n_p = 25 generates the most passage rate, indicating it is the most efficient in terms of token generation. The other models show a decreasing rate as the number of tokens increases, with n_p = 10 having the lowest rate. This could imply that the model with n_p = 25 is better suited for tasks requiring a high volume of text output. </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: Number of Feedback Repairs vs Number of Initial Programs ### Overview The heatmap illustrates the relationship between the number of initial programs (n_p) and the number of feedback repairs (n_f). The color intensity represents the frequency of feedback repairs, with darker shades indicating higher frequencies. ### Components/Axes - **X-axis**: Number of initial programs (n_p) ranging from 1 to 25. - **Y-axis**: Number of feedback repairs (n_f) ranging from 1 to 10. - **Legend**: The legend indicates the color intensity, with darker shades representing higher frequencies of feedback repairs. ### Detailed Analysis or ### Content Details - **Low Initial Programs (n_p = 1-5)**: The frequency of feedback repairs is relatively low, with values ranging from 0.78 to 0.87. - **Medium Initial Programs (n_p = 6-10)**: The frequency of feedback repairs increases, with values ranging from 0.80 to 0.92. - **High Initial Programs (n_p = 11-25)**: The frequency of feedback repairs is significantly higher, with values ranging from 0.81 to 1.00. ### Key Observations - **Trend**: There is a clear positive correlation between the number of initial programs and the number of feedback repairs. As the number of initial programs increases, the frequency of feedback repairs also increases. - **Outliers**: There are no significant outliers in the data, with all values falling within the expected range. ### Interpretation The heatmap suggests that as the number of initial programs increases, the frequency of feedback repairs also increases. This could indicate that more initial programs lead to more opportunities for feedback and repairs. The highest frequency of feedback repairs is observed in the range of 11-25 initial programs, suggesting that this is the optimal range for initial programs to achieve the highest frequency of feedback repairs. </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 $M_{P}=M_{F}∈\{\text{GPT-3.5, GPT-4}\}$ , 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 $(n_{p},n_{fr})∈\{1,2,5,10,25\}×\{1,3,5,10\}$ . 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 ( $≥ 1$ ) 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: $(n_{p},n_{fr})∈\{1,2,....,24,25\}×\{1\}$ . The plots are shown in Figure 6 for both $M_{P}=M_{F}∈\{\text{GPT-3.5},\text{GPT-4}\}$ 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 $n_{p}$ ( $≥ 5000$ ), where it increases pass rate by over 5 points. <details> <summary>x5.png Details</summary>  ### Visual Description ## Heatmap: Mean Passage Rate ### Overview The heatmap illustrates the mean passage rate of different models as the mean number of tokens generated increases. The color intensity represents the rate, with darker shades indicating higher rates. ### Components/Axes - **X-axis**: Mean number of tokens generated - **Y-axis**: Mean passage rate - **Legend**: Different models with corresponding colors and symbols ### Detailed Analysis or ### Content Details The heatmap shows a general trend where the mean passage rate increases with the mean number of tokens generated. Each model has a distinct color and symbol, indicating different parameters (n_p and n_fr). The models are as follows: - **n_p = 1**: Dark red, filled circle - **n_p = 2**: Dark orange, filled triangle - **n_p = 5**: Dark green, filled square - **n_p = 10**: Dark blue, filled diamond - **n_p = 25**: Dark purple, filled pentagon ### Key Observations - **n_p = 1**: The model with the highest mean passage rate, especially noticeable at higher token counts. - **n_p = 2**: Shows a moderate increase in passage rate. - **n_p = 5**: Exhibits a steady increase in passage rate. - **n_p = 10**: Shows a slight increase in passage rate. - **n_p = 25**: The model with the lowest mean passage rate, especially noticeable at lower token counts. ### Interpretation The data suggests that as the mean number of tokens generated increases, the mean passage rate also increases for all models. The model with n_p = 1 consistently shows the highest passage rate, indicating it might be more efficient or better at handling larger token counts. The model with n_p = 2 shows a moderate improvement, while n_p = 5 and n_p = 10 show steady increases. The model with n_p = 25 shows the lowest passage rate, which might indicate it is less efficient or better at handling smaller token counts. This information is crucial for selecting the most appropriate model for a given task based on the expected token count. </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: Feedback Repairs ### Overview The heatmap illustrates the relationship between the number of initial programs (n_p) and the number of feedback repairs (n_f) for a given dataset. The color gradient represents the frequency of feedback repairs, with darker shades indicating higher frequencies. ### Components/Axes - **X-axis**: Number of initial programs (n_p), ranging from 1 to 25. - **Y-axis**: Number of feedback repairs (n_f), ranging from 1 to 10. - **Legend**: The legend indicates the color coding for the frequency of feedback repairs, with darker shades representing higher frequencies. ### Detailed Analysis or ### Content Details - **Low n_p (1-5)**: The frequency of feedback repairs is relatively low, with values ranging from 0.90 to 1.05. - **Medium n_p (6-10)**: The frequency of feedback repairs increases, with values ranging from 0.91 to 1.08. - **High n_p (11-25)**: The frequency of feedback repairs is the highest, with values ranging from 0.93 to 1.09. ### Key Observations - **Trend**: There is a clear trend of increasing feedback repairs as the number of initial programs increases. - **Outliers**: There are no significant outliers in the data, with all values falling within the expected range. ### Interpretation The heatmap suggests that as the number of initial programs increases, the frequency of feedback repairs also increases. This could indicate that more programs lead to more feedback, which in turn leads to more repairs. The highest frequency of feedback repairs is observed in the highest number of initial programs, suggesting that a larger number of programs may require more attention and resources to address feedback issues. </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 $(n_{p},n_{f},n_{r})∈\{1,2,....,24,25\}×\{1\}×\{1\}$ , 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 $± 1$ standard deviation. Complete breakdown per difficulty in Appendix A. <details> <summary>x7.png Details</summary>  ### Visual Description ## Line Graph: Mean Pass Rate ### Overview The line graph displays the mean pass rate of different models as a function of the mean number of tokens generated. The models compared are GPT-4, GPT-3.5, and their variants with and without repair. ### Components/Axes - **X-axis**: Mean number of tokens generated - **Y-axis**: Mean pass rate - **Legend**: - **M_p**: GPT-4 (no repair) - **M_p**: GPT-4; M_F: GPT-4 - **M_p**: GPT-3.5 (no repair) - **M_p**: GPT-3.5; M_F: GPT-3.5 - **M_p**: GPT-3.5; M_F: GPT-4 ### Detailed Analysis or ### Content Details - **GPT-4 (no repair)**: The line is the highest, indicating the highest mean pass rate. It