## Bar Chart: Self-Correction Performance Comparison on MATH Dataset ### Overview The image is a bar chart comparing the performance (accuracy in percentage) of different Large Language Models (LLMs) on the MATH dataset. The chart compares the performance of "Base LLMs", "Self-Correction", and "Self-Correction + Our Cross-DPO" techniques across various models. ### Components/Axes * **Title:** Self-Correction Performance Comparison on MATH Dataset * **Y-axis:** Accuracy (%), with a scale from 40 to 85 in increments of 5. * **X-axis:** LLM Models: Llama3.1-8B-Instruct, DeepSeek-Math-7B, Qwen2.5-Math-7B, GPT-4o, Claude-3.5-Sonnet, Gemini-1.5-pro, SuperCorrect-Qwen-7B * **Legend:** Located at the top-left corner: * Light Blue: Base LLMs * Salmon: Self-Correction * Yellow: Self-Correction + Our Cross-DPO ### Detailed Analysis The chart presents accuracy percentages for each model under different conditions. The values are as follows: * **Llama3.1-8B-Instruct:** * Base LLMs (Light Blue): 51.9% * Self-Correction (Salmon): 49.8% * Difference: -2.1% * **DeepSeek-Math-7B:** * Base LLMs (Light Blue): 46.8% * Self-Correction (Salmon): 43.2% * Difference: -3.6% * **Qwen2.5-Math-7B:** * Base LLMs (Light Blue): 55.1% * Self-Correction (Salmon): 55.4% * Difference: +0.3% * **GPT-4o:** * Base LLMs (Light Blue): 76.6% * Self-Correction (Salmon): 77.8% * Difference: +1.2% * **Claude-3.5-Sonnet:** * Base LLMs (Light Blue): 71.1% * Self-Correction (Salmon): 73.4% * Difference: +2.3% * **Gemini-1.5-pro:** * Base LLMs (Light Blue): 67.7% * Self-Correction (Salmon): 69.1% * Difference: +1.4% * **SuperCorrect-Qwen-7B:** * Base LLMs (Light Blue): 70.2% * Self-Correction + Our Cross-DPO (Yellow): 75.4% * Difference: +5.2% ### Key Observations * For Llama3.1-8B-Instruct and DeepSeek-Math-7B, self-correction *decreases* the accuracy. * For Qwen2.5-Math-7B, GPT-4o, Claude-3.5-Sonnet, and Gemini-1.5-pro, self-correction *increases* the accuracy. * SuperCorrect-Qwen-7B with "Self-Correction + Our Cross-DPO" shows the highest accuracy among the models tested. ### Interpretation The chart indicates that the effectiveness of self-correction varies across different LLMs. For some models, it improves performance on the MATH dataset, while for others, it degrades performance. The "Self-Correction + Our Cross-DPO" technique appears to be particularly effective for the SuperCorrect-Qwen-7B model, resulting in a significant performance boost. This suggests that the benefits of self-correction are model-dependent and can be further enhanced by specific training techniques like Cross-DPO.

## Bar Chart: Self-Correction Performance Comparison on MATH Dataset ### Overview This bar chart compares the accuracy of several Large Language Models (LLMs) on the MATH dataset, evaluating performance with three different approaches: Base LLMs, Self-Correction, and Self-Correction combined with Our Cross-DPO. Accuracy is measured in percentage (%). ### Components/Axes * **X-axis:** LLM Names - Llama-3.8B-Instruct, DeepSeek-Math-7B, Qwen2.5-Math-7B, GPT-4, Claude-3.5-Sonnet, Gemini-1.5-pro, SuperCorrect-Qwen-7B. * **Y-axis:** Accuracy (%) - Scale ranges from 40% to 85%. * **Legend:** * Blue: Base LLMs * Red: Self-Correction * Orange: Self-Correction + Our Cross-DPO * **Title:** "Self-Correction Performance Comparison on MATH Dataset" ### Detailed Analysis The chart consists of grouped bar plots for each LLM, representing the accuracy achieved under each of the three conditions. Each LLM has three bars next to each other, one for each condition. Percentage change values are displayed above the bars for the Self-Correction and Self-Correction + Our Cross-DPO conditions, relative to the Base LLM performance. Here's a breakdown of the data points: * **Llama-3.8B-Instruct:** * Base LLMs: Approximately 51.9% * Self-Correction: Approximately 49.8% (-2.1% change) * Self-Correction + Our Cross-DPO: Approximately 43.2% (-3.6% change) * **DeepSeek-Math-7B:** * Base LLMs: Approximately 46.8% * Self-Correction: Approximately 43.2% (-3.6% change) * **Qwen2.5-Math-7B:** * Base LLMs: Approximately 55.1% * Self-Correction: Approximately 55.4% (+0.3% change) * **GPT-4:** * Base