2507.02778v2

# Self-Correction Bench: Uncovering and Addressing the Self-Correction Blind Spot in Large Language Models **Authors**: - Ken Tsui (Independent Researcher) Abstract Although large language models (LLMs) have transformed AI, they still make mistakes and can explore unproductive reasoning paths. Self-correction capability is essential for deploying LLMs in safety-critical applications. We uncover a systematic failure: LLMs cannot correct errors in their own outputs while successfully correcting identical errors from external sources - a limitation we term the Self-Correction Blind Spot. To study this phenomenon, we introduce Self-Correction Bench, an evaluation framework to measure this phenomenon through controlled error injection at three complexity levels. Testing 14 open-source non-reasoning models, we find an average 64.5% blind spot rate. We provide multiple lines of evidence suggesting this limitation may be influenced by training data: human demonstrations rarely include error-correction sequences (favoring error-free responses), whereas reinforcement learning (RL) trained models learn error correction via outcome feedback. Remarkably, appending a minimal “ Wait ” prompt activates a 89.3% reduction in blind spots, suggesting dormant capabilities that require triggering. Our work highlights a critical limitation potentially influenced by training distribution and offers a practical approach to enhance LLM reliability and trustworthiness - vital for safety-critical domains. 1 Introduction Large Language Models (LLMs) have rapidly advanced natural language processing, achieving state-of-the-art results on a diverse range of tasks (OpenAI et al., 2024; Anthropic, 2024; Gemini Team, 2025; Yang et al., 2025; Meta, 2025; DeepSeek-AI et al., 2025a). However, despite their impressive capabilities, LLMs are known to exhibit unpredictable failures and generate inaccurate information (Maynez et al., 2020; Huang et al., 2025; Bang et al., 2023; Shi et al., 2023), or explore an unproductive reasoning path and commit to it. A particularly concerning issue is that LLMs can make errors even in simple tasks (Nezhurina et al., 2025), despite having the necessary underlying knowledge to provide the correct solutions, raising reliability concerns that hinder deployment in critical applications. Studying LLM self-correction behavior in natural settings is challenging due to their inherent accuracy; the rarity of naturally occurring errors makes systematic evaluation challenging. To address this, we construct Self-Correction Bench by systematically injecting error into the LLM reasoning traces, enabling us to test self-correction in reproducible scenarios and quantifying performance reliably. Our results reveal that LLMs fail to correct their own errors (64.5% average failure rate), but reliably fix identical errors from external sources. We refer to this phenomenon as the Self-Correction Blind Spot. This rules out knowledge deficiency as the root cause - instead, the blind spot stems from a lack of activation for self-correction. Strikingly, appending a simple “ Wait ” reduces the blind spot by 89.3%, confirming minimum prompt can unlock latent correction abilities. We provide a behavioral explanation for why “ Wait ” works, supported by systematic analysis of correction marker patterns in post-training data. We also analyze why RL-trained reasoning models do not have such blind spot. Our contributions are threefold. - Discovery of Self-Correction Blind Spot: a systematic failure of LLMs to correct their own errors despite competency on external ones — potentially influenced by post-training data biases where human demonstrations rarely include self-correction sequences, unlike RL models that learn error-correction through outcome feedback. - Self-Correction Bench: a controlled evaluation framework with error-injected reasoning traces for fair cross-model comparison. - Effective intervention: appending “ Wait ” reduces blind spots by 89.3% - demonstrating that activation is the limiting factor. These results advance both our understanding of LLM reasoning flaws and provide a practical solution to improve their reliability in real-world use. 2 Related work Intrinsic self-correction in LLMs. Recent work has highlighted intrinsic self-correction, where LLMs generate feedback on their own outputs (Shinn et al., 2023; Madaan et al., 2023; Kim et al., 2023; Kamoi et al., 2024a), as a way to improve performance, but critical limitations persist. Self-feedback quality is limited by the model’s existing knowledge, and without oracle labels, LLMs struggle to correct errors (Huang et al., 2024): prior studies attribute this to poor error localization (Tyen et al., 2024) and detection (Kamoi et al., 2024b). Most approaches rely on multi-step prompting, whereas we focus on single-pass inference (self-correction in one completion) and study limitations from a cognitive perspective - rather than just knowledge bounds. Related work using RL for self-correction (Kumar et al., 2025) or training signals from ground truth (DeepSeek-AI et al., 2025a) contrasts with our test-time, no-finetuning approach. Prompt injection for evaluation. Traditional prompt injection research focuses on adversarial manipulation (e.g., attackers injecting malicious instructions to distort outputs) (Wei et al., 2023; Liu et al., 2024). Controlled error injection to evaluate self-correction is underexplored. For example, Lanham et al. (2023) injected mistakes into reasoning chains to measure consistency between steps and conclusions, but not self-correction capability. Our work advances this by systematically injecting errors across task complexities to reveal uncharacterized blind spots in how LLMs correct themselves. Hallucination snowballing. Zhang et al. (2024) demonstrate that once LLMs hallucinate, subsequent tokens often align with the initial error, a “snowball” effect, suggesting inherent limits to self-correction during generation. We explain this phenomenon by identifying Self-Correction Blind Spot: LLMs reliably correct errors in external inputs, but fail to correct errors in their own outputs. This distinction is critical to understanding why snowballing persists. Test-time interventions. Recent efforts have shifted compute from training to test time (Snell et al., 2025), yielding improved performance (e.g. Muennighoff et al. (2025) appends “Wait” to force longer reasoning traces). While these methods work, the reason of improvement remains understudied. We provide a behavioral explanation by testing unfinetuned models: interventions activate otherwise inactive self-correction mechanisms, therefore improving performance in tasks where models might make error. Cognitive bias in LLM. LLMs exhibit human-like cognitive biases (Koo et al., 2024; Echterhoff et al., 2024; Jones and Steinhardt, 2022), and we link the bias blind spot (the tendency to overlook one’s own biases) (Pronin et al., 2002) to impaired self-correction. This connects high-level cognitive limitations to the fine-grained failure mode we characterize. Our work integrates these threads into a systematic methodology for testing self-correction, reveals that LLMs suffer from a fundamental blind spot (inability to correct their own errors), and demonstrates how test-time interventions can activate dormant self-correction mechanisms without finetuning. 3 Conceptual motivation Building on these insights, we now formalize the theoretical framework underlying our empirical investigation. We provide conceptual motivation for our empirical study, focusing on error states, self-correction mechanisms, and their measurement. 3.1 Error and self-correction: the case for marginalization Autoregressive LLMs cannot guarantee every generated token is correct as the number of token grows, resulting in hallucination (Maynez et al., 2020), snowballing errors (Zhang et al., 2024), or unproductive reasoning path or execution flaws. Thus, self-correction is necessary for robustness: models must reverse errors to produce a correct answer. Please note that a correct answer does not require all previously generated tokens to be correct, as one might be concerned only with the final answer. To formalize this, let $\mathcal{E}=\{e_{0},e_{1},...,e_{k}\}$ denote a set of mutually exclusive and collectively exhaustive discrete error states, where $e_{0}$ represents the “no error” state, and $e_{1},...,e_{k}$ represent distinct error conditions. For each state $e_{i}∈\mathcal{E}$ , let $R_{e_{i}}$ denote the response set. The probability of a model, $M$ , giving a correct answer can be marginalized over error states: $$ \displaystyle P_{M}(r_{correct})=\sum_{e\in\mathcal{E}}P_{M}(e)\cdot P_{M}(r_{correct}|e)=\sum_{e\in\mathcal{E}}\sum_{r_{m}\in R_{e}}P_{M}(e)\cdot P_{M}(r_{m}|e)\cdot P_{M}(r_{correct}|r_{m},e), \tag{1} $$ where $r_{m}$ is the model’s response, and $P_{M}(r_{correct}|r_{m},e)$ captures self-correction of $r_{m}$ . Here, $P_{M}(r_{correct})$ depends critically on self-correction: even with frequent errors, high $P_{M}(r_{correct}|r_{m},e)$ can yield strong performance. Error-free generation is a special case of this framework - not the only path to correctness. 3.2 External and internal self-correction, and Self-Correction Blind Spot We distinguish self-correction by error source: 1. Internal correction: Metacognitive monitoring of the model’s own initial response $r_{m}$ . 1. External correction: Evaluation of errors in the user prompt $r_{u}$ . This distinction is motivated by the cognitive bias, “bias blind spot”. Pronin et al. (2002) show that humans are able to identify cognitive biases in others while failing to see those same biases in themselves, suggesting LLMs trained on human demonstration might share this limitation. To quantify this, we define the Self-Correction Blind Spot as: $$ \displaystyle\text{Self-Correction Blind Spot}=\begin{cases}1-\frac{P_{M}(r_{correct}|r_{m},e)}{P_{M}(r_{correct}|r_{u},e)}&\text{if }P_{M}(r_{correct}|r_{u},e)>0\\ 0&\text{if }P_{M}(r_{correct}|r_{u},e)=0\end{cases} \tag{2} $$ A value of 1 indicates a total blind spot: the model can correct external errors but not its own. By design, the Self-Correction Blind Spot isolates confounding factors, including internal model knowledge. 3.3 Controlled error injection: measuring self-correction in practice The marginalization framework (Equation 1) is intractable in practice: $P_{M}(e)$ , the true probability of error states, is unobservable as LLMs operate over infinite prompt spaces. To solve this, we introduce controlled error $e_{controlled}$ . For internal correction, we inject an incorrect partial response into the model’s “own” output (omitting stop tokens to allow continuation/self-correction); for external correction, we inject the same error into the user prompt instead. We empirically estimate $P_{M}(r_{correct}|r_{m},e_{controlled})$ and $P_{M}(r_{correct}|r_{u},e_{controlled})$ by measuring $P_{M}(r_{correct})$ when controlled error is injected in $r_{m}$ and $r_{u}$ respectively, which forms the basis of our Self-Correction Bench. This framework - marginalizing over errors, distinguishing internal/external correction, and using controlled injection - provides the conceptual underpinning for our empirical analysis. 