starts at around 0.4 and increases to about 0.6 as the number of tokens generated increases. - **GPT-4 (repair)**: The line is slightly lower than GPT-4 (no repair), starting at around 0.4 and increasing to about 0.55. - **GPT-3.5 (no repair)**: The line is the lowest, starting at around 0.3 and increasing to about 0.45. - **GPT-3.5 (repair)**: The line is the second lowest, starting at around 0.3 and increasing to about 0.4. ### Key Observations - The models with repair consistently show a lower mean pass rate compared to their unrepaired counterparts. - The difference in mean pass rate between GPT-4 (no repair) and GPT-4 (repair) is relatively small. - The models with repair show a more gradual increase in mean pass rate as the number of tokens generated increases. ### Interpretation The data suggests that the repair of the models does not significantly improve their mean pass rate. The models with repair show a similar trend to the unrepaired models, indicating that the repair does not provide a substantial advantage in this context. The slight increase in mean pass rate for the models with repair could be due to the fact that the repair process introduces some form of regularization or optimization that helps the model to generalize better. However, the improvement is not as significant as one might expect, which could be due to the complexity of the task or the specific characteristics of the data being generated. </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 $± 1$ 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 $20· 2=40$ 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 $f∈\{h_{i,j,1},h_{i,j,2},f_{i,j,1},f_{i,j,2}\}$ . 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 $1.57×$ 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 color intensity represents the rate, with darker shades indicating higher rates. ### Components/Axes - **X-axis**: Mean number of tokens generated - **Y-axis**: Mean passage rate - **Legend**: - **n_p = 1**: Dark blue - **n_p = 2**: Light blue - **n_p = 5**: Green - **n_p = 10**: Yellow - **n_p = 25**: Orange ### Detailed Analysis or ### Content Details The heatmap shows that as the mean number of tokens generated increases, the mean passage rate also increases. However, the rate of increase varies across different models. For instance, the model with n_p = 1 has the highest mean passage rate, while the model with n_p = 25 has the lowest. The models with n_p = 5 and n_p = 10 show intermediate rates. ### Key Observations - The model with n_p = 1 consistently has the highest mean passage rate. - The model with n_p = 25 has the lowest mean passage rate. - There is a noticeable trend where the mean passage rate increases with the number of tokens generated, but the rate of increase slows down as the number of tokens increases. ### Interpretation The heatmap suggests that the model with n_p = 1 is the most efficient in terms of passage rate, generating the most tokens with the highest rate. Conversely, the model with n_p = 25 is the least efficient, generating the fewest tokens with the lowest rate. The models with n_p = 5 and n_p = 10 show a balance between efficiency and the number of tokens generated. The trend indicates that increasing the number of tokens generated generally leads to an increase in passage rate, but the rate of increase diminishes as the number of tokens increases. </details> <details> <summary>x9.png Details</summary>  ### Visual Description ## Heatmap: Number of Feedback Repairs vs Number of Initial Programs ### Overview The heatmap illustrates the relationship between the number of initial programs (n_p) and the number of feedback repairs (n_f). The color gradient represents the frequency of feedback repairs, with darker shades indicating higher frequencies. ### Components/Axes - **X-axis**: Number of initial programs (n_p) ranging from 1 to 25. - **Y-axis**: Number of feedback repairs (n_f) ranging from 1 to 10. - **Legend**: The legend indicates the color coding for feedback repair frequencies, with darker shades representing higher frequencies. ### Detailed Analysis or ### Content Details The heatmap shows a clear trend where the number of feedback repairs increases with the number of initial programs. The highest frequency of feedback repairs is observed when there are 10 initial programs, with a frequency of 1.00. As the number of initial programs increases, the frequency of feedback repairs also increases, peaking at 25 initial programs with a frequency of 1.01. ### Key Observations - The highest frequency of feedback repairs is observed when there are 10 initial programs. - The frequency of feedback repairs increases with the number of initial programs. - There is a slight increase in the frequency of feedback repairs as the number of initial programs increases beyond 10. ### Interpretation The heatmap suggests that as the number of initial programs increases, the frequency of feedback repairs also increases. This could indicate that more initial programs may require more feedback repairs. The slight increase in frequency beyond 10 initial programs could suggest that there is a threshold beyond which the number of feedback repairs does not significantly increase. The interpretation of this data would depend on the specific context and goals of the study. </details> <details> <summary>x10.png Details</summary>  ### Visual Description ## Heatmap: Mean Passage Rate ### Overview The heatmap illustrates the mean passage rate of different models as the mean number of tokens generated increases. The color intensity represents the rate, with darker shades indicating higher rates. ### Components/Axes - **X-axis**: Mean number of tokens generated, ranging from 0 to 10,000. - **Y-axis**: Mean passage rate, ranging from 0.0 to 1.0. - **Legend**: - **n_p = 1**: Orange circles - **n_p = 2**: Yellow triangles - **n_p = 5**: Green squares - **n_p = 10**: Blue diamonds - **n_p = 25**: Purple hexagons ### Detailed Analysis or ### Content Details The heatmap shows a general trend where the mean passage rate increases with the mean number of tokens generated. However, the rate of increase varies across different models. For instance, the model with **n_p = 25** (purple hexagons) shows the highest mean passage rate, peaking around 1.0 tokens generated. In contrast, the model with **n_p = 1** (orange circles) has the lowest rate, staying close to 0.2 tokens generated. ### Key Observations - The model with **n_p = 25** consistently has the highest mean passage rate. - The rate of increase in passage rate is more pronounced for models with higher **n_p** values. - There are no significant outliers or anomalies in the data. ### Interpretation The heatmap suggests that as the mean number of tokens generated increases, the mean passage rate also increases. However, the rate of increase varies significantly among different models. The model with **n_p = 25** appears to be the most efficient in terms of passage rate, suggesting it may be better suited for tasks requiring high passage rates. The other models show a more gradual increase in passage rate, indicating they may be more suitable for tasks where the passage rate is not as critical. </details> <details> <summary>x11.png Details</summary>  ### Visual Description ## Heatmap: Number of Feedback Repairs vs Number of Initial Programs ### Overview The heatmap illustrates the relationship between the number of initial programs (n_p) and the number of feedback repairs (n_f). The color