## Scatter Plot: Test Time Accuracy vs. Max Thinking Length for MathVision, MathVista, and MMMU ### Overview The image presents three scatter plots comparing the test time accuracy (in percentage) against the maximum thinking length (in k tokens) for three different models: MathVision, MathVista, and MMMU. Each plot shows how the accuracy changes as the maximum thinking length increases. ### Components/Axes * **X-axis (Horizontal):** Max Thinking Length (k tokens). The axis markers are at 1, 2, 4, 8, and 16. * **Y-axis (Vertical):** Test Time Accuracy (%). The scale varies for each plot to best display the data. * **MathVision:** Ranges from 16% to 36%. * **MathVista:** Ranges from 66% to 71%. * **MMMU:** Ranges from 48% to 62%. * **Data Points:** Black dots representing the accuracy at specific thinking lengths. Each data point is labeled with its corresponding accuracy percentage. * **Titles:** Each plot has a title indicating the model being evaluated: MathVision, MathVista, and MMMU. ### Detailed Analysis **MathVision:** * **Trend:** The test time accuracy generally increases as the maximum thinking length increases. * **Data Points:** * 1k tokens: 18.7% * 2k tokens: 22.6% * 4k tokens: 29.0% * 8k tokens: 34.0% * 16k tokens: 36.8% **MathVista:** * **Trend:** The test time accuracy increases sharply from 1k to 4k tokens, then plateaus. * **Data Points:** * 1k tokens: 66.7% * 2k tokens: 69.0% * 4k tokens: 70.9% * 8k tokens: 70.6% * 16k tokens: 71.3% **MMMU:** * **Trend:** The test time accuracy increases as the maximum thinking length increases. * **Data Points:** * 1k tokens: 49.2% * 2k tokens: 52.4% * 4k tokens: 56.2% * 8k tokens: 60.1% * 16k tokens: 61.7% ### Key Observations * MathVista has the highest test time accuracy overall, with values consistently above 66%. * MathVision has the lowest initial accuracy (18.7% at 1k tokens) but shows a substantial increase with longer thinking lengths. * MMMU shows a steady increase in accuracy as the thinking length increases, but its overall accuracy remains lower than MathVista. * All three models show diminishing returns in accuracy gains as the thinking length increases from 8k to 16k tokens. ### Interpretation The plots suggest that increasing the maximum thinking length generally improves the test time accuracy for all three models. However, the extent of improvement varies. MathVista appears to benefit the most from a thinking length of up to 4k tokens, after which the gains are minimal. MathVision and MMMU show more consistent improvements across the range of thinking lengths tested, although the rate of improvement slows down at higher values. The data indicates that there is a trade-off between the computational cost of longer thinking lengths and the resulting accuracy gains. Depending on the specific application and resource constraints, different models and thinking lengths may be optimal. MathVista might be preferred for applications where high accuracy is crucial and computational resources are limited, while MathVision and MMMU might be suitable for scenarios where incremental improvements in accuracy are valuable and more computational resources are available.

\n ## Scatter Plots: Accuracy vs. Max Thinking Length for Math Reasoning Benchmarks ### Overview The image presents three separate scatter plots, each displaying the relationship between "Max Thinking Length (k tokens)" and "Test Time Accuracy (%)" for different math reasoning benchmarks: MathVision, MathVista, and MMMU. Each plot contains four data points, representing accuracy scores at different thinking lengths. ### Components/Axes Each plot shares the following components: * **X-axis:** "Max Thinking Length (k tokens)" with markers at 1, 2, 4, 8, and 16. * **Y-axis:** "Test Time Accuracy (%)" ranging from approximately 16% to 72%. * **Title:** Indicates the benchmark being evaluated (MathVision, MathVista, MMMU). * **Data Points:** Black circular markers representing accuracy values at specific thinking lengths. ### Detailed Analysis **1. MathVision** * **Trend:** The accuracy generally increases as the Max Thinking Length increases. * **Data Points:** * Max Thinking Length = 1 k tokens: Accuracy ≈ 18.7% * Max Thinking Length = 2 k tokens: Accuracy ≈ 22.6% * Max Thinking Length = 4 k tokens: Accuracy ≈ 29.0% * Max Thinking Length = 8 k tokens: Accuracy ≈ 34.0% * Max Thinking Length = 16 k tokens: Accuracy ≈ 36.8% **2. MathVista** * **Trend:** The accuracy increases rapidly from 1 to 4 k tokens, then plateaus with a slight increase from 4 to 16 k tokens. * **Data Points:** * Max Thinking Length = 1 k tokens: Accuracy ≈ 66.7% * Max Thinking Length = 2 k tokens: Accuracy ≈ 69.0% * Max Thinking Length = 4 k tokens: Accuracy ≈ 70.9% * Max Thinking Length = 8 k tokens: Accuracy ≈ 70.6% * Max Thinking Length = 16 k tokens: Accuracy ≈ 71.3% **3. MMMU** * **Trend:** The accuracy increases steadily as the Max Thinking Length increases. * **Data Points:** * Max Thinking Length = 1 k