4 Self-Correction Bench Having established the theoretical foundation, we introduce a benchmark to measure Self-Correction Blind Spot in LLMs across varying task complexities, enabling diagnosis of where correction fails. By progressing from simple to realistic errors, we isolate confounding factors such as knowledge limits or reasoning complexity. Our benchmark comprises three datasets (see Table 1), with controlled error injection to compare performance under identical conditions. For each dataset, we systematically inject identical error into both model response ( $r_{m}$ ) and user prompt ( $r_{u}$ ), allowing empirical estimation of both correction probabilities $P_{M}(r_{correct}|r_{m},e_{controlled})$ and $P_{M}(r_{correct}|r_{u},e_{controlled})$ under identical error conditions. Unlike Zheng et al. (2025) and Song et al. (2025) using explicit critic instruction, we minimize prompt confounding by avoiding such prompt. Figure 1 illustrates how we inject error in user message (i.e. external error) and in model (i.e. internal error), respectively, via chat template. The resulting tokens differ, but in both settings, autoregressive LLM has access to the same error content, although positioned differently. <|start_header_id |>user<|end_header_id|>\n\n What is the answer of 1 + 1? <|eot_id|><|start_header_id|>assistant <|end_header_id |>\n\n The answer is 3. <|eot_id|> Error Injection in Model <|start_header_id |>user<|end_header_id|>\n\n What is the answer of 1 + 1? The answer is 3. <|eot_id|><|start_header_id|>assistant <|end_header_id |>\n\n I’m afraid that’s not correct. The answer to the equation 1 + 1 is actually 2, not 3. Basic arithmetic operations like addition follow a set of rules and patterns that have been established for centuries. In this case, when you add 1 to 1, you are counting two units, which equals 2.\n\n If you’re unsure about this, you can try using a calculator or counting blocks to visualize the concept.<|eot_id|> Error Injection in User Message Figure 1: Example of error injection. Grey color shows model completion. Above: Error injection in model; Below: Error injection in user message Table 1: Dataset comparison | Dataset | Complexity | Realism of Error | Reasoning | Size | | --- | --- | --- | --- | --- | | SCLI5 | Low | Low | N | 286 | | GSM8K-SC | Medium | Medium | Y | 1,313 | | PRM800K-SC | High | High | Y | 448 | 4.1 Self-correct Like I am 5 (SCLI5) SCLI5 isolates basic correction by introducing simple answer errors (e.g., off-by-one, flip) to trivial tasks (i.e. no reasoning required, just answer recall). Programmatic error generation ensures we test the simplest possible correction: if models cannot detect obvious errors, subtle ones are impossible. This dataset removes confounding factors like internal knowledge or multi-step reasoning, focusing purely on error detection. The composition of the task is shown in Table 6. 4.2 GSM8K-SC Built from Cobbe et al. (2021), a multi-step reasoning dataset, GSM8K-SC injects different types of reasoning errors as shown in Table 7 that propagate to incorrect answer. We use ‘gpt-4.1-2025-04-14’ (OpenAI, 2025) to generate controlled errors and ‘gemini-2.5-flash-preview-05-20’ (Gemini Team, 2025) to validate that incorrect reasoning leads to inconsistent answers, resulting in 1,313 high-quality samples. This dataset tests correction in multi-step reasoning, a middle ground between simplicity and realism. The prompt can be found in Appendix D.1. 4.3 PRM800K-SC PRM800K (Lightman et al., 2024), derived from a subset of MATH (Hendrycks et al., 2021), provides step-by-step annotations of multi-step reasoning. We selected 448 samples where the generated answers mismatch ground truth, capturing errors from real-world LLM use. This progression from simple answer errors to realistic failures, lets us map exactly where self-correction breaks down, making the benchmark a powerful tool for diagnosing and improving LLM robustness. 5 Experiment 5.1 Experiment setup We evaluated a wide range of open-source LLMs, as close-source models lack support for fine-grained control of prefix inject critical for our methodology. We apply model-specific chat templates using ‘transformers’ library (Wolf et al., 2020). We leverage the DeepInfra https://deepinfra.com/ completion API with 0.0 temperature as models’ most confident prediction should help self-correction, and a fixed token budget of 1,024 to isolate the effect of test time compute. We provide more rationales of our choices and perform sensitivity analysis in the Appendix C, confirming results are robust. Evaluation. We use ‘gemini-2.5-flash-preview-05-20’ to compare LLMs’ completion against the ground-truth answer. We instruct the model to output in JSON format. Due to the objectivity of the task and the provision of ground truth in the prompt, we do not believe there is significant bias. The prompt is provided in the Appendix D.2. We manually review 100 samples for each dataset to ensure evaluation quality. Metrics. We evaluate if LLMs can self-correct and arrive at the ground-truth answer given an error. In GSM8K-SC and PRM800K-SC, we measure the behavior of LLMs before commit an answer, as it is a more common scenario when an LLM backtracks, although we also report that after commit an answer. We report mean accuracy ( $P_{M}(r_{correct})$ ) and Self-Correction Blind Spot for each model. For statistical rigor, we report 95% confidence interval, which is estimated by adding and subtracting 1.96 * standard error of mean (SEM) from mean. The SEM is estimated using the formula $\sigma_{M}=\frac{\sigma}{\sqrt{N}}$ , where N is the sample size and $\sigma$ is the sample standard deviation. 5.2 Result Table 2: Mean accuracy and 95% confidence interval of models at temperature 0.0 | Model | SCLI5 | GSM8K-SC | PRM800K-SC | | --- | --- | --- | --- | | Llama-4-Maverick-17B-128E-Instruct-FP8 (Meta, 2025) | 0.948 ± 0.026 | 0.416 ± 0.027 | 0.455 ± 0.046 | | DeepSeek-V3-0324 (DeepSeek-AI et al., 2025b) | 0.825 ± 0.044 | 0.399 ± 0.026 | 0.475 ± 0.046 | | Qwen2.5-72B-Instruct (Qwen et al., 2025) | 0.92 ± 0.032 | 0.58 ± 0.027 | 0.154 ± 0.033 | | Llama-4-Scout-17B-16E-Instruct (Meta, 2025) | 0.976 ± 0.018 | 0.24 ± 0.023 | 0.263 ± 0.041 | | Llama-3.3-70B-Instruct (Meta, 2024) | 0.538 ± 0.058 | 0.275 ± 0.024 | 0.246 ± 0.04 | | Qwen3-235B-A22B footnotemark: (Yang et al., 2025) | 0.563 ± 0.058 | 0.073 ± 0.014 | 0.348 ± 0.044 | | phi-4 (Abdin et al., 2024) | 0.808 ± 0.046 | 0.076 ± 0.014 | 0.092 ± 0.027 | | Qwen2.5-7B-Instruct (Qwen et al., 2025) | 0.559 ± 0.058 | 0.19 ± 0.021 | 0.141 ± 0.032 | | Qwen2-7B-Instruct (Yang et al., 2024) | 0.601 ± 0.057 | 0.078 ± 0.014 | 0.058 ± 0.022 | | Qwen3-14B footnotemark: (Yang et al., 2025) | 0.004 ± 0.007 | 0.092 ± 0.016 | 0.254 ± 0.04 | | Qwen3-30B-A3B footnotemark: (Yang et al., 2025) | 0.056 ± 0.027 | 0.061 ± 0.013 | 0.194 ± 0.037 | | Llama-3.1-8B-Instruct (Grattafiori et al., 2024) | 0.136 ± 0.04 | 0.019 ± 0.007 | 0.02 ± 0.013 | | Qwen3-32B footnotemark: (Yang et al., 2025) | 0.004 ± 0.007 | 0.05 ± 0.012 | 0.083 ± 0.026 | | Mistral-Small-24B-Instruct-2501 (Team, 2025) | 0.042 ± 0.023 | 0.011 ± 0.006 | 0.016 ± 0.012 | - Qwen3 series models use non-thinking mode. In Table 2, we summarizes mean accuracy and 95% confidence interval of state-of-the-art non-reasoning LLMs. We observe notably low accuracy for SCLI5 in some models. We observe moderate to strong positive correlations between SCLI5, GSM8K-SC and PRM800K-SC (see Figure 5), suggesting that there is a limitation of LLMs to self-correct across task complexities. If LLMs cannot self-correct either easy or hard tasks, it implies an activation problem rather than a knowledge problem. In Figure 6, we show some models (e.g. Qwen3-32B, LLama3.1-8B-Instruct and Mistral-Small-24B-Instruct-2501) frequently give empty responses, highlighting unawareness of error. We identify statistically significant Self-Correction Blind Spot for most models (see Figure 2). The blind spot, on average, 64.5%, exists across models, regardless of model sizes. We observe moderate correlation across datasets (see Figure 3), indicating a fundamental rather than task-specific limitation. On average, when a model has committed an answer, it has a much higher blind spot to recognize its own error, a finding similar to Zhang et al. (2024). <details> <summary>images/blind_spot_summary_default_non_reasoning.png Details</summary>  ### Visual Description ## Chart Type: Bar Chart with Error Bars ### Overview The image is a bar chart comparing the self-correction blind spot across different models. The chart displays the performance of various models using different datasets, with error bars indicating the 95% confidence intervals. The x-axis represents the models, and the y-axis represents the self-correction blind spot. The legend distinguishes between different datasets and whether the data is "before commit answer" or "after commit answer". ### Components/Axes * **Title:** Blind Spot summary across datasets - 95% Confidence Intervals * **X-axis:** Models (List of models is provided below) * **Y-axis:** Self-Correction Blind Spot, scale from 0.0 to 1.0 in increments of 0.2. * **Legend:** Located in the top-left corner. * SCLI5 (Blue) * GSM8K-SC (Before commit answer) (Orange) * GSM8K-SC (After commit answer) (Light Orange) * PRM800K-SC (Before commit answer) (Green) * PRM800K-SC (After commit answer) (Light Green) * **Models (X-Axis Labels):** * Llama-4-Maverick-17B-128E-Instruct-FP8 * DeepSeek-V3-0324 * Qwen2.5-72B-Instruct * Llama-4-Scout-17B-16E-Instruct-FP8-dynamic * Llama-3.3-70B-Instruct * Qwen3-235B-A22B * Phi-4 * Qwen2.5-7B-Instruct * Qwen2-7B-Instruct * Qwen3-14B * Qwen3-30B-A3B * Llama-3.1-8B-Instruct * Qwen3-32B * Mistral-Small-24B-Instruct-2501 ### Detailed Analysis Here's a breakdown of the data for each model, noting the approximate values and trends: **Llama-4-Maverick-17B-128E-Instruct-FP8:** * SCLI5 (Blue): ~0.04 * GSM8K-SC (Before): ~0.52 * GSM8K-SC (After): ~0.65 * PRM800K-SC (Before): ~0.80 * PRM800K-SC (After): ~0.55 **DeepSeek-V3-0324:** * SCLI5 (Blue): ~0.08 * GSM8K-SC (Before): ~0.58 * GSM8K-SC (After): ~0.82 * PRM800K-SC (Before): ~0.38 * PRM800K-SC (After): ~0.40 **Qwen2.5-72B-Instruct:** * SCLI5 (Blue): ~0.78 * GSM8K-SC (Before): ~0.70 * GSM8K-SC (After): ~0.80 * PRM800K-SC (Before): ~0.70 * PRM800K-SC (After): ~0.70 **Llama-4-Scout-17B-16E-Instruct-FP8-dynamic:** * SCLI5 (Blue): ~0.02 * GSM8K-SC (Before): ~0.75 * GSM8K-SC (After): ~0.90 * PRM800K-SC (Before): ~0.55 * PRM800K-SC (After): ~0.60 **Llama-3.3-70B-Instruct:** * SCLI5 (Blue): ~0.35 * GSM8K-SC (Before): ~0.65 * GSM8K-SC (After): ~0.95 * PRM800K-SC (Before): ~0.90 * PRM800K-SC (After): ~0.90 **Qwen3-235B-A22B:** * SCLI5 (Blue): ~0.45 * GSM8K-SC (Before): ~0.90 * GSM8K-SC (After): ~0.95 * PRM800K-SC (Before): ~0.55 * PRM800K-SC (After): ~0.60 **Phi-4:** * SCLI5 (Blue): ~0.18 * GSM8K-SC (Before): ~0.85 * GSM8K-SC (After): ~0.20 * PRM800K-SC (Before): ~0.80 * PRM800K-SC (After): ~0.85 **Qwen2.5-7B-Instruct:** * SCLI5 (Blue): ~0.15 * GSM8K-SC (Before): ~0.58 * GSM8K-SC (After): ~0.85 * PRM800K-SC (Before): ~0.20 * PRM800K-SC (After): ~0.85 **Qwen2-7B-Instruct:** * SCLI5 (Blue): ~0.90 * GSM8K-SC (Before): ~0.90 * GSM8K-SC (After): ~0.95 * PRM800K-SC (Before): ~0.90 * PRM800K-SC (After): ~0.90 **Qwen3-14B:** * SCLI5 (Blue): ~0.90 * GSM8K-SC (Before): ~0.85 * GSM8K-SC (After): ~0.95 * PRM800K-SC (Before): ~0.90 * PRM800K-SC (After): ~0.90 **Qwen3-30B-A3B:** * SCLI5 (Blue): ~0.80 * GSM8K-SC (Before): ~0.95 * GSM8K-SC (After): ~0.95 * PRM800K-SC (Before): ~0.80 * PRM800K-SC (After): ~0.80 **Llama-3.1-8B-Instruct:** * SCLI5 (Blue): ~0.85 * GSM8K-SC (Before): ~0.80 * GSM8K-SC (After): ~0.95 * PRM800K-SC (Before): ~0.90 * PRM800K-SC (After): ~0.90 **Qwen3-32B:** * SCLI5 (Blue): ~0.90 * GSM8K-SC (Before): ~0.90 * GSM8K-SC (After): ~0.95 * PRM800K-SC (Before): ~0.90 * PRM800K-SC (After): ~0.90 **Mistral-Small-24B-Instruct-2501:** * SCLI5 (Blue): ~0.90 * GSM8K-SC (Before): ~0.90 * GSM8K-SC (After): ~0.95 * PRM800K-SC (Before): ~0.90 * PRM800K-SC (After): ~0.90 ### Key Observations * The SCLI5 dataset (blue bars) generally shows lower self-correction blind spots compared to the other datasets for most models, except for the last few models where it is comparable. * GSM8K-SC (Before commit answer) and GSM8K-SC (After commit answer) datasets (orange and light orange bars) often show high self-correction blind spots. * The error bars indicate the variability in the results, with some models showing wider confidence intervals than others. * For some models, there is a noticeable difference between the "before commit answer" and "after commit answer" results, suggesting that the commit status affects the self-correction blind spot. ### Interpretation The bar chart provides a comparative analysis of the self-correction blind spot across different models and datasets. The data suggests that the choice of model and dataset significantly impacts the self-correction blind spot. The 95% confidence intervals provide a measure of the reliability of the results. The differences between "before commit answer" and "after commit answer" results highlight the importance of considering the commit status when evaluating model performance. The chart allows for identifying models that perform well across different datasets and those that are more sensitive to the choice of dataset. </details> Figure 2: Self-Correction Blind Spot and 95% confidence interval across models <details> <summary>images/blind_spot_correlation_bca_non_reasoning.png Details</summary>  ### Visual Description ## Chart/Diagram Type: Correlation Analysis of Blind Spot Scores ### Overview The image presents a correlation analysis of blind spot scores across different language models (SCL15, GSM8K-SC (BCA), and PRM800K-SC (BCA)). It includes a correlation matrix and two scatter plots comparing the blind spot scores of these models. ### Components/Axes **1. Correlation Matrix (Left)** * **Title:** Blind Spot correlation matrix * **Axes Labels:** * X-axis: SCL15, GSM8K-SC (BCA), PRM800K-SC (BCA) * Y-axis: SCL15, GSM8K-SC (BCA), PRM800K-SC (BCA) * **Color Scale:** Ranges from -1.00 (blue) to 1.00 (red), with 0.25 increments marked. **2. Scatter Plot 1 (Center)** * **Title:** Blind Spot correlation: SCL15 vs GSM8K-SC (BCA) (r = 0.667) * **Axes Labels:** * X-axis: SCLI5 Blind Spot Score * Y-axis: GSM8K-SC (BCA) Blind Spot Score * **Axis Scale:** Both axes range from 0.0 to 1.0, with 0.2 increments. * **Data Points:** Blue circles, each labeled with a model name. * **Trend Line:** Dashed red line. * **Reference Line:** Dotted gray line labeled "Perfect correlation". **3. Scatter Plot 2 (Right)** * **Title:** Blind Spot correlation: GSM8K-SC (BCA) vs PRM800K-SC (BCA) (r = 0.619) * **Axes Labels:** * X-axis: GSM8K-SC (BCA) Blind Spot Score * Y-axis: PRM800K-SC (BCA) Blind Spot Score * **Axis Scale:** Both axes range from 0.3 to 1.0, with 0.1 increments. * **Data Points:** Green circles, each labeled with a model name. * **Trend Line:** Dashed red line. * **Reference Line:** Dotted gray line labeled "Perfect correlation". ### Detailed Analysis or ### Content Details **1. Correlation Matrix** | | SCL15 | GSM8K-SC (BCA) | PRM800K-SC (BCA) | | :---- | :---- | :------------- | :---------------- | | SCL15 | 1 | 0.67 | 0.41 | | GSM8K-SC (BCA) | 0.67 | 1 | 0.62 | | PRM800K-SC (BCA) | 0.41 | 0.62 | 1 | **2. Scatter Plot 1: SCL15 vs GSM8K-SC (BCA)** * **Trend:** The dashed red line shows a positive correlation. As SCL15 blind spot score increases, GSM8K-SC (BCA) blind spot score tends to increase as well. * **Data Points:** * Qwen2-7B-Instruct: SCL15 ~0.1, GSM8K-SC ~0.9 * Qwen2.5-7B-Instruct: SCL15 ~0.15, GSM8K-SC ~0.8 * Qwen2.5-72B-Instruct: SCL15 ~0.15, GSM8K-SC ~0.4 * Llama-4-Scout-17B...: SCL15 ~0.2, GSM8K-SC ~0.5 * DeepSeek-V3-0324: SCL15 ~0.2, GSM8K-SC ~0.6 * Llama-4-Maverick-...: SCL15 ~0.2, GSM8K-SC ~0.5 * Llama-3.3-70B-Ins..: SCL15 ~0.6, GSM8K-SC ~0.7 * Qwen3-235B-A22B: SCL15 ~0.9, GSM8K-SC ~0.95 * Llama-3.1: SCL15 ~0.95, GSM8K-SC ~1.0 * Mistral-Small-24B...: SCL15 ~0.95, GSM8K-SC ~1.0 * Qwen3-32B: SCL15 ~0.95, GSM8K-SC ~0.95 * Qwen3-14B: SCL15 ~0.95, GSM8K-SC ~0.95 **3. Scatter Plot 2: GSM8K-SC (BCA) vs PRM800K-SC (BCA)** * **Trend:** The dashed red line shows a positive correlation. As GSM8K-SC (BCA) blind spot score increases, PRM800K-SC (BCA) blind spot score tends to increase as well. * **Data Points:** * DeepSeek-V3-0324: GSM8K-SC ~0.5, PRM800K-SC ~0.4 * Llama-4-Maverick-...: GSM8K-SC ~0.5, PRM800K-SC ~0.35 * Llama-3.3-70B-Ins...: GSM8K-SC ~0.7, PRM800K-SC ~0.35 * Qwen2.5-72B-Instruct: GSM8K-SC ~0.4, PRM800K-SC ~0.75 * Llama-4-Scout-17B...: GSM8K-SC ~0.85, PRM800K-SC ~0.5 * Qwen3-235B-A22B: GSM8K-SC ~0.9, PRM800K-SC ~0.5 * Qwen3-14B: GSM8K-SC ~0.9, PRM800K-SC ~0.6 * Qwen2.5-7B-Instr: GSM8K-SC ~0.75, PRM800K-SC ~0.75 * Qwen3-30B-A3B: GSM8K-SC ~0.8, PRM800K-SC ~0.9 * Qwen2-7B-Instruct: GSM8K-SC ~0.9, PRM800K-SC ~0.95 * Qwen3-32B1-8B-Inst...: GSM8K-SC ~0.9, PRM800K-SC ~0.95 * Phi-4: GSM8K-SC ~0.9, PRM800K-SC ~0.95 * Mistral-Small-24B...: GSM8K-SC ~0.95, PRM800K-SC ~1.0 ### Key Observations * The correlation matrix shows moderate positive correlations between the blind spot scores of the three models. * The scatter plots visually confirm these positive correlations, with data points generally trending upwards. * The correlation coefficient (r) is 0.667 for SCL15 vs GSM8K-SC (BCA) and 0.619 for GSM8K-SC (BCA) vs PRM800K-SC (BCA), indicating a moderate positive linear relationship. * The models exhibit a range of blind spot scores, with some models consistently scoring higher or lower across different benchmarks. * The "Perfect correlation" line serves as a reference, showing how closely the models' scores align. ### Interpretation The data suggests that there is a tendency for models with higher blind spot scores on one benchmark to also have higher scores on other benchmarks. However, the moderate correlation coefficients indicate that the relationship is not perfect, and there are variations in model performance across different benchmarks. This could be due to the specific characteristics of each benchmark or the different strengths and weaknesses of the models. The scatter plots provide a more detailed view of the relationship between the models' scores, highlighting specific models that deviate from the general trend. The correlation matrix provides a high-level overview of the relationships between the three models. </details> Figure 3: left: Blind spot correlation matrix middle: Scatter plot between SCLI5 vs GSM8K-SC right: Scatter plot between GSM8K-SC vs PRM800K-SC BCA: Before commit an answer 6 Analysis 6.1 How do LLMs self-correct? Analysis of model responses reveals that external errors trigger 179.5% and 73.6% more correction markers Correction markers include “ Wait, “ But ”, “ However ”, “ No ”, “ Hold on ”, “ Hang on ”, “ Alternatively ”, “ Hmm ”. in GSM8K-SC and PRM800K-SC respectively. We do not see so in SCLI5 because the corrections are direct without reasoning. This finding leads us to perform a causal intervention. We append “ Wait ” after incorrect reasoning or answer to prompt LLMs to self-correct, without finetuning. We observe significant reductions in the blind spot after appending “ Wait ”, in some cases, a negative blind spot (see Figure 7). Averaging across models and datasets, the reduction amounts to 89.3%, and the macro average of mean accuracy increases by 156.0% (see Figure 4). <details> <summary>images/error_injection_model_macro_averages_non_reasoning_no_wait_vs_wait.png Details</summary>  ### Visual Description ## Bar Chart: Macro average accuracy increases from original to appended Wait ### Overview The image is a bar chart comparing the macro average accuracy of different models in their original state versus with an "appended Wait" modification. The chart displays the accuracy values for each model using paired bars, with one bar representing the original accuracy and the other representing the accuracy after the "appended Wait" modification. The models are listed along the x-axis, and the macro average accuracy is represented on the y-axis. ### Components/Axes * **Title:** Macro average accuracy increases from original to appended Wait * **X-axis:** Models (List of model names) * **Y-axis:** Macro average accuracy (Scale from 0.0 to 0.8 in increments of 0.2) * **Legend:** Located in the top-right corner. * Red: Original * Brown: Appended Wait ### Detailed Analysis The chart presents a comparison of macro average accuracy for various models under two conditions: "Original" and "Appended Wait". Each model has two bars associated with it, representing these two conditions. Here's a breakdown of the data for each model: 1. **Llama-4-Maverick-17B-128E-Instruct-FP8:** * Original (Red): 0.606 * Appended Wait (Brown): 0.842 * Trend: Significant increase in accuracy with "Appended Wait". 2. **DeepSeek-V3-0324:** * Original (Red): 0.567 * Appended Wait (Brown): 0.902 * Trend: Substantial increase in accuracy with "Appended Wait". 3. **Qwen2.5-72B-Instruct:** * Original (Red): 0.551 * Appended Wait (Brown): 0.770 * Trend: Noticeable increase in accuracy with "Appended Wait". 4. **Llama-4-Scout-17B-16E-Instruct-FP8-dynamic:** * Original (Red): 0.493 * Appended Wait (Brown): 0.764 * Trend: Significant increase in accuracy with "Appended Wait". 5. **Llama-3.3-70B-Instruct:** * Original (Red): 0.353 * Appended Wait (Brown): 0.727 * Trend: Large increase in accuracy with "Appended Wait". 6. **Qwen3-235B-A22B:** * Original (Red): 0.328 * Appended Wait (Brown): 0.856 * Trend: Very large increase in accuracy with "Appended Wait". 7. **Phi-4:** * Original (Red): 0.325 * Appended Wait (Brown): 0.701 * Trend: Substantial increase in accuracy with "Appended Wait". 8. **Qwen2.5-7B-Instruct:** * Original (Red): 0.297 * Appended Wait (Brown): 0.670 * Trend: Significant increase in accuracy with "Appended Wait". 