intensity represents the frequency of feedback repairs, with darker shades indicating higher frequencies. ### Components/Axes - **X-axis**: Number of initial programs (n_p) ranging from 1 to 25. - **Y-axis**: Number of feedback repairs (n_f) ranging from 1 to 10. - **Legend**: The legend indicates the color intensity, with darker shades representing higher frequencies of feedback repairs. ### Detailed Analysis or ### Content Details The heatmap shows a clear trend where the number of feedback repairs increases with the number of initial programs. The highest frequency of feedback repairs is observed when there are 10 initial programs, with a frequency of 0.98. As the number of initial programs increases, the frequency of feedback repairs also increases, peaking at 25 initial programs with a frequency of 0.84. ### Key Observations - The highest frequency of feedback repairs is observed when there are 10 initial programs. - The frequency of feedback repairs decreases as the number of initial programs increases beyond 10. - There is a significant increase in the frequency of feedback repairs as the number of initial programs increases from 1 to 5. ### Interpretation The data suggests that as the number of initial programs increases, the frequency of feedback repairs also increases. This could indicate that more initial programs lead to more opportunities for feedback and repairs. The peak frequency of feedback repairs at 10 initial programs might suggest that this is the optimal number of initial programs for the system to receive the most feedback and repairs. However, the decrease in frequency as the number of initial programs increases beyond 10 might indicate that the system becomes less responsive or that the additional programs do not provide enough opportunities for feedback and repairs. </details> <details> <summary>x12.png Details</summary>  ### Visual Description ## Heatmap: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The heatmap illustrates the mean pass rate of a system as a function of the mean number of tokens generated. The x-axis represents the mean number of tokens generated, while the y-axis represents the mean pass rate. ### Components/Axes - **X-axis**: Mean number of tokens generated (ranging from 0 to 10,000) - **Y-axis**: Mean pass rate (ranging from 0.0 to 1.0) - **Legend**: - **Brown circles**: n_p = 1 - **Yellow triangles**: n_p = 2 - **Green squares**: n_p = 5 - **Blue diamonds**: n_p = 10 - **Purple stars**: n_p = 25 - **Black dots**: n_fr = 1 - **Orange triangles**: n_fr = 3 - **Blue squares**: n_fr = 5 - **Green circles**: n_fr = 10 - **Purple triangles**: n_fr = 25 ### Detailed Analysis or ### Content Details The heatmap shows that as the mean number of tokens generated increases, the mean pass rate generally increases as well. However, the rate of increase is not uniform across all categories. For example, the system with n_p = 1 and n_fr = 1 (brown circles) shows a relatively stable pass rate, while the system with n_p = 25 and n_fr = 25 (purple stars) shows a slight decrease in pass rate as the number of tokens generated increases. ### Key Observations - The system with n_p = 1 and n_fr = 1 (brown circles) has the lowest mean pass rate and the most stable performance. - The system with n_p = 25 and n_fr = 25 (purple stars) has the highest mean pass rate and the most variability in performance. - The systems with n_p = 2 and n_fr = 3 (yellow triangles and orange triangles) show a moderate increase in pass rate as the number of tokens generated increases. - The systems with n_p = 5 and n_fr = 5 (green squares and blue diamonds) show a slight increase in pass rate as the number of tokens generated increases. - The systems with n_p = 10 and n_fr = 10 (blue diamonds and green circles) show a slight increase in pass rate as the number of tokens generated increases. ### Interpretation The heatmap suggests that the system's performance is influenced by both the number of tokens generated and the number of tokens received. The system with the highest number of tokens generated (n_p = 25) and the highest number of tokens received (n_fr = 25) shows the best performance, while the system with the lowest number of tokens generated (n_p = 1) and the lowest number of tokens received (n_fr = 1) shows the worst performance. The systems with moderate numbers of tokens generated and received show a balanced performance. The slight increase in pass rate as the number of tokens generated increases suggests that the system is able to handle more tokens, but the rate of increase is not uniform across all categories. </details> <details> <summary>x13.png Details</summary>  ### Visual Description ## Heatmap: Feedback Repairs ### Overview The heatmap illustrates the relationship between the number of initial programs (n_p) and the number of feedback repairs (n_f) for a given dataset. The color gradient represents the frequency of feedback repairs, with darker shades indicating higher frequencies. ### Components/Axes - **X-axis**: Number of initial programs (n_p) ranging from 1 to 25. - **Y-axis**: Number of feedback repairs (n_f) ranging from 1 to 10. - **Legend**: The legend indicates the color coding for the frequency of feedback repairs, with darker shades representing higher frequencies. ### Detailed Analysis or ### Content Details - **Low Number of Initial Programs (n_p < 5)**: The frequency of feedback repairs is relatively low, with values ranging from 0.78 to 0.87. - **Medium Number of Initial Programs (5 ≤ n_p < 10)**: The frequency of feedback repairs increases significantly, with values ranging from 0.91 to 1.09. - **High Number of Initial Programs (n_p ≥ 10)**: The frequency of feedback repairs is consistently high, with values ranging from 1.05 to 1.13. ### Key Observations - **Trend**: As the number of initial programs increases, the frequency of feedback repairs also increases. - **Outliers**: There are no significant outliers in the data, with all values falling within the expected range. ### Interpretation The heatmap suggests that as the number of initial programs increases, the frequency of feedback repairs also increases. This could indicate that more complex programs require more feedback to ensure they are functioning correctly. The high frequency of feedback repairs for programs with more than 10 initial programs suggests that these programs are more prone to errors or require more attention to detail. The consistent high frequency of feedback repairs for programs with more than 10 initial programs could indicate that these programs are more complex or require more resources to maintain. </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 ## Heatmap: Mean Passage Rate ### Overview The heatmap illustrates the mean passage rate of different models as the mean number of tokens generated increases. The color intensity represents the rate, with darker shades indicating higher rates. ### Components/Axes - **X-axis**: Mean number of tokens generated, ranging from 0 to 10,000. - **Y-axis**: Mean passage rate, ranging from 0.0 to 1.0. - **Legend**: - **n_p = 1**: Dark orange - **n_p = 2**: Light orange - **n_p = 5**: Yellow - **n_p = 10**: Light blue - **n_p = 25**: Dark blue - **n_fr = 1**: Dark gray - **n_fr = 3**: Light gray - **n_fr = 5**: Medium gray - **n_fr = 10**: Dark gray - **n_fr = 25**: Light gray ### Detailed Analysis or ### Content Details - **n_p = 1**: The model with the least number of parameters (1) shows a relatively stable mean passage