## Line Chart: Best-of-N accuracy with different models ### Overview The image is a line chart comparing the "Best-of-N" accuracy of three different models (InternVL-2.5-8B-MPO, GPT-4.1-mini (4-14-25), and o4-mini (4-16-25)) as the number of selected CoTs (Chain of Thoughts) increases from 2 to 8. The chart displays accuracy (%) on the y-axis and the number of selected CoTs (k) on the x-axis. ### Components/Axes * **Title:** Best-of-N accuracy with different models * **X-axis:** * Label: Number of selected CoTs (k) * Scale: 2, 4, 6, 8 * **Y-axis:** * Label: Accuracy (%) * Scale: 65.0, 67.5, 70.0, 72.5, 75.0, 77.5, 80.0, 82.5, 85.0 * **Legend:** Located in the center of the chart. * Blue line with circle markers: InternVL-2.5-8B-MPO * Red line with square markers: GPT-4.1-mini (4-14-25) * Green line with cross markers: o4-mini (4-16-25) * **Horizontal dashed lines:** * Blue dashed line at approximately 65.3% * Red dashed line at approximately 71.5% * Green dashed line at approximately 80.7% ### Detailed Analysis * **InternVL-2.5-8B-MPO (Blue):** The line slopes upward. * At 2 CoTs: Accuracy is approximately 65.3% * At 4 CoTs: Accuracy is approximately 66.5% * At 6 CoTs: Accuracy is approximately 67.7% * At 8 CoTs: Accuracy is approximately 69.0% * **GPT-4.1-mini (4-14-25) (Red):** The line slopes upward. * At 2 CoTs: Accuracy is approximately 71.8% * At 4 CoTs: Accuracy is approximately 72.5% * At 6 CoTs: Accuracy is approximately 73.3% * At 8 CoTs: Accuracy is approximately 74.4% * **o4-mini (4-16-25) (Green):** The line slopes upward. * At 2 CoTs: Accuracy is approximately 81.7% * At 4 CoTs: Accuracy is approximately 82.5% * At 6 CoTs: Accuracy is approximately 84.0% * At 8 CoTs: Accuracy is approximately 85.3% ### Key Observations * The o4-mini model consistently outperforms the other two models across all numbers of selected CoTs. * The InternVL-2.5-8B-MPO model has the lowest accuracy among the three models. * All three models show an increase in accuracy as the number of selected CoTs increases. * The dashed lines appear to represent a baseline accuracy for each model, potentially without the use of CoTs. ### Interpretation The chart illustrates the impact of increasing the number of selected Chain of Thoughts (CoTs) on the accuracy of three different models. The o4-mini model demonstrates the highest accuracy, suggesting it benefits most from the CoT approach or is inherently better at the task being evaluated. The increasing trend in accuracy for all models indicates that using more CoTs generally improves performance, although the extent of improvement varies between models. The horizontal dashed lines may represent the baseline accuracy of each model without CoTs, providing a reference point for evaluating the effectiveness of the CoT strategy.

## Line Chart: Best-of-N Accuracy with Different Models ### Overview This line chart displays the Best-of-N accuracy of three different models – InternVL-2.5-8B-MPO, GPT-4.1-mini (4-14-25), and o4-mini (4-16-25) – as a function of the number of selected CoTs (Contexts or Chains of Thought). The x-axis represents the number of selected CoTs in thousands (k), ranging from 2 to 8. The y-axis represents the accuracy in percentage, ranging from 65% to 85%. ### Components/Axes * **Title:** Best-of-N accuracy with different models * **X-axis Label:** Number of selected CoTs (k) * **Y-axis Label:** Accuracy (%) * **Legend:** * InternVL-2.5-8B-MPO (Blue, dashed line with circle markers) * GPT-4.1-mini (4-14-25) (Red, dashed line with square markers) * o4-mini (4-16-25) (Green, dashed line with cross markers) * **X-axis Markers:** 2, 4, 6, 8 * **Y-axis Markers:** 65, 70, 75, 80, 85 ### Detailed Analysis * **InternVL-2.5-8B-MPO (Blue):** The line slopes upward, indicating increasing accuracy with more selected CoTs. * At 2k CoTs: Approximately 65.5% accuracy. * At 4k CoTs: Approximately 66.5% accuracy. * At 6k CoTs: Approximately 68.5% accuracy. * At 8k CoTs: Approximately 69.5% accuracy. * **GPT-4.1-mini (4-14-25) (Red):** The line initially remains relatively flat, then decreases slightly before increasing again. * At 2k CoTs: Approximately 72.5% accuracy. * At 4k CoTs: Approximately 72.5% accuracy. * At 6k CoTs: Approximately 71.5% accuracy. * At 8k CoTs: Approximately 72.5% accuracy. * **o4-mini (4-16-25) (Green):** The line slopes consistently upward, showing