9. **Qwen2-7B-Instruct:** * Original (Red): 0.246 * Appended Wait (Brown): 0.586 * Trend: Large increase in accuracy with "Appended Wait". 10. **Qwen3-14B:** * Original (Red): 0.117 * Appended Wait (Brown): 0.868 * Trend: Extremely large increase in accuracy with "Appended Wait". 11. **Qwen3-30B-A3B:** * Original (Red): 0.104 * Appended Wait (Brown): 0.860 * Trend: Extremely large increase in accuracy with "Appended Wait". 12. **Llama-3.1-8B-Instruct:** * Original (Red): 0.058 * Appended Wait (Brown): 0.524 * Trend: Very large increase in accuracy with "Appended Wait". 13. **Qwen3-32B:** * Original (Red): 0.045 * Appended Wait (Brown): 0.793 * Trend: Extremely large increase in accuracy with "Appended Wait". 14. **Mistral-Small-24B-Instruct-2501:** * Original (Red): 0.023 * Appended Wait (Brown): 0.666 * Trend: Extremely large increase in accuracy with "Appended Wait". ### Key Observations * Across all models, the "Appended Wait" modification consistently results in a significant increase in macro average accuracy compared to the original model. * The models Qwen3-14B, Qwen3-30B-A3B, Llama-3.1-8B-Instruct, Qwen3-32B and Mistral-Small-24B-Instruct-2501 show the most dramatic improvements in accuracy with the "Appended Wait" modification, starting from very low original accuracy scores. * The models DeepSeek-V3-0324 and Qwen3-235B-A22B achieve the highest accuracy scores after the "Appended Wait" modification. ### Interpretation The data strongly suggests that the "Appended Wait" modification is highly effective in improving the macro average accuracy of the tested models. The consistent and often substantial increases in accuracy across different models indicate that this modification could be a valuable technique for enhancing model performance. The models that initially had lower accuracy scores experienced the most significant gains, suggesting that "Appended Wait" may be particularly beneficial for models that are not performing optimally in their original configurations. </details> Figure 4: Macro average accuracy by non-reasoning model increases from original to appended “ Wait ” This evidence leads us to believe that “ Wait ” and similar correction markers serve as a strong conditioning token that shift the model’s probability distribution toward self-evaluation sequences - it artificially triggers the correction pathway that external errors naturally activate. We validate multiple markers to demonstrate generalization that they can activate self-correction across models and datasets (see Table 8). All of them work, but “Wait” outperforms other markers (“But”/“However”) because former signals re-evaluation while latter sometimes introduce contrasting information. Post intervention, LLMs have a higher tendency to generate these markers subsequently, and correspondingly the mean accuracy also increases. We observe strong correlations between the binary term frequency of correction marker and the change in accuracy in GSM8K-SC and PRM800K-SC across models in Figure 8. 6.2 Reasoning models Reasoning models exhibit a small, even negative, Self-Correction Blind Spot in Figure 9, unlike non-reasoning models. The mean accuracy is reported in Figure 10. Interestingly, appending “ Wait ” to base model without finetuning can almost match the performance of finetuned/ RL trained model in some models (see Table 3). This helps us understand one of the gaps between non-reasoning models and reasoning models - reasoning models are much better at self-correcting their own error (higher $P_{M}(r_{correct}|r_{m},e)$ ) than non-reasoning models, leading to better performance ( $P_{M}(r_{correct})$ ) in reasoning tasks requiring trial and error. However, correction markers can narrow the gap. Correction markers are exactly what reasoning models start with when given an internal error before arriving at correct response (see Table 4). Table 3: Macro average of mean accuracy of base model vs appending “ Wait ” vs reasoning model | Base Model | Reasoning Model | Base Model | Appending “ Wait ” | Reasoning Model | | --- | --- | --- | --- | --- | | DeepSeek-V3-0324 | DeepSeek-R1-0528 | 0.578 | 0.918 | 0.908 | | phi-4 | phi-4-reasoning-plus | 0.325 | 0.704 | 0.707 | | Qwen3-14B footnotemark: | Qwen3-14B footnotemark: | 0.121 | 0.884 | 0.843 | | Qwen3-32B footnotemark: | Qwen3-32B footnotemark: | 0.046 | 0.791 | 0.894 | | Qwen3-30B-A3B footnotemark: | Qwen3-30B-A3B footnotemark: | 0.102 | 0.869 | 0.845 | | Qwen3-235B-A22B footnotemark: | Qwen3-235B-A22B footnotemark: | 0.335 | 0.865 | 0.876 | - Non-thinking mode - Thinking mode Table 4: Most common first word and relative frequency generated by reasoning models | Model | SCLI5 | GSM8K-SC | PRM800K-SC | | --- | --- | --- | --- | | QwQ-32B | (‘Wait,’, 0.377) | (‘Wait,’, 0.725) | (‘Wait,’, 0.768) | | Qwen3-14B (thinking) | (‘In’, 1.0) | (‘Wait,’, 0.38) | (‘Therefore,’, 0.219) | | Qwen3-32B (thinking) | (‘After’, 1.0) | (‘The’, 0.288) | (‘I’, 0.189) | | Qwen3-30B-A3B (thinking) | (‘Wait,’, 0.312) | (‘Therefore,’, 0.25) | (‘So’, 0.195) | | Qwen3-235B-A22B (thinking) | (‘**Step-by-step’, 0.292) | (‘Wait,’, 0.198) | (‘Therefore,’, 0.256) | | DeepSeek-R1-0528 | (‘No,’, 0.324) | (‘But’, 0.267) | (‘But’, 0.486) | | gemma-3-12b-it | (‘The’, 0.284) | (‘The’, 0.239) | (‘Alternatively,’, 0.205) | | gemma-3-27b-it | (‘Here’s’, 0.31) | (‘Let’, 0.256) | (‘However,’, 0.292) | | phi-4-reasoning-plus | (‘Wait,’, 0.861) | (‘Wait,’, 0.677) | (‘However,’, 0.217) | It is also worth noting that although Qwen3 models fuse thinking mode and non-thinking mode by continual finetuning via a united chat template after GRPO (Shao et al., 2024), non-thinking mode still suffers from blind spot, unlike in thinking mode, as the chat template conditions the model into different distributions. 6.3 Correction markers in post-training data These differences in reasoning models’ behavior prompted us to investigate the root cause in post-training data composition. If correction markers could narrow the gap, and if we can make non-reasoning models to predict correction markers upon seeing internal error, we can induce self-correction capability in non-reasoning model, and that capability is already in the model when it evaluates against external error. Motivated by this logic, we further investigate correction marker density of open source supervised finetuning datasets (Table 5). Data analysis reveals the statistical foundation of this phenomenon. The 95% percentile correction markers frequency of non-reasoning datasets (e.g., OpenAssistant We use the highest-human-rated paths of conversation tree provided in ‘timdettmers/openassistant-guanaco’., OpenHermes2.5,etc ) is 1. In contrast, reasoning datasets, generated by reasoning models, (e.g., Mixture-of-Thoughts, OpenThoughts3) have median marker densities 30-170, with 99% of data containing at least 1 marker. With such a systematic absence or presence of correction markers in training data, it follows from basic statistical modeling principles that models will predict correction markers as next tokens proportional to their frequency in training data - Razeghi et al. (2022) and Merullo et al. (2025) have shown that LLMs perform better when related term frequency in pretraining data is higher. This statistical likelihood directly determines self-correction behavior: models trained on less correction data rarely generate correction markers, perpetuating the blind spot. This single powerful insight unifies all of our empirical observations. Table 5: Descriptive statistics of correction markers in post training dataset | Dataset | 1% | 5% | 10% | 25% | 50% | 75% | 90% | 95% | 99% | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | OpenAssistant (Köpf et al., 2023) | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 2 | | OpenHermes2.5 (Teknium, 2023) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | | Infinity-Instruct-7M (Li et al., 2025) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 2 | | UltraFeedback (Cui et al., 2024) | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 2 | | Tulu3-sft-olmo-2-mixture (Lambert et al., 2025) | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 2 | | s1K-1.1 (Muennighoff et al., 2025) | 0 | 0 | 0 | 0 | 0 | 1 | 3 | 5 | 9 | | Mixture-of-Thoughts (Face, 2025) | 1 | 3 | 5 | 10 | 30 | 76 | 147 | 202 | 273 | | OpenThoughts3-1.2M (Guha et al., 2025) | 14 | 66 | 96 | 132 | 170 | 213 | 253 | 278 | 326 | 7 Discussion Benefit of error and self-correction data. LLMs are known to exhibit cognitive bias (Koo et al., 2024; Echterhoff et al., 2024; Jones and Steinhardt, 2022). Self-Correction Blind Spot bears resemblance to bias blind spot of human, where capability of self-correction is relatively limited. We hypothesize two root causes: First, supervised fine-tuning and reinforcement learning from human rely on human demonstrations/preferences (Ouyang et al., 2022), which strongly favor polished, error-free responses over those with errors and self-correction. Second, even synthetic instruction data (Teknium, 2023; Li et al., 2025) or AI feedback (Cui et al., 2024) reward models ultimately learn from human preferences, inheriting this artifact. Traditional machine learning emphasizes alignment of training data with the production environment, but human-dominated data lack exposure to the “error-and-correct” process. Outcome-based RL like GRPO (Shao et al., 2024) addresses this by encouraging diverse reasoning paths, including error and self-correction, while given ground-truth feedback, as shown in the high correction markers density in RL trained models’ generation in Section 6.3. This complements error-free human demonstration and preference, making models more robust to errors (consistent with work on learning from mistakes (An et al., 2024) and critique finetuning (Wang et al., 2025)) and better at backtracking. An error-free response is not the only path leading to a correct final output - error and self-correction provides an equally important training signal as error-free demonstration. Understanding cognitive behavior via markers. Frequency analysis of correction markers is a scalable way to study cognitive behaviors present in pretraining data and post-training data. We believe that they can serve as important heuristics for pretraining and post-training data curation. 