rate, peaking around 80% at around 2,000 tokens generated. - **n_p = 2**: This model has a slightly higher mean passage rate compared to n_p = 1, peaking around 85% at around 2,000 tokens generated. - **n_p = 5**: The model with 5 parameters shows a steady increase in mean passage rate, reaching around 90% at around 10,000 tokens generated. - **n_p = 10**: This model has the highest mean passage rate, peaking around 95% at around 10,000 tokens generated. - **n_p = 25**: The model with the most parameters (25) shows the highest mean passage rate, peaking around 98% at around 10,000 tokens generated. ### Key Observations - There is a clear trend of increasing mean passage rate with the number of parameters. - The model with the most parameters (n_p = 25) consistently outperforms the others. - The model with the least number of parameters (n_p = 1) shows the least performance. ### Interpretation The heatmap suggests that increasing the number of parameters in a model generally leads to a higher mean passage rate. This is consistent with the idea that more parameters allow the model to learn more complex patterns and relationships in the data. The model with the most parameters (n_p = 25) demonstrates the best performance, indicating that it has learned the most from the training data. This finding is significant for the development of language models, as it suggests that larger models may be more effective in generating coherent and contextually appropriate responses. </details> <details> <summary>x15.png Details</summary>  ### Visual Description ## Heatmap: Number of Feedback Repairs vs. Number of Initial Programs ### Overview The heatmap illustrates the relationship between the number of initial programs and the number of feedback repairs. The color gradient represents the frequency of feedback repairs, with darker shades indicating higher frequencies. ### Components/Axes - **X-axis**: Number of initial programs (n_p) with values ranging from 1 to 25. - **Y-axis**: Number of feedback repairs (n_f) with values ranging from 1 to 10. - **Legend**: The legend indicates the color coding for feedback repair frequencies, with darker shades representing higher frequencies. ### Detailed Analysis or ### Content Details The heatmap shows a general trend where the number of feedback repairs increases with the number of initial programs. However, the increase is not linear. For example, with 1 initial program, there are approximately 1.05 feedback repairs, while with 25 initial programs, there are around 1.04 feedback repairs. The highest frequency of feedback repairs is observed with 1 initial program, where the number of feedback repairs is close to 10. ### Key Observations - The highest frequency of feedback repairs is observed with 1 initial program. - The frequency of feedback repairs decreases as the number of initial programs increases. - There is a slight increase in feedback repairs with each additional initial program, but the increase is relatively small. ### Interpretation The heatmap suggests that the number of initial programs has a positive correlation with the number of feedback repairs. This could indicate that programs with more initial programs may require more feedback to improve their quality. However, the relationship is not perfectly linear, and there are some fluctuations in the number of feedback repairs with different numbers of initial programs. The slight increase in feedback repairs with each additional initial program could be due to the fact that more programs may have more complex issues that require more feedback to resolve. </details> <details> <summary>x16.png Details</summary>  ### Visual Description ## Heatmap: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The heatmap illustrates the mean pass rate of a system as a function of the mean number of tokens generated. The x-axis represents the mean number of tokens generated, while the y-axis represents the mean pass rate. ### Components/Axes - **X-axis**: Mean number of tokens generated (ranging from 0 to 10,000) - **Y-axis**: Mean pass rate (ranging from 0.0 to 1.0) - **Legend**: - **n_p = 1**: Brown circles - **n_p = 2**: Yellow triangles - **n_p = 5**: Green squares - **n_p = 10**: Blue diamonds - **n_p = 25**: Purple hexagons - **n_fr = 1**: Black circles - **n_fr = 3**: Gray triangles - **n_fr = 5**: Light blue squares - **n_fr = 10**: Dark blue diamonds - **n_fr = 25**: Orange hexagons ### Detailed Analysis or ### Content Details The heatmap shows that as the mean number of tokens generated increases, the mean pass rate generally increases as well. However, the rate of increase varies depending on the number of parameters (n_p) and the number of features (n_fr). For example, with n_p = 1 and n_fr = 1, the mean pass rate increases more slowly compared to n_p = 2 and n_fr = 1. Similarly, with n_p = 25 and n_fr = 25, the mean pass rate increases more rapidly compared to n_p = 1 and n_fr = 1. ### Key Observations - The highest mean pass rate is observed with n_p = 25 and n_fr = 25. - The lowest mean pass rate is observed with n_p = 1 and n_fr = 1. - There is a noticeable trend of increasing mean pass rate with increasing mean number of tokens generated for all combinations of n_p and n_fr. ### Interpretation The heatmap suggests that increasing the mean number of tokens generated generally improves the mean pass rate of the system. However, the improvement is not uniform across all combinations of parameters. The optimal combination of parameters (n_p and n_fr) for the highest mean pass rate is n_p = 25 and n_fr = 25. This indicates that the system performs best when it has a high number of parameters and features. </details> <details> <summary>x17.png Details</summary>  ### Visual Description ## Heatmap: Number of Feedback Repairs vs Number of Initial Programs ### Overview The heatmap illustrates the relationship between the number of initial programs and the number of feedback repairs. The color gradient represents the frequency of feedback repairs, with darker shades indicating higher frequencies. ### Components/Axes - **X-axis**: Number of initial programs (n_p) ranging from 1 to 25. - **Y-axis**: Number of feedback repairs (n_f) ranging from 1 to 10. - **Legend**: The legend indicates the color coding for feedback repair frequencies, with darker shades representing higher frequencies. ### Detailed Analysis or ### Content Details The heatmap shows a clear trend where the number of feedback repairs increases with the number of initial programs. The highest frequency of feedback repairs is observed when there are 25 initial programs, with a frequency of 1.09. The lowest frequency is observed when there is only 1 initial program, with a frequency of 0.88. ### Key Observations - The heatmap shows a positive correlation between the number of initial programs and the number of feedback repairs. - The highest frequency of feedback repairs is observed when there are 25 initial programs. - The lowest frequency of feedback repairs is observed when there is only 1 initial program. ### Interpretation The data suggests that as the number of initial programs increases, the number of feedback repairs also increases. This could be due to the fact that more initial programs may lead to more complex systems, which require more feedback to ensure they are functioning correctly. The positive correlation between the number of initial programs and the number of feedback repairs could be a useful metric for evaluating the effectiveness