a clear positive correlation between the number of selected CoTs and accuracy. * At 2k CoTs: Approximately 81.5% accuracy. * At 4k CoTs: Approximately 82.5% accuracy. * At 6k CoTs: Approximately 84.0% accuracy. * At 8k CoTs: Approximately 85.0% accuracy. ### Key Observations * The o4-mini model consistently exhibits the highest accuracy across all tested numbers of CoTs. * The InternVL-2.5-8B-MPO model shows the lowest accuracy, but its performance improves steadily with more CoTs. * GPT-4.1-mini's accuracy remains relatively stable, with a slight dip at 6k CoTs. * The accuracy gains diminish as the number of CoTs increases, particularly for the o4-mini model. ### Interpretation The chart demonstrates the impact of increasing the number of selected Contexts (CoTs) on the Best-of-N accuracy of different language models. The o4-mini model appears to be the most effective in leveraging additional CoTs to improve its performance. The InternVL-2.5-8B-MPO model benefits the most from increasing the number of CoTs, suggesting it is more sensitive to the quality and diversity of the contexts provided. The relatively stable performance of GPT-4.1-mini suggests it may have already reached a performance plateau or is less reliant on the number of CoTs. The diminishing returns observed with increasing CoTs indicate that there is a point beyond which adding more contexts does not significantly improve accuracy. This could be due to redundancy in the contexts or limitations in the model's ability to effectively process and integrate a large number of inputs. The chart highlights the trade-off between computational cost (increasing the number of CoTs) and accuracy gains.

## Line Chart: Best-of-N Accuracy with Different Models ### Overview The image is a line chart titled "Best-of-N accuracy with different models." It compares the performance of three distinct AI models as a function of the number of selected Chain-of-Thought (CoT) reasoning paths, denoted as 'k'. The chart demonstrates how accuracy improves for each model as more CoT paths are considered. ### Components/Axes * **Title:** "Best-of-N accuracy with different models" (centered at the top). * **Y-Axis:** Labeled "Accuracy (%)". The scale runs from 65.0 to 85.0, with major tick marks every 2.5 units (65.0, 67.5, 70.0, 72.5, 75.0, 77.5, 80.0, 82.5, 85.0). * **X-Axis:** Labeled "Number of selected CoTs (k)". The scale shows discrete values: 2, 4, 6, and 8. * **Legend:** Positioned in the top-left quadrant of the plot area. It contains three entries: 1. **InternVL-2.5-8B-MPO:** Represented by a blue line with circular markers. 2. **GPT-4.1-mini (4-14-25):** Represented by a red line with square markers. 3. **o4-mini (4-16-25):** Represented by a green line with 'x' (cross) markers. * **Baseline Indicators:** Each model has a corresponding horizontal dashed line in its color, indicating a baseline accuracy level (likely the model's performance without CoT selection or with k=1). ### Detailed Analysis The chart plots three data series, each showing a positive, roughly linear trend where accuracy increases with the number of selected CoTs (k). **1. InternVL-2.5-8B-MPO (Blue Line, Circle Markers)** * **Trend:** Slopes gently upward from left to right. * **Data Points (Approximate):** * k=2: ~65.2% * k=4: ~66.5% * k=6: ~67.8% * k=8: ~68.9% * **Baseline (Blue Dashed Line):** Positioned at approximately 65.4%. **2. GPT-4.1-mini (4-14-25) (Red Line, Square Markers)** * **Trend:** Slopes upward, with a slightly steeper incline than the blue line. * **Data Points (Approximate):** * k=2: ~71.8% * k=4: ~72.5% * k=6: ~73.2% * k=8: ~74.4% * **Baseline (Red Dashed Line):** Positioned at approximately 71.5%. **3. o4-mini (4-16-25) (Green Line, Cross Markers)** * **Trend:** Slopes upward with the steepest incline of the three models. * **Data Points (Approximate):** * k=2: ~81.5% * k=4: ~82.5% * k=6: ~84.2% * k=8: ~85.2% * **Baseline (Green Dashed Line):** Positioned at approximately 80.5%. ### Key Observations 1. **Consistent Hierarchy:** The o4-mini model consistently achieves the highest accuracy across all values of k, followed by GPT-4.1-mini, and then InternVL-2.5-8B-MPO. The performance gaps between models are significant and remain relatively stable. 