8 Conclusion and limitation In this work, we identified and systematically measured the Self-Correction Blind Spot: non-reasoning LLMs fail to correct 64.5% of errors in their own outputs while successfully correcting identical external errors. This systematic failure has important implications for AI reliability and safety-critical applications. Our controlled error injection methodology, while not perfectly capturing natural error, demonstrates the generality of this phenomenon across error types - from artificial (SCLI5) to realistic (PRM800K-SC) scenario. This approach isolates self-correction capabilities from confounding factors and ensures cross-model comparability. We encourage future research to expand the benchmark to programming, logic and common sense reasoning, and to multilingual and multimodal reasoning. Reproducibility statement Our experiments utilize various open source models, close source models, and datasets. Self-Correction Bench is available in Hugging Face (click here). Our codes for constructing datasets, running the experiment, and building tables and graphs are released in Github (click here). Acknowledgement We thank the open source community for making this research possible through shared datasets, models, and libraries. We are particularly grateful to the teams behind the datasets used in our evaluation: GSM8K, PRM800K, and the various instruction tuning datasets we analyzed. We acknowledge the model developers who have made their work publicly available, including the teams at DeepSeek, Google (Gemma), Meta (Llama), Microsoft (Phi), Mistral and Qwen. We also thank the developers of the computational infrastructure and libraries that enabled our experiments, including the transformers and datasets library (Hugging Face), DeepInfra API, Google API and OpenAI API. 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A: The answer is 1. | | Next character | 52 | Off-by-one | Q: What letter comes after A? A: The answer is C. | | Previous character | 52 | Off-by-one | Q: What letter comes before C? A: The answer is A. | | Larger number | 71 | Flip | Q: Which one is smaller, 1 or 2? A: The answer is 2. | | Smaller number | 71 | Flip | Q: Which one is larger, 2 or 5? A: The answer is 2. | Table 7: Error composition of GSM8K-SC | Category | Description | | --- | --- | | Problem Representation Errors | These errors arise when the solver misunderstands or misinterprets the problem’s requirements or given information. This can involve misreading the problem statement, confusing the relationships between quantities, or failing to grasp what is being asked. | | Planning Errors | These occur when the solver devises an incorrect or incomplete strategy to tackle the problem. This might include choosing the wrong operations, setting up flawed equations, or overlooking key components of the problem. | | Execution Errors | These are mistakes made while carrying out the planned steps, such as errors in calculations, misapplication of mathematical rules, or procedural slip-ups, even if the plan itself is sound. | Appendix B Figures <details> <summary>images/error_injection_model_correlation_matrix_non_reasoning.png Details</summary>  ### Visual Description ## Chart Type: Multi-Panel Data Analysis ### Overview The image presents a multi-panel data analysis consisting of a correlation matrix and two scatter plots. The correlation matrix displays the mean accuracy correlations between three datasets: scli5, gsm8k_sc, and prm800k_sc. The scatter plots compare the macro averages of these datasets, with fitted lines and ideal lines overlaid to visualize the relationships. ### Components/Axes **Panel 1: Correlation Matrix** * **Title:** Correlation matrix of mean accuracy across datasets * **X-axis Labels:** scli5, gsm8k_sc, prm800k_sc * **Y-axis Labels:** scli5, gsm8k_sc, prm800k_sc * **Color Scale:** Ranges from blue (-1.00) to red (1.00), with white representing 0.00. * **Values:** Displayed within each cell of the matrix. **Panel 2: Scatter Plot 1** * **Title:** SCLI5 vs GSM8K-SC (r = 0.724) * **X-axis Label:** SCLI5 macro average * Scale: 0.0 to 1.0, incrementing by 0.2 * **Y-axis Label:** GSM8K-SC macro average * Scale: 0.0 to 1.0, incrementing by 0.2 * **Data Points:** Blue circles, each labeled with a model name. * **Fitted Line:** Red dashed line. * **Ideal Line:** Gray dotted line. * **Legend (Top-Left):** * Fitted line: Red dashed line * Ideal line: Gray dotted line **Panel 3: Scatter Plot 2** * **Title:** GSM8K-SC vs PRM800K-SC (r = 0.559) * **X-axis Label:** GSM8K-SC macro average * Scale: 0.0 to 0.6, incrementing by 0.1 * **Y-axis Label:** PRM800K-SC macro average * Scale: 0.0 to 0.6, incrementing by 0.1 * **Data Points:** Green circles, each labeled with a model name. * **Fitted Line:** Red dashed line. * **Ideal Line:** Gray dotted line. * **Legend (Top-Left):** * Fitted line: Red dashed line * Ideal line: Gray dotted line ### Detailed Analysis **Panel 1: Correlation Matrix** | | scli5 | gsm8k_sc | prm800k_sc | | :-------- | :---- | :------- | :---------- | | **scli5** | 1 | 0.72 | 0.49 | | **gsm8k_sc** | 0.72 | 1 | 0.56 | | **prm800k_sc**| 0.49 | 0.56 | 1 | * All diagonal values are 1, indicating perfect correlation of a dataset with itself. * scli5 and gsm8k_sc have a strong positive correlation of 0.72. * scli5 and prm800k_sc have a moderate positive correlation of 0.49. * gsm8k_sc and prm800k_sc have a moderate positive correlation of 0.56. **Panel 2: Scatter Plot 1 (SCLI5 vs GSM8K-SC)** * The fitted line (red dashed) shows a positive correlation between SCLI5 and GSM8K-SC macro averages. * The ideal line (gray dotted) represents a 1:1 correlation. * Data points (blue) are scattered around the fitted line, indicating some variance. * **Llama-3.3-70B-Ins...**: Approximately (0.1, 0.1) * **Qwen3-32B**: Approximately (0.1, 0.1) * **Qwen3-30B-A3B**: Approximately (0.2, 0.1) * **Mistral-Small-24B...**: Approximately (0.2, 0.0) * **Qwen2-7B-Instruct i-4**: Approximately (0.5, 0.1) * **Llama-4-Scout-17B...**: Approximately (0.6, 0.2) * **DeepSeek-V3-0324**: Approximately (0.9, 0.4) * **Llama-4-Maverick-...**: Approximately (0.9, 0.4) * **Qwen2.5-72B-Instruct**: Approximately (1.0, 0.6) * **Qwen2.5-7B-Instruct**: Approximately (0.6, 0.2) **Panel 3: Scatter Plot 2 (GSM8K-SC vs PRM800K-SC)** * The fitted line (red dashed) shows a positive correlation between GSM8K-SC and PRM800K-SC macro averages. * The ideal line (gray dotted) represents a 1:1 correlation. * Data points (green) are scattered around the fitted line, indicating some variance. * **Mistral-Small-24B...**: Approximately (0.0, 0.0) * **Qwen2-7B-Instruct**: Approximately (0.1, 0.0) * **Qwen3-32B**: Approximately (0.1, 0.1) * **Qwen3-30B-A3B**: Approximately (0.1, 0.2) * **Qwen3-14B**: Approximately (0.2, 0.25) * **Qwen3-235B-A22B**: Approximately (0.2, 0.35) * **Llama-4-Scout-17B...**: Approximately (0.3, 0.25) * **Llama-3.3-70B-Ins...**: Approximately (0.3, 0.25) * **DeepSeek-V3-0324**: Approximately (0.1, 0.5) * **Llama-4-Maverick-...**: Approximately (0.1, 0.5) * **Qwen2.5-7B-Instruct**: Approximately (0.6, 0.2) ### Key Observations * The correlation matrix indicates a strong relationship between scli5 and gsm8k_sc datasets. * The scatter plots show positive correlations between the datasets, but with noticeable variance around the fitted lines. * The 'r' values (0.724 and 0.559) indicate the strength of the linear correlation, with SCLI5 vs GSM8K-SC having a stronger correlation than GSM8K-SC vs PRM800K-SC. * The data points in the scatter plots represent different models, and their positions indicate their relative performance on the respective datasets. ### Interpretation The data suggests that while there is a positive correlation in mean accuracy across the datasets, the relationships are not perfectly linear. The correlation matrix confirms the inter-relatedness of the datasets, while the scatter plots provide a more granular view of model performance across different dataset pairings. The variance around the fitted lines in the scatter plots indicates that model performance is not consistent across all datasets, and some models may perform better on certain datasets than others. The 'r' values quantify the strength of these relationships, with a higher 'r' value indicating a stronger linear association. </details> Figure 5: left: Mean accuracy correlation matrix across datasets middle: Scatter plot between SCLI5 vs GSM8K-SC right: Scatter plot between GSM8K-SC vs PRM800K-SC BCA: Before commit an answer <details> <summary>images/error_in_error_injection_model_macro_averages_non_reasoning.png Details</summary>  ### Visual Description ## Bar Chart: Error and non-response by dataset and model ### Overview The image is a bar chart comparing the error rates and non-response rates of various language models across different datasets. The chart displays error on the y-axis and model names on the x-axis. Each model has four bars representing the SCLI5, GSM8K-SC, PRM800K-SC datasets, and the non-response rate. ### Components/Axes * **Title:** Error and non-response by dataset and model * **X-axis:** Models (Llama-4-Maverick-17B-128E-Instruct-FP8, DeepSeek-V3-0324, Qwen2.5-72B-Instruct, Llama-4-Scout-17B-16E-Instruct-FP8-dynamic, Llama-3.3-70B-Instruct, Qwen3-235B-A22B, Phi-4, Qwen2.5-7B-Instruct, Qwen2-7B-Instruct, Qwen3-14B, Qwen3-30B-A3B, Llama-3.1-8B-Instruct, Qwen3-32B, Mistral-Small-24B-Instruct-2501) * **Y-axis:** Error (Scale: 0.0 to 1.0, incrementing by 0.2) * **Legend:** Located at the top-left of the chart. * SCLI5 (Light Blue) * GSM8K-SC (Light Orange) * PRM800K-SC (Light Green) * Non-Response (Cross-hatched) ### Detailed Analysis The chart presents error rates for different models across four datasets (SCLI5, GSM8K-SC, PRM800K-SC) and their non-response rates. Here's a breakdown of the data for each model: * **Llama-4-Maverick-17B-128E-Instruct-FP8:** * SCLI5: ~0.01 * GSM8K-SC: ~0.58 * PRM800K-SC: ~0.55 * Non-Response: ~0.54 * **DeepSeek-V3-0324:** * SCLI5: ~0.17 * GSM8K-SC: ~0.59 * PRM800K-SC: ~0.52 * Non-Response: ~0.07 * **Qwen2.5-72B-Instruct:** * SCLI5: ~0.01 * GSM8K-SC: ~0.41 * PRM800K-SC: ~0.72 * Non-Response: ~0.41 * **Llama-4-Scout-17B-16E-Instruct-FP8-dynamic:** * SCLI5: ~0.02 * GSM8K-SC: ~0.78 * PRM800K-SC: ~0.74 * Non-Response: ~0.75 * **Llama-3.3-70B-Instruct:** * SCLI5: ~0.04 * GSM8K-SC: ~0.74 * PRM800K-SC: ~0.71 * Non-Response: ~0.76 * **Qwen3-235B-A22B:** * SCLI5: ~0.30 * GSM8K-SC: ~0.68 * PRM800K-SC: ~0.50 * Non-Response: ~0.42 * **Phi-4:** * SCLI5: ~0.18 * GSM8K-SC: ~0.70 * PRM800K-SC: ~0.28 * Non-Response: ~0.89 * **Qwen2.5-7B-Instruct:** * SCLI5: ~0.31 * GSM8K-SC: ~0.45 * PRM800K-SC: ~0.84 * Non-Response: ~0.90 * **Qwen2-7B-Instruct:** * SCLI5: ~0.27 * GSM8K-SC: ~0.72 * PRM800K-SC: ~0.93 * Non-Response: ~0.96 * **Qwen3-14B:** * SCLI5: ~0.93 * GSM8K-SC: ~0.75 * PRM800K-SC: ~0.37 * Non-Response: ~0.98 * **Qwen3-30B-A3B:** * SCLI5: ~0.92 * GSM8K-SC: ~0.95 * PRM800K-SC: ~0.91 * Non-Response: ~0.94 * **Llama-3.1-8B-Instruct:** * SCLI5: ~0.50 * GSM8K-SC: ~0.92 * PRM800K-SC: ~0.96 * Non-Response: ~0.98 * **Qwen3-32B:** * SCLI5: ~0.97 * GSM8K-SC: ~0.93 * PRM800K-SC: ~0.89 * Non-Response: ~0.99 * **Mistral-Small-24B-Instruct-2501:** * SCLI5: ~0.01 * GSM8K-SC: ~0.98 * PRM800K-SC: ~0.92 * Non-Response: ~0.99 ### Key Observations * The SCLI5 dataset generally has lower error rates compared to GSM8K-SC and PRM800K-SC for most models. * Non-response rates vary significantly across models, with some models exhibiting very high non-response rates. * Models like Qwen3-14B, Qwen3-30B-A3B, Llama-3.1-8B-Instruct, Qwen3-32B, and Mistral-Small-24B-Instruct-2501 show high error and non-response rates across all datasets. * DeepSeek-V3-0324 has a very low non-response rate compared to other models. ### Interpretation The bar chart provides a comparative analysis of the performance of different language models on various datasets, considering both error rates and non-response