of a system or program. </details> <details> <summary>x18.png Details</summary>  ### Visual Description ## Heatmap: Mean Passage Rate ### Overview The heatmap illustrates the mean passage rate of different models as the mean number of tokens generated increases. The models are represented by different colors and symbols, and the rate is measured on the y-axis. ### Components/Axes - **X-axis**: Mean number of tokens generated, ranging from 0 to 10,000. - **Y-axis**: Mean passage rate, ranging from 0.0 to 1.0. - **Legend**: - **Orange circles**: \( n_p = 1 \) - **Yellow triangles**: \( n_p = 2 \) - **Green squares**: \( n_p = 5 \) - **Blue diamonds**: \( n_p = 10 \) - **Purple stars**: \( n_p = 25 \) - **Data points**: Each point represents the mean passage rate for a specific combination of \( n_p \) and \( n_{fr} \). ### Detailed Analysis or ### Content Details - The orange circles ( \( n_p = 1 \)) show the lowest mean passage rate, ranging from approximately 0.1 to 0.2. - The yellow triangles ( \( n_p = 2 \)) have a slightly higher rate, between 0.2 and 0.3. - The green squares ( \( n_p = 5 \)) exhibit a moderate rate, between 0.3 and 0.4. - The blue diamonds ( \( n_p = 10 \)) have the highest mean passage rate, between 0.4 and 0.5. - The purple stars ( \( n_p = 25 \)) show the highest rate, between 0.5 and 0.6. ### Key Observations - The mean passage rate increases with the mean number of tokens generated for all models. - The rate increases more steeply for models with higher \( n_p \) values. - There is a noticeable difference in the rate between models with different \( n_p \) values, with higher \( n_p \) values generally showing higher rates. ### Interpretation The data suggests that as the mean number of tokens generated increases, the mean passage rate also increases. This trend is consistent across all models. The rate increases more steeply for models with higher \( n_p \) values, indicating that models with more parameters may generate more coherent and relevant passages. The significant difference in rate between models with different \( n_p \) values highlights the importance of model architecture in determining the quality of generated passages. </details> <details> <summary>x19.png Details</summary>  ### Visual Description ## Heatmap: Number of feedback-repairs vs Number of initial programs ### Overview The heatmap illustrates the relationship between the number of initial programs (n_p) and the number of feedback-repairs (n_f) in a given dataset. The color intensity represents the frequency of feedback-repairs, with darker shades indicating higher frequencies. ### Components/Axes - **X-axis**: Number of initial programs (n_p) ranging from 1 to 25. - **Y-axis**: Number of feedback-repairs (n_f) ranging from 1 to 10. - **Legend**: The legend indicates the color coding for the frequency of feedback-repairs, with darker shades representing higher frequencies. ### Detailed Analysis or ### Content Details - **Low n_p (1-5)**: The heatmap shows a relatively stable frequency of feedback-repairs, with values ranging from 1.01 to 1.19. - **Medium n_p (6-10)**: The frequency of feedback-repairs increases significantly, with values ranging from 1.10 to 1.16. - **High n_p (11-25)**: The frequency of feedback-repairs remains relatively high, with values ranging from 1.13 to 1.19. ### Key Observations - **Trend**: There is a clear trend of increasing feedback-repairs as the number of initial programs increases. - **Outliers**: No significant outliers are observed in the data. - **Anomalies**: The data points are consistent with the trend, showing a positive correlation between the number of initial programs and feedback-repairs. ### Interpretation The heatmap suggests that as the number of initial programs increases, the number of feedback-repairs also tends to increase. This could indicate that more initial programs lead to more opportunities for feedback and, consequently, more feedback-repairs. The consistent color intensity across different ranges of initial programs suggests that the relationship between the number of initial programs and feedback-repairs is relatively stable. </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 Graph: Mean Pass Rate ### Overview The line graph displays the mean pass rate of different models as a function of the mean number of tokens generated. The models compared are GPT-4, GPT-3.5, and their variants with and without repair. ### Components/Axes - **X-axis**: Mean number of tokens generated, ranging from 0 to 10,000. - **Y-axis**: Mean pass rate, ranging from 0.0 to 1.0. - **Legend**: Located at the bottom right, indicating the models and their pass rates. ### Detailed Analysis or ### Content Details - **GPT-4 (no repair)**: The line is the darkest blue, indicating the lowest mean pass rate. - **GPT-4; M_F = GPT-4**: The line is a lighter blue, showing a higher mean pass rate compared to GPT-4 (no repair). - **GPT-3.5 (no repair)**: The line is the lightest blue, indicating the highest mean pass rate among the models. - **GPT-3.5; M_F = GPT-3.5**: The line is a darker shade of blue, showing a pass rate similar to GPT-3.5 (no repair). - **GPT-3.5; M_F = GPT-4**: The line is the lightest blue, indicating the highest mean pass rate among the variants. ### Key Observations - The pass rate increases with the mean number of tokens generated for all models. - GPT-3.5 (no repair) consistently has the highest pass rate. - The GPT-4 variant with repair (M_F = GPT-4) shows a significant improvement in pass rate compared to GPT-4 (no repair). - The GPT-3.5 variant with repair (M_F = GPT-3.5) shows a slight improvement in pass rate compared to GPT-3.5 (no repair). ### Interpretation The data suggests that the use of repair mechanisms in the GPT-4 model leads to a higher mean pass rate across different token counts. The GPT-3.5 model with repair also shows a slight improvement in pass rate compared to its variant without repair. This indicates that repair mechanisms can enhance the performance of language models, particularly in terms of pass rate. </details> <details> <summary>x21.png Details</summary>  ### Visual Description ## Line Graph: Mean Pass Rate ### Overview The line graph depicts the mean pass rate of different versions of GPT models as a function of the mean number of tokens generated. The graph compares the performance of GPT-4, GPT-3.5, and their repaired versions. ### Components/Axes - **X-axis**: Mean number of tokens generated - **Y-axis**: Mean pass rate - **Legend**: Differentiates between GPT-4 (no repair), GPT-4 (repaired), GPT-3.5 (no repair), and GPT-3.5 (repaired) ### Detailed Analysis or ### Content Details - **GPT-4 (no repair)**: The line is the lowest, indicating the lowest mean pass rate across all token counts. - **GPT-4 (repaired)**: The line is the highest, showing the highest mean pass rate. - **GPT-3.5 (no repair)**: The line is slightly above GPT-4 (no repair), indicating a higher pass rate than GPT-4 but lower than GPT-4 (repaired). - **GPT-3.5 (repaired)**: The line is the second highest, showing a significant improvement in pass rate compared to GPT-3.5 (no repair). ### Key Observations - The repaired versions of GPT-4 and GPT-3.5 show a significant improvement in mean pass rate. - The difference in pass rate between the repaired and non-repaired versions is most pronounced at higher token counts. - There is a general trend of increasing pass rate with the increase in token count for all models. ### Interpretation The data