2. **Positive Scaling:** All three models show a clear benefit from increasing the number of selected CoTs (k). The accuracy gain from k=2 to k=8 is approximately 3.7% for InternVL, 2.6% for GPT-4.1-mini, and 3.7% for o4-mini. 3. **Baseline Comparison:** For each model, the plotted accuracy at k=2 is already above its respective dashed baseline, indicating that even selecting from just two CoT paths provides a measurable improvement over the baseline. 4. **Marginal Diminishing Returns:** While the trend is positive, the rate of improvement appears to slow slightly for each model as k increases (the lines are slightly concave down), suggesting diminishing marginal returns from adding more CoT paths. ### Interpretation This chart provides empirical evidence for the "Best-of-N" sampling strategy in AI reasoning tasks. The data suggests that: * **CoT Selection is Effective:** Generating multiple reasoning paths (CoTs) and selecting among them (likely based on a confidence metric or verifier) reliably improves final answer accuracy compared to a single-path baseline for all tested models. * **Model Capability is Paramount:** While the strategy improves all models, the underlying capability of the base model (o4-mini > GPT-4.1-mini > InternVL) is the primary determinant of absolute performance. The best strategy cannot close the fundamental gap between model generations or architectures. * **Practical Trade-off:** The positive but sub-linear scaling indicates a trade-off between computational cost (generating and evaluating k paths) and accuracy gain. The optimal 'k' in practice would balance this trade-off, as moving from k=6 to k=8 yields a smaller gain than moving from k=2 to k=4. * **Consistency of Improvement:** The fact that all models follow the same trend reinforces the generalizability of the Best-of-N technique across different model families and sizes. The specific dates in the model names (4-14-25, 4-16-25) may indicate versioning or release dates, suggesting this is a comparison of contemporaneous models.

## Line Chart: Best-of-N accuracy with different models ### Overview The chart compares the accuracy of three AI models (InternVL-2.5-8B-MPO, GPT-4.1-mini, and o4-mini) across different numbers of selected Chain-of-Thought (CoT) steps (k=2,4,6,8). Accuracy is measured in percentage, with distinct performance trends observed for each model. ### Components/Axes - **X-axis**: Number of selected CoTs (k) - Discrete values at 2, 4, 6, 8 - **Y-axis**: Accuracy (%) - Continuous scale from 65% to 85% - **Legend**: Located in bottom-left quadrant - Blue circles: InternVL-2.5-8B-MPO - Red squares: GPT-4.1-mini (4-14-25) - Green crosses: o4-mini (4-16-25) - **Dashed reference line**: Green dashed line at 80.5% accuracy ### Detailed Analysis 1. **InternVL-2.5-8B-MPO** (Blue line): - Accuracy increases from 65.2% (k=2) to 68.5% (k=8) - Linear upward trend with consistent slope - Data points: (2,65.2), (4,66.8), (6,67.6), (8,68.5) 2. **GPT-4.1-mini** (Red line): - Accuracy rises from 72.1% (k=2) to 74.5% (k=8) - Steeper slope than InternVL, with sharper increases at k=4 and k=6 - Data points: (2,72.1), (4,73.2), (6,73.8), (8,74.5) 3. **o4-mini** (Green line): - Highest performance across all k values - Accuracy starts at 81.5% (k=2) and reaches 85.2% (k=8) - Slightly concave upward curve with diminishing returns - Data points: (2,81.5), (4,82.3), (6,84.1), (8,85.2) ### Key Observations - All models show improved accuracy with more CoT steps - o4-mini maintains >10% accuracy advantage over GPT-4.1-mini - Green dashed line at 80.5% intersects o4-mini's performance at k=2 - InternVL-2.5-8B-MPO shows the most gradual improvement curve - GPT-4.1-mini demonstrates strongest performance gains between k=2→4 and k=4→6 ### Interpretation The data suggests that increasing CoT steps improves model performance across all architectures, with o4-mini demonstrating superior base capabilities and scalability. The green dashed line at 80.5% appears to represent a performance threshold, which o4-mini exceeds even at minimal CoT steps (k=2). The InternVL model shows the most linear improvement pattern, suggesting more predictable scaling with CoT expansion. The GPT-4.1-mini's sharper mid-range gains indicate potential optimization opportunities in its CoT implementation. These results highlight the importance of CoT step selection in model performance optimization, with o4-mini emerging as the most efficient architecture for this task.