LLMs: Approximately 73.4% * Self-Correction: Approximately 76.6% (+1.2% change) * **Claude-3.5-Sonnet:** * Base LLMs: Approximately 71.1% * Self-Correction: Approximately 73.4% (+2.3% change) * **Gemini-1.5-pro:** * Base LLMs: Approximately 67.7% * Self-Correction: Approximately 70.2% (+1.4% change) * **SuperCorrect-Qwen-7B:** * Base LLMs: Approximately 75.4% * Self-Correction + Our Cross-DPO: Approximately 75.4% (+5.2% change) ### Key Observations * For Llama-3.8B-Instruct and DeepSeek-Math-7B, self-correction *decreases* accuracy compared to the base LLM. * Qwen2.5-Math-7B shows a slight improvement with self-correction. * GPT-4, Claude-3.5-Sonnet, and Gemini-1.5-pro all show improvements with self-correction. * SuperCorrect-Qwen-7B shows the largest improvement with the combined self-correction and Cross-DPO approach. * The largest performance difference between base LLM and the combined approach is observed with SuperCorrect-Qwen-7B. ### Interpretation The data suggests that the effectiveness of self-correction techniques varies significantly depending on the underlying LLM. For some models (Llama-3.8B-Instruct, DeepSeek-Math-7B), self-correction appears to be detrimental, potentially due to the models' inherent limitations or the specific implementation of the self-correction process. However, for more capable models (GPT-4, Claude-3.5-Sonnet, Gemini-1.5-pro), self-correction improves accuracy. The substantial improvement observed with SuperCorrect-Qwen-7B, when combined with Cross-DPO, indicates that a well-tuned self-correction process, leveraging techniques like Cross-DPO, can significantly enhance performance on the MATH dataset. The negative changes for Llama and DeepSeek suggest that these models may benefit from a different self-correction strategy or further pre-training. The MATH dataset is a challenging benchmark for mathematical reasoning, and the results highlight the importance of model capacity and the quality of the self-correction mechanism.

## Bar Chart: Self-Correction Performance Comparison on MATH Dataset ### Overview This is a grouped bar chart comparing the accuracy (in percentage) of various Large Language Models (LLMs) on the MATH dataset under three different conditions: the base model, the model with self-correction, and the model with self-correction enhanced by a method called "Cross-DPO." The chart visualizes the performance change introduced by self-correction and the additional impact of the Cross-DPO technique. ### Components/Axes * **Chart Title:** "Self-Correction Performance Comparison on MATH Dataset" * **Y-Axis:** Labeled "Accuracy (%)". The scale runs from 40 to 85, with major gridlines at intervals of 5%. * **X-Axis:** Lists seven different LLM models. From left to right: 1. Llama3.1-8B-Instruct 2. DeepSeek-Math-7B 3. Qwen2.5-Math-7B 4. GPT-4o 5. Claude-3.5-Sonnet 6. Gemini-1.5-pro 7. SuperCorrect-Qwen-7B * **Legend:** Positioned in the top-left corner of the chart area. * **Blue Bar:** "Base LLMs" * **Red Bar:** "Self-Correction" * **Yellow Bar:** "Self-Correction + Our Cross-DPO" * **Data Annotations:** Each bar has its exact accuracy percentage written above it. For the "Self-Correction" (red) and "Self-Correction + Our Cross-DPO" (yellow) bars, a green or red arrow and a percentage value indicate the change from the corresponding "Base LLMs" (blue) bar. ### Detailed Analysis The performance data for each model, extracted by matching bar colors to the legend, is as follows: 1. **Llama3.1-8B-Instruct** * Base LLMs (Blue): 51.9% * Self-Correction (Red): 49.8% * **Trend:** The red bar is shorter than the blue bar. The annotation shows a **-2.1%** change (red arrow), indicating self-correction decreased accuracy. 2. **DeepSeek-Math-7B** * Base LLMs (Blue): 46.8% * Self-Correction (Red): 43.2% * **Trend:** The red bar is shorter than the blue bar. The annotation shows a **-3.6%** change (red arrow), indicating self-correction decreased accuracy. 3. **Qwen2.5-Math-7B** * Base LLMs (Blue): 55.1% * Self-Correction (Red): 55.4% * **Trend:** The red bar is marginally taller than the blue bar. The annotation shows a **+0.3%** change (green arrow), indicating a very slight improvement from self-correction. 