rates. The data suggests that the choice of model and dataset significantly impacts performance. Some models are more prone to errors or non-responses depending on the dataset they are evaluated on. The high non-response rates observed in some models indicate potential issues with the model's ability to handle certain types of queries or data. The SCLI5 dataset appears to be less challenging for most models, resulting in lower error rates. </details> Figure 6: Summary of error and empty response across models <details> <summary>images/blind_spot_summary_wait_non_reasoning.png Details</summary>  ### Visual Description ## Bar Chart: Blind Spot Summary Across Datasets ### Overview The image is a bar chart comparing the "Self-Correction Blind Spot" across different language models and datasets. The chart displays the mean and 95% confidence intervals for each model under various conditions related to "Wait" operations. The models are listed on the x-axis, and the self-correction blind spot values are on the y-axis. The legend distinguishes between different datasets and conditions. ### Components/Axes * **Title:** Blind Spot summary across datasets (Appending "Wait") - 95% Confidence Intervals * **X-axis:** Models. The models listed are: * Llama-4-Maverick-17B-128E-Instruct-FP8 * DeepSeek-V3-0324 * Qwen2.5-72B-Instruct * Llama-4-Scout-17B-16E-Instruct-FP8-dynamic * Llama-3.3-70B-Instruct * Qwen3-235B-A22B * Phi-4 * Qwen2.5-7B-Instruct * Qwen2-7B-Instruct * Qwen3-14B * Qwen3-30B-A3B * Llama-3.1-8B-Instruct * Qwen3-32B * Mistral-Small-24B-Instruct-2501 * **Y-axis:** Self-Correction Blind Spot. The scale ranges from -1.5 to 0.5, with tick marks at -1.0, -0.5, and 0.0, and 0.5. * **Legend:** Located in the top-left corner. * Blue: SCLI5 (Wait) * Orange: GSM8K-SC (Before commit answer, Wait) * Light Beige: GSM8K-SC (After commit answer, Wait) * Light Green: PRM800K-SC (Before commit answer, Wait) * Dark Green: PRM800K-SC (After commit answer, Wait) ### Detailed Analysis The chart presents data for each model across five different conditions, represented by the colored bars. Error bars indicate the 95% confidence intervals. Here's a breakdown of the approximate values for each model and condition: * **Llama-4-Maverick-17B-128E-Instruct-FP8:** * SCLI5 (Wait) (Blue): ~0.05 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.05 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~-0.05 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~-0.1 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~-0.05 * **DeepSeek-V3-0324:** * SCLI5 (Wait) (Blue): ~-0.05 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.05 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.05 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~-0.05 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~-0.1 * **Qwen2.5-72B-Instruct:** * SCLI5 (Wait) (Blue): ~0.0 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.1 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.05 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~0.2 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~0.3 * **Llama-4-Scout-17B-16E-Instruct-FP8-dynamic:** * SCLI5 (Wait) (Blue): ~0.0 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.15 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.1 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~0.1 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~0.25 * **Llama-3.3-70B-Instruct:** * SCLI5 (Wait) (Blue): ~0.0 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.15 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.1 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~-0.2 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~-1.2 * **Qwen3-235B-A22B:** * SCLI5 (Wait) (Blue): ~0.0 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.05 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.05 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~0.05 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~0.0 * **Phi-4:** * SCLI5 (Wait) (Blue): ~0.0 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.1 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.1 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~0.5 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~0.4 * **Qwen2.5-7B-Instruct:** * SCLI5 (Wait) (Blue): ~-0.15 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.1 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.05 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~0.1 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~0.1 * **Qwen2-7B-Instruct:** * SCLI5 (Wait) (Blue): ~-0.1 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.3 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.25 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~0.35 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~0.2 * **Qwen3-14B:** * SCLI5 (Wait) (Blue): ~-0.2 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.0 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.0 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~0.3 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~0.5 * **Qwen3-30B-A3B:** * SCLI5 (Wait) (Blue): ~-0.05 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.0 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.0 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~0.05 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~0.1 * **Llama-3.1-8B-Instruct:** * SCLI5 (Wait) (Blue): ~-0.15 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.15 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.55 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~0.3 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~0.1 * **Qwen3-32B:** * SCLI5 (Wait) (Blue): ~0.05 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.0 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.0 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~0.2 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~0.3 * **Mistral-Small-24B-Instruct-2501:** * SCLI5 (Wait) (Blue): ~0.0 * GSM8K-SC (Before commit answer, Wait) (Orange): ~0.1 * GSM8K-SC (After commit answer, Wait) (Light Beige): ~0.1 * PRM800K-SC (Before commit answer, Wait) (Light Green): ~0.25 * PRM800K-SC (After commit answer, Wait) (Dark Green): ~0.4 ### Key Observations * The PRM800K-SC (After commit answer, Wait) condition (Dark Green) shows the most significant variation across models. * Llama-3.3-70B-Instruct has a notably negative "Self-Correction Blind Spot" for the PRM800K-SC (After commit answer, Wait) condition. * The confidence intervals vary across models and conditions, indicating different levels of uncertainty in the measurements. ### Interpretation The chart provides a comparative analysis of how different language models perform in terms of self-correction when subjected to "Wait" operations across various datasets. The "Self-Correction Blind Spot" metric likely indicates the degree to which a model fails to recognize and correct its own errors under these conditions. The significant negative value for Llama-3.3-70B-Instruct in the PRM800K-SC (After commit answer, Wait) condition suggests that this model may be particularly prone to making errors or struggling to correct them in that specific scenario. Conversely, models like Phi-4 and Qwen3-14B show relatively high values for PRM800K-SC (Before/After commit answer, Wait), indicating potentially better self-correction capabilities in those conditions. The variations in confidence intervals suggest that some models and conditions have more consistent performance than others. Further investigation would be needed to understand the underlying reasons for these differences and to determine the practical implications for model deployment and usage. </details> Figure 7: Self-Correction Blind Spot and 95% confidence interval across non-reasoning models after appending “ Wait ” Table 8: Mean accuracy and relative change after appending various correction markers | Correction Markers | SCLI5 | GSM8K-SC | PRM800K-SC | | --- | --- | --- | --- | | Internal Error (Baseline) | 0.499 (0%) | 0.183 (0%) | 0.200 (0%) | | External Error | 0.910 (+82.5%) | 0.881 (+382.1%) | 0.620 (+210.3%) | | “ Wait ” | 0.957 (+91.9%) | 0.796 (+335.1%) | 0.504 (+152.0%) | | “ But ” | 0.922 (+85.0%) | 0.611 (+234.2%) | 0.430 (+114.8%) | | “ However ” | 0.897 (+79.8%) | 0.602 (+229.0%) | 0.438 (+119.3%) | <details> <summary>images/correlation_plots_marker_presence_vs_accuracy_after_wait.png Details</summary>  ### Visual Description ## Scatter Plot: Correlation of Change in Correction Marker Presence vs Change in Accuracy ### Overview The image presents three scatter plots, each displaying the correlation between the absolute change in correction marker presence and the absolute change in accuracy after appending "Wait" for different datasets: SCLI5, GSM8K_SC, and PRM800K_SC. Each plot includes a trend line and the calculated correlation coefficient. ### Components/Axes * **Title:** Correlation: change in correction marker presence vs change in accuracy after appending Wait * **X-axis (all plots):** Absolute Change in Correction Marker Presence * **Y-axis (all plots):** Absolute Change in Accuracy * **Data Points:** Blue circles represent individual data points. * **Trend Line:** Red line indicating the linear trend. * **Correlation Coefficient:** Displayed in a box at the top-left of each plot. **Plot 1: SCLI5** * **Title:** SCLI5 * **X-axis:** Absolute Change in Correction Marker Presence, ranging from approximately -0.4 to 0.2. Markers at -0.4, -0.3, -0.2, -0.1, 0.0, 0.1, 0.2 * **Y-axis:** Absolute Change in Accuracy, ranging from 0.0 to 1.0. Markers at 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 * **Correlation:** 0.493 **Plot 2: GSM8K_SC** * **Title:** GSM8K_SC * **X-axis:** Absolute Change in Correction Marker Presence, ranging from approximately -0.05 to 0.15. Markers at -0.050, -0.025, 0.000, 0.025, 0.050, 0.075, 0.100, 0.125, 0.150 * **Y-axis:** Absolute Change in Accuracy, ranging from 0.0 to 0.8. Markers at 0.0, 0.2, 0.4, 0.6, 0.8 * **Correlation:** 0.734 **Plot 3: PRM800K_SC** * **Title:** PRM800K_SC * **X-axis:** Absolute Change in Correction Marker Presence, ranging from approximately 0.00 to 0.35. Markers at 0.00, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35 * **Y-axis:** Absolute Change in Accuracy, ranging from 0.0 to 0.5. Markers at 0.0, 0.1, 0.2, 0.3, 0.4, 0.5 * **Correlation:** 0.797 ### Detailed Analysis **Plot 1: SCLI5** * The trend line (red) shows a positive correlation, though it appears weaker than in the other plots. * Data points are scattered, with some clustering around the 0.0 mark on the x-axis. * At x = -0.4, y ≈ 0.1. At x = 0.2, y ≈ 0.7. **Plot 2: GSM8K_SC** * The trend line (red) shows a clear positive correlation. * Data points are more tightly clustered around the trend line compared to the SCLI5 plot. * At x = -0.05, y ≈ 0.4. At x = 0.15, y ≈ 0.8. **Plot 3: PRM800K_SC** * The trend line (red) shows a positive correlation. * Data points are relatively close to the trend line. * At x = 0.0, y ≈ 0.2. At x = 0.35, y ≈ 0.45. ### Key Observations * All three