suggests that the repair of GPT models significantly improves their performance in terms of mean pass rate. This is particularly noticeable in the repaired versions of GPT-4 and GPT-3.5, which outperform their non-repaired counterparts across all token counts. The improvement is most pronounced at higher token counts, indicating that the repair might be more effective in handling more complex or longer text. The trend of increasing pass rate with token count suggests that the models become more proficient in generating accurate responses as the input text length increases. </details> <details> <summary>x22.png Details</summary>  ### Visual Description ## Heatmap: Mean Pass Rate vs. Mean Number of Tokens Generated ### Overview The heatmap illustrates the mean pass rate of different models as the mean number of tokens generated increases. The models compared are GPT-4, GPT-3.5, and their variants with and without repair mechanisms. ### Components/Axes - **X-axis**: Mean number of tokens generated, ranging from 0 to 10,000. - **Y-axis**: Mean pass rate, ranging from 0.0 to 1.0. - **Legend**: - **M_p**: GPT-4 (no repair) - **M_p; M_f**: GPT-4; GPT-4 - **M_p**: GPT-3.5 (no repair) - **M_p; M_f**: GPT-3.5; GPT-3.5 - **M_p**: GPT-3.5; GPT-4 ### Detailed Analysis or ### Content Details The heatmap shows that the mean pass rate generally increases with the mean number of tokens generated. However, the rate of increase varies between the models. GPT-4 (no repair) has the highest mean pass rate, followed by GPT-4 with repair (M_p; M_f). GPT-3.5 (no repair) and GPT-3.5 with repair (M_p; M_f) have lower pass rates compared to GPT-4. The pass rate for GPT-3.5 with repair (M_p; M_f) is slightly higher than GPT-3.5 (no repair) across all token counts. ### Key Observations - GPT-4 (no repair) consistently has the highest mean pass rate. - GPT-4 with repair (M_p; M_f) shows a slight improvement in pass rate compared to GPT-4 (no repair). - GPT-3.5 (no repair) and GPT-3.5 with repair (M_p; M_f) have lower pass rates. - The pass rate for GPT-3.5 with repair (M_p; M_f) is marginally higher than GPT-3.5 (no repair). ### Interpretation The data suggests that the mean pass rate of language models generally improves with the number of tokens generated. The models with repair mechanisms (M_p; M_f) tend to have higher pass rates compared to their variants without repair (M_p). This could indicate that repair mechanisms help in improving the quality and coherence of the generated text. However, the improvement is relatively small, suggesting that the models are already quite effective in generating text with a high pass rate. </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 ## Tasks ### Setup: - Use a laptop or desktop computer, not a phone ### Task: Debug five incorrect Python programs - Each program is an incorrect attempt to solve a coding challenge - Your answer should explain what the program is doing wrong - Expect ~10 minutes per task ### Task format - Each task is in a separate website - Submit your answer using the Google form embedded in each page - No other data is being collected ### Interpretation The image outlines a task format for debugging five incorrect Python programs. The setup instructions specify that participants should use a laptop or desktop computer, not a phone. The task involves identifying and explaining the errors in five separate Python programs, with an expected time of 10 minutes per task. The task format indicates that each program will be presented on a separate website, and participants will submit their answers using a Google form embedded on each page. The image does not provide any additional information or data. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/2.jpg Details</summary>  ### Visual Description ## Your Answer ### Overview The image is a screenshot of a programming problem statement. The problem involves a program that calculates the shortest path in a graph, but it is incorrectly treating the task as a min-cut graph problem. The program should use Dijkstra's algorithm to find the shortest path. ### Components/Axes - **Problem Description**: The problem description states that numbers which start or end with zeros (such as '01' 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. - **Main Issue**: The main issue with the provided code is that it only considers direct subordinates when trying to find the k-th officer in the command spreading sequence. However, the problem asks for the order in which officers receive the command, including indirect subordinates. To fix this, we need to traverse the tree of officers and construct the command spreading sequence before finding the k-th element. ### Detailed Analysis or ### Content Details - **Problem Description**: The problem description is clear and concise. It specifies the conditions for a number to be considered a valid palindrome and the incorrect behavior of the program. - **Main Issue**: The main issue is that the program is not considering indirect subordinates when finding the k-th officer in the command spreading sequence. This is a critical error that needs to be addressed. - **Solution**: The solution involves traversing the tree of officers and constructing the command spreading sequence before finding the k-th element. This ensures that the program considers all officers, including indirect subordinates. ### Key Observations - **Invalid Palindromes**: The program incorrectly considers '00' as a valid palindrome, which is not a valid palindrome. - **Incorrect Path Calculation**: The program is incorrectly treating the task as a min-cut graph problem, which is not the correct approach. ### Interpretation The data suggests that the program is not correctly implementing the shortest path algorithm. The main issue is that the program is not considering indirect subordinates when finding the k-th officer in the command spreading sequence. This is a critical error that needs to be addressed. The solution involves traversing the tree of officers and constructing the command spreading sequence before finding the k-th element. This ensures that the program considers all officers, including indirect subordinates. The program should use Dijkstra's algorithm to find the shortest path. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/3.jpg Details</summary>  ### Visual Description ## Heatmap: Sales Performance by Region and Product Category ### Overview The heatmap displays sales performance across different regions and product categories. The color intensity represents the volume of sales, with darker shades indicating higher sales. ### Components/Axes - **X-Axis**: Represents different regions (e.g., North America, Europe, Asia). - **Y-Axis**: Represents different product categories (e.g., Electronics, Clothing, Home Goods). - **Color Legend**: Indicates the sales volume, with darker shades representing higher sales. ### Detailed Analysis or ### Content Details - **North America**: Shows the highest sales volume in the Electronics category, followed by Clothing and Home Goods. - **Europe**: Has moderate sales in all categories, with Electronics having the highest volume. - **Asia**: Exhibits the lowest sales volume across all categories. - **Color Intensity**: Darker shades indicate higher sales, with the darkest shade representing the highest sales volume. ### Key Observations - **North America**: Dominates the Electronics category with the highest sales volume. - **Europe**: Has a balanced distribution of sales across all categories. - **Asia**: Has the lowest sales volume across all categories. ### Interpretation The heatmap suggests that North America is the most lucrative market for the product categories displayed, particularly in the Electronics category. Europe has a moderate performance, while Asia shows the least sales volume. This data could be used to inform marketing strategies, resource allocation, and product development. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/4.jpg Details</summary>  ### Visual Description ## Problem Specification ### Overview 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. In their desperation, the election officials turn to you and ask you to write a program to count the vote! ### Components/Axes - **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 $2$ 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 100000 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 Marci Graham Joseph Ivors Connie Froggatt Penny Franklin Connie Froggatt Bruce Stanger Connie Froggatt Barbara Skinner *** ``` - Sample Output: ``` Connie Froggatt ``` - **Remember**: all input/output of the program should be handled through stdin and stdout. ### Detailed Analysis or ### Content Details The program should read a list of votes cast and determine the winner based on the majority rule. If a candidate has more than 50% of the votes, they are declared the winner. If no candidate has a majority, a runoff is declared. ### Key Observations - The input consists of a list of votes cast, with each line containing the name of a candidate. - The output should be the name of the winner or "Runoff" if no candidate has a majority. - The program should handle input/output through stdin and stdout. ### Interpretation The problem specification outlines a scenario where schoolboard elections are being contested. A proposal to swap school start times for elementary and high school students, a controversial new dress code proposal, and a proposal to raise real estate taxes to pay for a new football practice facility are mentioned. The election officials are seeking a program to count the votes and determine the winner based on the majority rule. The program should handle input/output through stdin and stdout. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/5.jpg Details</summary>  ### Visual Description ## 2. Incorrect Program ### Overview The image displays a screenshot of a computer program interface with a title "Incorrect Program" at the top. Below the title, there is a block of code written in Python, which is a programming language. The code is intended to create a simple voting system where users can input candidate names and vote for them. The program then calculates the total number of votes and determines the winner based on the highest number of votes. ### Components/Axes - **Title**: "Incorrect Program" - **Code Block**: The Python code is written in a text editor with syntax highlighting, indicating different elements of the code such as keywords, variables, and functions. - **Legend**: There is no legend visible in the image, as the focus is on the code and the interface. ### Detailed Analysis or ### Content Details The Python code is as follows: ```python from collections import defaultdict votes = defaultdict(int) 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") ``` ### Key Observations - The program uses a `defaultdict` from the `collections` module to count the votes for each candidate. - The `while` loop continues until the user inputs an empty string, indicating the end of the voting process. - The `sum(votes.values())` function calculates the total number of votes. - The `max(votes.values())` function finds the highest number of votes. - The list comprehension `[name for name, count in votes.items() if count == max_votes]` identifies the candidate(s) with the highest number of votes. - The program checks if there is a single winner and if the winner has more than half of the total votes. If so, it prints the winner; otherwise, it prints "Runoff". ### Interpretation The image shows a simple voting program that is intended to be run on a computer. The program is incorrect because it does not handle the case where there is a runoff between two candidates with the same highest number of votes. The program should print "Runoff" in such a case to indicate that a second round of voting is necessary. The program also does not handle the case where the user inputs an invalid candidate name, which could lead to errors or unexpected behavior. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/6.jpg Details</summary>  ### Visual Description ## Error Message ### Overview The image displays an error message from a Python program. The error message indicates that the program failed to execute a specific test case. ### Components/Axes - **Error Message**: The main text of the error message. - **Input**: A list of names, presumably the input data for the program. - **Program Output**: The output of the program, which is "Runoff!!". - **Expected Output**: The expected output of the program, which is "Connie Froggatt". ### Detailed Analysis or ### Content Details - The error message contains an example input, which is a list of names. - The program's incorrect output is "Runoff!!". - The expected output is "Connie Froggatt". ### Key Observations - The error message indicates that the program failed to execute the test case with the input "Penny Franklin". - The program's output does not match the expected output, indicating a bug or error in the program. ### Interpretation The error message suggests that the program failed to execute a specific test case with the input "Penny Franklin". The program's output is "Runoff!!", which does not match the expected output "Connie Froggatt". This indicates a bug or error in the program. The error message provides a tip on how to copy-paste the input to a file and pipe it to the program to troubleshoot the issue. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/7.jpg Details</summary>  ### Visual Description ## 4. Model Explanations ### Overview The image contains a section titled "Model Explanations" which provides two explanations for a coding issue related to determining if there is a majority of votes. The explanations are presented in a structured format with clear headings and detailed descriptions. ### Components/Axes - **Explanation 1**: This explanation discusses the code's logic for checking if the maximum votes are strictly greater than half of the total votes to determine if there is a majority. It also mentions that the code should check if the maximum votes are greater than or equal to half of the total votes. - **Explanation 2**: This explanation provides a concise explanation of the issue, stating that the code checks for a simple majority by comparing `max_votes` to `total_votes / 2`. It clarifies that if `max_votes` is equal to half of `total_votes`, it will not be considered a simple majority, and the condition should check if `max_votes` is strictly greater than half of `total_votes`. ### Detailed Analysis or ### Content Details - **Explanation 1**: The explanation emphasizes the importance of checking if the maximum votes are strictly greater than half of the total votes to ensure a clear majority. It also highlights the need to consider the case where the maximum votes are equal to half of the total votes. - **Explanation 2**: The explanation focuses on the logic of checking for a simple majority by dividing the total votes by 2. It corrects the misconception that a simple majority can be achieved if `max_votes` is equal to half of `total_votes`. ### Key Observations - **Explanation 1**: The explanation correctly identifies the need for a strict condition to determine a majority. - **Explanation 2**: The explanation correctly identifies the need for a condition that checks if `max_votes` is strictly greater than half of `total_votes` to determine a simple majority. ### Interpretation The data suggests that there are two different approaches to determining if there is a majority of votes. Explanation 1 provides a more rigorous approach by checking if the maximum votes are strictly greater than half of the total votes, while Explanation 2 provides a simpler approach by checking if `max_votes` is equal to half of `total_votes`. The interpretation highlights the importance of considering the specific requirements of the problem when determining the appropriate approach. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/8.jpg Details</summary>  ### Visual Description ## Answer Form ### Overview The image displays a screenshot of an online form titled "Answer Form." The form is designed to collect an explanation of what a program is doing wrong. The form includes a section for the user to sign in to Google to save their progress, with a link to learn more about the sign-in process. There is also a red asterisk indicating that the "Your Explanation" field is required. ### Components/Axes - **Title**: Answer Form - **Header**: Your Explanation - **Sign-in Section**: Sign in to Google to save your progress. Learn more - **Required Field**: Your Explanation * - **Explanation Field**: Your answer - **Submit Button**: Submit - **Clear Form**: Clear form - **Legend**: Not visible in the image ### Detailed Analysis or Content Details The form is designed to be interactive, with a clear call-to-action to submit the explanation. The "Your Explanation" field is highlighted in red, indicating that it is a required field. The form also includes a note that the user should provide a self-contained explanation, rather than simply copying the first model's explanation. ### Key Observations - The form is designed to be user-friendly, with clear instructions and a simple layout. - The required field is emphasized with a red asterisk, ensuring that users do not overlook this important step. - The form includes a submit button and a clear form option, making it easy for users to complete. ### Interpretation The form is likely part of a larger system or program that requires users to provide feedback or explanations. The requirement for a self-contained explanation suggests that the program may be complex or require a detailed understanding to fully comprehend. The form's design is intended to be straightforward and easy to use, with clear instructions and a simple layout. The requirement for a self-contained explanation indicates that the program may be designed to be used in a collaborative or interactive manner, where users need to provide detailed information to fully understand the program's functionality. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/9.jpg Details</summary>  ### Visual Description ## Study Tips ### Overview The image is a screenshot of a study tips document. It contains a list of advice for students to help them improve their study habits and performance. ### Components/Axes - **Title**: Study Tips - **Subtitle**: We are very grateful for your help! - **Tips**: - Make sure you understand the task first! The programs have subtle logic errors, not just simple compiler errors. - Try to write clear and concise explanations, with proper grammar and punctuation. - Feel free to use (or not use) the model explanations when writing your answers; but make sure your answer is self-contained! - The tasks vary in difficulty. Feel free to allocate your time as you see fit; we are not measuring how quickly you complete the tasks or anything like that! - Feel free to use external tools: - Use pen and paper or a whiteboard to help you reason about the task at hand. - Use a Python IDE to execute and debug the code. - Search online for help. - Have a question? Ask before moving on with the study! ### Detailed Analysis or ### Content Details The document provides practical advice for students to improve their study habits. It emphasizes the importance of understanding the task before attempting to solve it, using clear and concise explanations, and self-containment in writing answers. The document also suggests using external tools such as pen and paper, a Python IDE, and online resources to aid in understanding and solving tasks. Additionally, it encourages students to ask questions before moving on to the next task. ### Key Observations The document is well-organized and easy to read. It provides clear and concise advice for students to improve their study habits. The use of external tools and online resources is a good suggestion for students who may need additional help. ### Interpretation The document is a helpful resource for students who are looking to improve their study habits. It provides practical advice for students to improve their understanding of tasks and to use external tools to aid in their learning. The document also encourages students to ask questions before moving on to the next task, which is an important skill for students to develop. Overall, the document is a valuable resource for students who are looking to improve their study habits and performance. </details> <details> <summary>extracted/2306.09896v1/figures/appendix/instructions/10.jpg Details</summary>  ### Visual Description ## FAQ: Frequently Asked Questions ### Overview The image displays a list of frequently asked questions (FAQs) related to a study or project. The questions are presented in a bulleted format, and the answers are provided below each question. ### Components/Axes - **Question 1**: "Are you collecting data as I visit the website?" - **Answer**: "No - none at all. Only your final answers are recorded." - **Question 2**: "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." - **Question 3**: "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." ### Detailed Analysis or ### Content Details The image does not contain any charts, diagrams, or data tables. It is a straightforward list of questions and answers. ### Key Observations - The questions are related to a study or project that involves models fixing code. - The answers indicate that data collection is not ongoing, and only final answers are recorded. - The study aims to investigate the effectiveness of models in fixing code when given human feedback. - The model explanations are not evaluated for usefulness but are provided to help with debugging. ### Interpretation The data suggests that the study is focused on evaluating the performance of models in fixing code when given human feedback. The answers indicate that data collection is not ongoing, and only final answers are recorded. The study aims to investigate the effectiveness of models in fixing code when given human feedback. The model explanations are not evaluated for usefulness but are provided to help with debugging. The overall interpretation is that the study is focused on evaluating the performance of models in fixing code when given human feedback. </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 $20· 2· 2=80$ 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