4. **GPT-4o** * Base LLMs (Blue): 76.6% * Self-Correction (Red): 77.8% * **Trend:** The red bar is taller than the blue bar. The annotation shows a **+1.2%** change (green arrow), indicating self-correction improved accuracy. 5. **Claude-3.5-Sonnet** * Base LLMs (Blue): 71.1% * Self-Correction (Red): 73.4% * **Trend:** The red bar is taller than the blue bar. The annotation shows a **+2.3%** change (green arrow), indicating self-correction improved accuracy. 6. **Gemini-1.5-pro** * Base LLMs (Blue): 67.7% * Self-Correction (Red): 69.1% * **Trend:** The red bar is taller than the blue bar. The annotation shows a **+1.4%** change (green arrow), indicating self-correction improved accuracy. 7. **SuperCorrect-Qwen-7B** * Base LLMs (Blue): 70.2% * Self-Correction + Our Cross-DPO (Yellow): 75.4% * **Trend:** This model group only shows the Base and the enhanced condition. The yellow bar is significantly taller than the blue bar. The annotation shows a **+5.2%** change (green arrow), indicating the Cross-DPO method provided a substantial boost over the base model. ### Key Observations * **Variable Impact of Self-Correction:** The effect of standard self-correction (red bars) is inconsistent. It leads to a performance **decrease** for Llama3.1-8B-Instruct (-2.1%) and DeepSeek-Math-7B (-3.6%), a negligible increase for Qwen2.5-Math-7B (+0.3%), and a moderate increase for the larger models GPT-4o, Claude-3.5-Sonnet, and Gemini-1.5-pro. * **Strong Performance of Larger Models:** The base accuracy (blue bars) is generally higher for the proprietary models (GPT-4o, Claude-3.5-Sonnet, Gemini-1.5-pro) compared to the smaller, open-source models listed on the left. * **Significant Gain from Cross-DPO:** The "Self-Correction + Our Cross-DPO" condition (yellow bar) is only shown for the SuperCorrect-Qwen-7B model, where it yields the largest single improvement on the chart (+5.2%). * **Highest Overall Accuracy:** GPT-4o with self-correction achieves the highest displayed accuracy at 77.8%. ### Interpretation The data suggests that the efficacy of self-correction as a technique for improving mathematical reasoning in LLMs is highly model-dependent. It is not a universal enhancer and can even be detrimental to some models (like Llama3.1-8B-Instruct and DeepSeek-Math-7B in this test). The positive gains observed in larger, more capable base models (GPT-4o, Claude, Gemini) might indicate that self-correction requires a certain threshold of foundational reasoning ability to be beneficial. The most notable result is the performance of "SuperCorrect-Qwen-7B" with the added "Cross-DPO" method. The +5.2% jump is the largest improvement shown, implying that this specific technique (Cross-DPO) may be a more effective or targeted way to leverage self-correction for performance gains on the MATH dataset compared to standard self-correction alone. The chart serves as evidence that simply applying self-correction is insufficient; the method of implementation (like Cross-DPO) and the base model's characteristics are critical factors for success.

## Bar Chart: Self-Correction Performance Comparison on MATH Dataset ### Overview The bar chart compares the accuracy of different language models (LLMs) on a MATH dataset after applying self-correction techniques. The chart shows the baseline accuracy, self-correction accuracy, and the accuracy after applying self-correction with a cross-DPO method. ### Components/Axes - **X-axis**: List of different language models: Llama3.1-8B-Instruct, DeepSeek-Math-7B, Qwen2.5-Math-7B, GPT-40, Claude-3.5-Sonnet, Gemini-1.5-pro, SuperCorrect-Qwen-7B. - **Y-axis**: Accuracy percentage, ranging from 40% to 85%. - **Legend**: Three categories of accuracy: Base LLMs, Self-Correction, Self-Correction + Our Cross-DPO. ### Detailed Analysis or ### Content Details - **Llama3.1-8B-Instruct**: The baseline accuracy is 51.9%, and after self-correction, it increases to 55.1%. The accuracy with self-correction and cross-DPO is 55.4%. - **DeepSeek-Math-7B**: The baseline accuracy is 46.8%, and after self-correction, it decreases to 43.2%. The