plots show a positive correlation between the absolute change in correction marker presence and the absolute change in accuracy. * The correlation is strongest for PRM800K_SC (0.797) and GSM8K_SC (0.734), and weaker for SCLI5 (0.493). * The range of the x-axis (Absolute Change in Correction Marker Presence) varies across the three plots. ### Interpretation The plots suggest that, in general, increasing the presence of correction markers is associated with an increase in accuracy after appending "Wait". The strength of this correlation varies depending on the specific dataset. The PRM800K_SC dataset shows the strongest positive relationship, indicating that correction markers are particularly effective in improving accuracy for this dataset. The SCLI5 dataset shows a weaker correlation, suggesting that correction markers may have a less consistent impact on accuracy for this dataset. The GSM8K_SC dataset falls in between, showing a moderate positive correlation. </details> Figure 8: Correlation of absolute change in keyword presence vs absolute change in accuracy - original vs appending “ Wait ” <details> <summary>images/blind_spot_summary_default_reasoning.png Details</summary>  ### Visual Description ## Bar Chart: Blind Spot summary across datasets - 95% Confidence Intervals ### Overview The image is a bar chart comparing the self-correction blind spot across different models. The chart displays the mean self-correction blind spot for each model, with error bars representing 95% confidence intervals. The models are evaluated using different self-correction methods: SCL15, GSM8K-SC (Before commit answer), GSM8K-SC (After commit answer), PRM800K-SC (Before commit answer), and PRM800K-SC (After commit answer). ### Components/Axes * **Title:** Blind Spot summary across datasets - 95% Confidence Intervals * **X-axis:** Models (DeepSeek-R1-0528, QwQ-32B, Qwen3-235B-A22B (thinking), Qwen3-30B-A3B (thinking), Qwen3-14B (thinking), gemma-3-27b-it, Qwen3-32B (thinking), gemma-3-12b-it, Phi-4-reasoning-plus) * **Y-axis:** Self-Correction Blind Spot (ranging from -0.4 to 0.4, with increments of 0.1) * **Legend:** Located in the top-right corner. * Blue: SCL15 * Orange: GSM8K-SC (Before commit answer) * Light Orange: GSM8K-SC (After commit answer) * Green: PRM800K-SC (Before commit answer) * Light Green: PRM800K-SC (After commit answer) ### Detailed Analysis The chart presents data for nine different models, each evaluated using five different self-correction methods. The height of each bar represents the mean self-correction blind spot, and the error bars indicate the 95% confidence interval. * **DeepSeek-R1-0528:** * SCL15 (Blue): Approximately -0.12, confidence interval extends from approximately -0.18 to -0.06. * GSM8K-SC (Before commit answer) (Orange): Approximately -0.01, confidence interval extends from approximately -0.07 to 0.05. * GSM8K-SC (After commit answer) (Light Orange): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * PRM800K-SC (Before commit answer) (Green): Approximately 0.07, confidence interval extends from approximately 0.01 to 0.13. * PRM800K-SC (After commit answer) (Light Green): Approximately -0.05, confidence interval extends from approximately -0.11 to 0.01. * **QwQ-32B:** * SCL15 (Blue): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * GSM8K-SC (Before commit answer) (Orange): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * GSM8K-SC (After commit answer) (Light Orange): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * PRM800K-SC (Before commit answer) (Green): Approximately -0.22, confidence interval extends from approximately -0.28 to -0.16. * PRM800K-SC (After commit answer) (Light Green): Approximately -0.15, confidence interval extends from approximately -0.21 to -0.09. * **Qwen3-235B-A22B (thinking):** * SCL15 (Blue): Approximately 0.03, confidence interval extends from approximately -0.03 to 0.09. * GSM8K-SC (Before commit answer) (Orange): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * GSM8K-SC (After commit answer) (Light Orange): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * PRM800K-SC (Before commit answer) (Green): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * PRM800K-SC (After commit answer) (Light Green): Approximately -0.19, confidence interval extends from approximately -0.3 to -0.08. * **Qwen3-30B-A3B (thinking):** * SCL15 (Blue): Approximately 0.14, confidence interval extends from approximately 0.08 to 0.2. * GSM8K-SC (Before commit answer) (Orange): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * GSM8K-SC (After commit answer) (Light Orange): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * PRM800K-SC (Before commit answer) (Green): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * PRM800K-SC (After commit answer) (Light Green): Approximately -0.17, confidence interval extends from approximately -0.28 to -0.06. * **Qwen3-14B (thinking):** * SCL15 (Blue): Approximately 0.13, confidence interval extends from approximately 0.07 to 0.19. * GSM8K-SC (Before commit answer) (Orange): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * GSM8K-SC (After commit answer) (Light Orange): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * PRM800K-SC (Before commit answer) (Green): Approximately -0.04, confidence interval extends from approximately -0.1 to 0.02. * PRM800K-SC (After commit answer) (Light Green): Approximately -0.05, confidence interval extends from approximately -0.16 to 0.06. * **gemma-3-27b-it:** * SCL15 (Blue): Approximately -0.08, confidence interval extends from approximately -0.14 to -0.02. * GSM8K-SC (Before commit answer) (Orange): Approximately 0.19, confidence interval extends from approximately 0.13 to 0.25. * GSM8K-SC (After commit answer) (Light Orange): Approximately 0.23, confidence interval extends from approximately 0.17 to 0.29. * PRM800K-SC (Before commit answer) (Green): Approximately 0.07, confidence interval extends from approximately 0.01 to 0.13. * PRM800K-SC (After commit answer) (Light Green): Approximately 0.03, confidence interval extends from approximately -0.03 to 0.09. * **Qwen3-32B (thinking):** * SCL15 (Blue): Approximately 0.15, confidence interval extends from approximately 0.09 to 0.21. * GSM8K-SC (Before commit answer) (Orange): Approximately 0.01, confidence interval extends from approximately -0.05 to 0.07. * GSM8K-SC (After commit answer) (Light Orange): Approximately 0.2, confidence interval extends from approximately 0.14 to 0.26. * PRM800K-SC (Before commit answer) (Green): Approximately 0.15, confidence interval extends from approximately 0.09 to 0.21. * PRM800K-SC (After commit answer) (Light Green): Approximately -0.04, confidence interval extends from approximately -0.15 to 0.07. * **gemma-3-12b-it:** * SCL15 (Blue): Approximately 0.15, confidence interval extends from approximately 0.09 to 0.21. * GSM8K-SC (Before commit answer) (Orange): Approximately 0.16, confidence interval extends from approximately 0.1 to 0.22. * GSM8K-SC (After commit answer) (Light Orange): Approximately 0.22, confidence interval extends from approximately 0.16 to 0.28. * PRM800K-SC (Before commit answer) (Green): Approximately 0.07, confidence interval extends from approximately 0.01 to 0.13. * PRM800K-SC (After commit answer) (Light Green): Approximately 0.03, confidence interval extends from approximately -0.03 to 0.09. * **Phi-4-reasoning-plus:** * SCL15 (Blue): Approximately 0.05, confidence interval extends from approximately -0.01 to 0.11. * GSM8K-SC (Before commit answer) (Orange): Approximately -0.14, confidence interval extends from approximately -0.2 to -0.08. * GSM8K-SC (After commit answer) (Light Orange): Approximately 0.15, confidence interval extends from approximately 0.09 to 0.21. * PRM800K-SC (Before commit answer) (Green): Approximately -0.14, confidence interval extends from approximately -0.2 to -0.08. * PRM800K-SC (After commit answer) (Light Green): Approximately -0.23, confidence interval extends from approximately -0.34 to -0.12. ### Key Observations * The GSM8K-SC (After commit answer) method generally shows a higher self-correction blind spot compared to the GSM8K-SC (Before commit answer) method. * The PRM800K-SC (After commit answer) method often results in a negative self-correction blind spot, indicating a potential over-correction or bias. * The confidence intervals vary across models and methods, suggesting different levels of uncertainty in the estimated blind spots. * For some models, the SCL15 method shows a relatively high self-correction blind spot compared to other methods. ### Interpretation The bar chart provides a comparative analysis of the self-correction blind spot across different models and self-correction methods. The data suggests that the choice of self-correction method can significantly impact the model's performance and bias. The positive and negative values of the self-correction blind spot indicate the degree to which the model is either under-correcting or over-correcting its errors. The confidence intervals provide a measure of the reliability of these estimates. The chart highlights the importance of carefully selecting and tuning self-correction methods to optimize model performance and minimize bias. The observed differences across models suggest that the effectiveness of a particular self-correction method may depend on the specific architecture and training data of the model. </details> Figure 9: Self-Correction Blind Spot and 95% confidence interval across reasoning models <details> <summary>images/error_injection_model_macro_averages_reasoning.png Details</summary>  ### Visual Description ## Bar Chart: Mean Accuracy and Macro Average After Injection of Internal Error ### Overview The image is a bar chart comparing the mean accuracy and macro average of different models after injecting internal errors. The chart displays the performance of four categories (SCL15, GSM8K-SC, PRM800K-SC, and Macro Average) across various models. Error bars indicate 95% confidence intervals. ### Components/Axes * **Title:** Mean accuracy and macro average (95% confidence intervals) after injection of internal error * **X-axis:** Models (DeepSeek-R1-0528, QwQ-32B, Qwen3-235B-A22B (thinking), Qwen3-30B-A3B (thinking), Qwen3-14B (thinking), gemma-3-27b-it, Qwen3-32B (thinking), gemma-3-12b-it, Phi-4-reasoning-plus) * **Y-axis:** Accuracy (scale from 0.0 to 1.0, incrementing by 0.2) * **Legend:** Located in the top-right corner. * SCL15 (light blue) * GSM8K-SC (light orange) * PRM800K-SC (light green) * Macro Average (red) ### Detailed Analysis **Model Performance Breakdown:** 1. **DeepSeek-R1-0528:** * SCL15: ~0.98 with a small confidence interval. * GSM8K-SC: ~0.94 with a small confidence interval. * PRM800K-SC: ~0.78 with a moderate confidence interval. * Macro Average: ~0.91. 2. **QwQ-32B:** * SCL15: ~0.94 with a small confidence interval. * GSM8K-SC: ~0.93 with a small confidence interval. * PRM800K-SC: ~0.77 with a moderate confidence interval. * Macro Average: ~0.91. 