accuracy with self-correction and cross-DPO is 43.5%. - **Qwen2.5-Math-7B**: The baseline accuracy is 55.1%, and after self-correction, it increases to 57.3%. The accuracy with self-correction and cross-DPO is 57.6%. - **GPT-40**: The baseline accuracy is 73.4%, and after self-correction, it increases to 75.7%. The accuracy with self-correction and cross-DPO is 76.0%. - **Claude-3.5-Sonnet**: The baseline accuracy is 67.7%, and after self-correction, it increases to 70.1%. The accuracy with self-correction and cross-DPO is 70.4%. - **Gemini-1.5-pro**: The baseline accuracy is 70.2%, and after self-correction, it increases to 72.5%. The accuracy with self-correction and cross-DPO is 72.8%. - **SuperCorrect-Qwen-7B**: The baseline accuracy is 75.4%, and after self-correction, it increases to 77.6%. The accuracy with self-correction and cross-DPO is 78.0%. ### Key Observations - The language models with self-correction show a significant improvement in accuracy compared to the baseline. - The language models with self-correction and cross-DPO show the highest accuracy, indicating the effectiveness of the cross-DPO method. - There is a noticeable increase in accuracy for all models after applying self-correction, with the highest increase observed in the SuperCorrect-Qwen-7B model. ### Interpretation The data suggests that self-correction techniques can significantly improve the accuracy of language models on the MATH dataset. The cross-DPO method appears to be particularly effective, as it leads to the highest accuracy across all models. This improvement is crucial for applications that require high accuracy, such as educational tools and scientific research. The results also highlight the potential of self-correction methods in enhancing the performance of language models, which can have a positive impact on various fields that rely on accurate language processing.

# Self-Correction Performance Comparison on MATH Dataset ## Chart Structure - **Title**: "Self-Correction Performance Comparison on MATH Dataset" - **X-Axis**: Model names (categorical) - **Y-Axis**: Accuracy (%) [40% to 85%] - **Legend**: Located in top-left corner - Blue: Base LLMs - Red: Self-Correction - Yellow: Self-Correction + Our Cross-DPO ## Data Series 1. **Base LLMs** (Blue) 2. **Self-Correction** (Red) 3. **Self-Correction + Our Cross-DPO** (Yellow) ## Key Data Points & Annotations | Model | Base LLMs (%) | Self-Correction (%) | Self-Correction + Cross-DPO (%) | Change vs Base LLMs | |------------------------|---------------|---------------------|----------------------------------|---------------------| | Llama3.1-8B-Instruct | 51.9 | 49.8 | - | -2.1% | | DeepSeek-Math-7B | 46.8 | 43.2 | - | -3.6% | | Qwen2.5-Math-7B | 55.1 | 55.4 | - | +0.3% | | GPT-4o | 76.6 | 77.8 | - | +1.2% | | Claude-3.5-Sonnet | 71.1 | 73.4 | - | +2.3% | | Gemini-1.5-pro | 67.7 | 69.1 | - | +1.4% | | SuperCorrect-Qwen-7B | 70.2 | 75.4 | 75.4 | +5.2% | ## Spatial Grounding - **Legend Position**: Top-left corner - **Bar Colors**: - Blue bars: Base LLMs - Red bars: Self-Correction - Yellow bar: Self-Correction + Cross-DPO (only for SuperCorrect-Qwen-7B) ## Trend Verification 1. **Llama3.1-8B-Instruct**: Base LLMs (51.9%) → Self-Correction (49.8%) [↓] 2. **DeepSeek-Math-7B**: Base LLMs (46.8%) → Self-Correction (43.2%) [↓] 3. **Qwen2.5-Math-7B**: Base LLMs (55.1%) → Self-Correction (55.4%) [↑] 4. **GPT-4o**: Base LLMs (76.6%) → Self-Correction (77.8%) [↑] 5. **Claude-3.5-Sonnet**: Base LLMs (71.1%) → Self-Correction (73.4%) [↑] 6. **Gemini-1.5-pro**: Base LLMs (67.7%) → Self-Correction (69.1%) [↑] 7. **SuperCorrect-Qwen-7B**: - Base LLMs (70.2%) → Self-Correction (75.4%) [↑] - Self-Correction + Cross-DPO (75.4%) [→] ## Critical Observations 1. **Performance Gains**: - Self-Correction improves accuracy in 5/7 models - Cross-DPO further enhances performance in SuperCorrect-Qwen-7B (+5.2%) 2. **Largest Improvement**: SuperCorrect-Qwen-7B shows the most significant gain (+5.2%) 3. **Performance Loss**: - Llama3.1-8B-Instruct and DeepSeek-Math-7B show declines (-2.1% and -3.6%) ## Language Notes - All text is in English - No non-English content detected