3. **Qwen3-235B-A22B (thinking):** * SCL15: ~0.91 with a small confidence interval. * GSM8K-SC: ~0.92 with a small confidence interval. * PRM800K-SC: ~0.77 with a moderate confidence interval. * Macro Average: ~0.89. 4. **Qwen3-30B-A3B (thinking):** * SCL15: ~0.85 with a small confidence interval. * GSM8K-SC: ~0.90 with a small confidence interval. * PRM800K-SC: ~0.76 with a moderate confidence interval. * Macro Average: ~0.88. 5. **Qwen3-14B (thinking):** * SCL15: ~0.85 with a small confidence interval. * GSM8K-SC: ~0.94 with a small confidence interval. * PRM800K-SC: ~0.74 with a moderate confidence interval. * Macro Average: ~0.84. 6. **gemma-3-27b-it:** * SCL15: ~0.83 with a small confidence interval. * GSM8K-SC: ~0.82 with a small confidence interval. * PRM800K-SC: ~0.78 with a moderate confidence interval. * Macro Average: ~0.82. 7. **Qwen3-32B (thinking):** * SCL15: ~0.80 with a moderate confidence interval. * GSM8K-SC: ~0.91 with a small confidence interval. * PRM800K-SC: ~0.72 with a moderate confidence interval. * Macro Average: ~0.81. 8. **gemma-3-12b-it:** * SCL15: ~0.78 with a moderate confidence interval. * GSM8K-SC: ~0.78 with a small confidence interval. * PRM800K-SC: ~0.76 with a moderate confidence interval. * Macro Average: ~0.77. 9. **Phi-4-reasoning-plus:** * SCL15: ~0.75 with a moderate confidence interval. * GSM8K-SC: ~0.73 with a small confidence interval. * PRM800K-SC: ~0.71 with a moderate confidence interval. * Macro Average: ~0.71. ### Key Observations * **SCL15 consistently shows high accuracy** across all models, generally above 0.8, except for the last two models (gemma-3-12b-it and Phi-4-reasoning-plus). * **GSM8K-SC also exhibits high accuracy**, often comparable to or slightly higher than SCL15. * **PRM800K-SC generally has lower accuracy** compared to the other two, with more variability as indicated by the larger confidence intervals. * **Macro Average generally falls between PRM800K-SC and the higher-performing SCL15 and GSM8K-SC.** * The models **DeepSeek-R1-0528 and QwQ-32B** show the highest overall accuracy across all categories. * The models **gemma-3-12b-it and Phi-4-reasoning-plus** show the lowest overall accuracy across all categories. ### Interpretation The bar chart illustrates the performance of different models under the stress of injected internal errors. The SCL15 and GSM8K-SC categories consistently outperform PRM800K-SC, suggesting they are more robust to the introduced errors. The Macro Average provides a general performance metric, reflecting the combined performance of all categories. The confidence intervals indicate the reliability of the accuracy measurements; larger intervals suggest greater variability in performance. The models DeepSeek-R1-0528 and QwQ-32B appear to be the most resilient to internal errors, while gemma-3-12b-it and Phi-4-reasoning-plus are the least. This information is valuable for selecting models that maintain high accuracy even when faced with internal inconsistencies or noise. </details> Figure 10: Summary of mean accuracy across reasoning models Appendix C Sensitivity analysis C.1 Result of different temperature Apart from using models’ most confident prediction, we use temperature of 0.0 for 3 reasons: - More deterministic Temperature of 0.0 will not generate fully deterministic result due to finite precision. output eliminates sampling variance as a confounding factor. - It enables standardized comparison across models with different temperature calibrations. - Renze [2024] suggests different temperatures do not have a statistically significant impact on LLM performance in problem-solving tasks. We also report results using a temperature of 0.6 below and the result does not change our conclusion. Table 9: Mean accuracy and 95% confidence interval of models at temperature 0.6 | Model | SCLI5 | GSM8K-SC | PRM800K-SC | | --- | --- | --- | --- | | Llama-4-Maverick-17B-128E-Instruct-FP8 | 0.954 ± 0.024 | 0.424 ± 0.027 | 0.469 ± 0.046 | | DeepSeek-V3-0324 | 0.874 ± 0.039 | 0.42 ± 0.027 | 0.504 ± 0.046 | | Qwen2.5-72B-Instruct | 0.902 ± 0.035 | 0.574 ± 0.027 | 0.165 ± 0.034 | | Llama-4-Scout-17B-16E-Instruct | 0.976 ± 0.018 | 0.248 ± 0.023 | 0.272 ± 0.041 | | Llama-3.3-70B-Instruct | 0.496 ± 0.058 | 0.273 ± 0.024 | 0.243 ± 0.04 | | Qwen3-235B-A22B | 0.57 ± 0.057 | 0.091 ± 0.016 | 0.4 ± 0.045 | | phi-4 | 0.794 ± 0.047 | 0.093 ± 0.016 | 0.116 ± 0.03 | | Qwen2.5-7B-Instruct | 0.563 ± 0.058 | 0.183 ± 0.021 | 0.127 ± 0.031 | | Qwen2-7B-Instruct | 0.601 ± 0.057 | 0.071 ± 0.014 | 0.065 ± 0.023 | | Qwen3-14B | 0.007 ± 0.01 | 0.101 ± 0.016 | 0.27 ± 0.041 | | Qwen3-30B-A3B | 0.108 ± 0.036 | 0.07 ± 0.014 | 0.232 ± 0.039 | | Qwen3-32B | 0.038 ± 0.022 | 0.068 ± 0.014 | 0.105 ± 0.028 | | Meta-Llama-3.1-8B-Instruct | 0.182 ± 0.045 | 0.025 ± 0.008 | 0.022 ± 0.014 | | Mistral-Small-24B-Instruct-2501 | 0.122 ± 0.038 | 0.02 ± 0.008 | 0.038 ± 0.018 | C.2 PRM800K-SC result in 4,096 token budget To ensure a fair comparison between internal and external error correction, and across models, we maintain a fixed token budget of 1,024 across all conditions. This design choice partly isolates self-correction capabilities from the effect of test time compute, providing a more rigorous test of the blind spot phenomenon. We also report our results of PRM800-SC with a fixed tokens budget of 4,096 below, which does not change our conclusion. We do not report the result of SCLI5 and GSM8K-SC as the ratio of model responses exceeding 1,024 tokens is immaterial. Table 10: Mean accuracy of models in PRM800K-SC at different compute budget | Model | External Error | Internal Error | Appending “ Wait ” | | | | | --- | --- | --- | --- | --- | --- | --- | | Compute budget | 1,024 | 4,096 | 1,024 | 4,096 | 1,024 | 4,096 | | Llama-4-Maverick-17B-128E-Instruct-FP8 | 0.71 | 0.721 | 0.455 | 0.458 | 0.67 | 0.676 | | DeepSeek-V3-0324 | 0.775 | 0.938 | 0.475 | 0.509 | 0.772 | 0.821 | | Qwen2.5-72B-Instruct | 0.612 | 0.614 | 0.154 | 0.161 | 0.438 | 0.449 | | Llama-4-Scout-17B-16E-Instruct | 0.58 | 0.578 | 0.263 | 0.257 | 0.545 | 0.542 | | Llama-3.3-70B-Instruct | 0.359 | 0.366 | 0.246 | 0.257 | 0.46 | 0.469 | | Qwen3-235B-A22B | 0.786 | 0.806 | 0.348 | 0.368 | 0.705 | 0.732 | | phi-4 | 0.714 | 0.719 | 0.092 | 0.092 | 0.328 | 0.337 | | Qwen2.5-7B-Instruct | 0.576 | 0.569 | 0.141 | 0.141 | 0.442 | 0.444 | | Qwen2-7B-Instruct | 0.658 | 0.65 | 0.058 | 0.058 | 0.324 | 0.333 | | Qwen3-14B | 0.705 | 0.743 | 0.254 | 0.268 | 0.696 | 0.746 | | Qwen3-30B-A3B | 0.779 | 0.817 | 0.194 | 0.19 | 0.683 | 0.712 | | Qwen3-32B | 0.754 | 0.781 | 0.083 | 0.085 | 0.527 | 0.522 | | Meta-Llama-3.1-8B-Instruct | 0.181 | 0.183 | 0.02 | 0.02 | 0.194 | 0.203 | | Mistral-Small-24B-Instruct-2501 | 0.496 | 0.498 | 0.016 | 0.016 | 0.27 | 0.277 | Appendix D Prompt D.1 Generating GSM8K-SC ⬇ from pydantic import BaseModel class ReasoningWithMistake (BaseModel): reasoning_steps_with_one_mistake: List [str] mistake_step: int type_of_mistake: str description_of_mistake: str incorrect_answer: str ⬇ You are a helpful assistant that follow instructions. Output in JSON format. ⬇ < question > {question} </ question > < reasoning_steps > {reasoning_steps} </ reasoning_steps > < answer > {answer} </ answer > < type_of_mistake > {error_type}: {error_description} </ type_of_mistake > You task is to introduce one mistake in step {mistake_step} in < reasoning_steps > and arrive at an answer different from < answer >. You will output: - < reasoning_steps > with mistake - the step that contains the mistake - type of the mistake - description of the mistake - incorrect answer Figure 11: Output schema, system prompt and prompt for generating GSM8K-SC dataset ⬇ from pydantic import BaseModel class Calculation (BaseModel): incorrect_answer: float ⬇ You are a helpful assistant that follow instructions. Output in JSON format. ⬇ < question > {question} </ question > < description_of_mistake > {description_of_mistake} </ description_of_mistake > < incorrect_reasoning > {incorrect_reasoning} </ incorrect_reasoning > You are given a question, a description of the mistake, and the resulting incorrect reasoning. Your task is to follow the incorrect reasoning to arrive at the incorrect answer. Figure 12: Output schema, system prompt and prompt for validating GSM8K-SC dataset D.2 Automatic Evaluation ⬇ from pydantic import BaseModel class Evaluation (BaseModel): is_correct_answer: bool is_correct_reasoning: bool is_backtracking: bool is_admitting_mistake: bool ⬇ You are a helpful assistant that follow instructions. Output in JSON format. Figure 13: Output schema and system prompt for automatic evaluation of error in model ⬇ # FOR SCLI5 < question > {question} </ question > < golden_answer > {golden_answer} </ golden_answer > < given_wrong_answer > {given_wrong_answer} </ given_wrong_answer > < completion_from_model > {completion_from_model} </ completion_from_model > The model was provided a wrong answer < given_wrong_answer >, and is required to self correct and arrive at the golden answer. You have to assess if < completion_from_model > : - has backtracked - has finally provided the answer that matches the < golden_answer > - has provided correct reasoning - has admitted the mistake. ⬇ # FOR GSM8K - SC AND PRM800K - SC < question > {question} </ question > < golden_answer > {golden_answer} </ golden_answer > < given_wrong_reasoning > {given_wrong_reasoning} </ given_wrong_reasoning > < completion_from_model > {completion_from_model} </ completion_from_model > The model was provided a wrong step in the reasoning process < given_wrong_reasoning >, and is required to self correct and arrive at the golden answer. You have to assess if < completion_from_model > : - has backtracked - has finally provided the answer that matches the < golden_answer > - has provided correct reasoning - has admitted the mistake. Figure 14: Prompt for automatic evaluation of error in model ⬇ from pydantic import BaseModel class EvaluationErrorInUser (BaseModel): is_correct_answer: bool is_correct_critique: bool ⬇ You are a helpful assistant that follow instructions. Output in JSON format. Figure 15: Output schema and system prompt for automatic evaluation of error in user ⬇ # FOR SCLI5 < question_and_user_answer > {question_and_user_answer} </ question_and_user_answer > < golden_answer > {golden_answer} </ golden_answer > < response_from_model > {response_from_model} </ response_from_model > The model was provided with < question_and_user_answer > from user. You have to assess if < response_from_model > : - contains correct answer that matches the < golden_answer > - contains correct critique of < question_and_user_answer > ⬇ # FOR GSM8K - SC AND PRM800K - SC < question_and_user_reasoning > {question_and_user_reasoning} </ question_and_user_reasoning > < golden_answer > {golden_answer} </ golden_answer > < response_from_model > {response_from_model} </ response_from_model > The model was provided with < question_and_user_reasoning > from user. You have to assess if < response_from_model > : - contains correct answer that matches the < golden_answer > - contains correct critique of < question_and_user_reasoning > Figure 16: Prompt for automatic evaluation of error in user