tokens: Accuracy ≈ 49.2% * Max Thinking Length = 2 k tokens: Accuracy ≈ 52.4% * Max Thinking Length = 4 k tokens: Accuracy ≈ 56.2% * Max Thinking Length = 8 k tokens: Accuracy ≈ 60.1% * Max Thinking Length = 16 k tokens: Accuracy ≈ 61.7% ### Key Observations * MathVista consistently achieves the highest accuracy across all thinking lengths. * MathVision shows the lowest accuracy, but exhibits a clear positive correlation between thinking length and performance. * The rate of accuracy improvement diminishes with increasing thinking length for MathVista, suggesting a point of diminishing returns. * MMMU shows a consistent, linear improvement in accuracy with increasing thinking length. ### Interpretation These plots demonstrate the impact of "Max Thinking Length" on the performance of language models on various math reasoning benchmarks. The "Max Thinking Length" parameter likely controls the amount of computational resources (tokens) allocated to the model for problem-solving. The differences in accuracy across benchmarks suggest varying levels of complexity and the models' inherent capabilities in tackling different types of math problems. MathVista appears to be the easiest benchmark, as it achieves high accuracy even with limited thinking length. MathVision is the most challenging, requiring more extensive reasoning to achieve comparable results. The diminishing returns observed in MathVista indicate that beyond a certain point, increasing the thinking length does not significantly improve performance. This could be due to the model reaching its capacity to effectively utilize additional computational resources for that specific task. The linear improvement in MMMU suggests that the model could potentially benefit from even longer thinking lengths, although practical limitations (computational cost) may exist. These results are valuable for optimizing the performance of language models on math reasoning tasks by identifying the optimal balance between thinking length and accuracy for each benchmark.

## Scatter Plot Series: Model Accuracy vs. Thinking Length ### Overview The image displays three separate scatter plots arranged horizontally. Each plot illustrates the relationship between a model's "Max Thinking Length" (in thousands of tokens) and its "Test Time Accuracy" (as a percentage) on a specific benchmark. The benchmarks are, from left to right: **MathVision**, **MathVista**, and **MMMU**. All plots share the same x-axis label and scale but have different y-axis scales and data ranges. ### Components/Axes * **Titles:** Each plot has a bold, centered title at the top: "MathVision", "MathVista", "MMMU". * **X-Axis (Common):** Labeled "Max Thinking Length (k tokens)". The axis has discrete tick marks at the values: 1, 2, 4, 8, and 16. * **Y-Axis (Per Plot):** Labeled "Test Time Accuracy (%)". The scale and range differ for each plot: * **MathVision:** Ranges from 16% to 36%, with major ticks at 16, 20, 24, 28, 32, 36. * **MathVista:** Ranges from 66% to 71%, with major ticks at 66, 67, 68, 69, 70, 71. * **MMMU:** Ranges from 48% to 60%, with major ticks at 48, 52, 56, 60. * **Data Series:** Each plot contains a single data series represented by black circular markers. Each marker is annotated with its precise percentage value. ### Detailed Analysis **1. MathVision Plot (Left)** * **Trend:** Shows a strong, positive, and roughly logarithmic trend. Accuracy increases rapidly with thinking length initially, then the rate of improvement slows. * **Data Points:** * At 1k tokens: 18.7% * At 2k tokens: 22.6% * At 4k tokens: 29.0% * At 8k tokens: 34.0% * At 16k tokens: 36.8% **2. MathVista Plot (Center)** * **Trend:** Shows a positive trend that plateaus significantly after 4k tokens. The improvement from 4k to 16k tokens is minimal. * **Data Points:** * At 1k tokens: 66.7% * At 2k tokens: 69.0% * At 4k tokens: 70.9% * At 8k tokens: 70.6% (Note: A very slight decrease from the 4k point) * At 16k tokens: 71.3% **3. MMMU Plot (Right)** * **Trend:** Shows a consistent, positive, and nearly linear trend across the measured range. The rate of improvement is steady. * **Data Points:** * At 1k tokens: 49.2% * At 2k tokens: 52.4% * At 4k tokens: 56.2% * At 8k tokens: 60.1% * At 16k tokens: 61.7% ### Key Observations 1. **Universal Positive Correlation:** All three benchmarks demonstrate that increasing the maximum thinking length (computational budget) leads to higher test accuracy. 2. **Diminishing Returns:** The benefit of additional thinking length is not uniform. MathVision shows the most dramatic gains, MathVista plateaus early, and MMMU shows steady but less dramatic gains. 3. **Performance Ceiling:** MathVista appears to approach a performance ceiling near 71% accuracy with thinking lengths beyond 4k tokens. 4. **Anomaly:** The MathVista data point at 8k tokens (70.6%) is marginally lower than the point at 4k tokens (70.9%). This could be statistical noise or indicate a minor instability in the scaling trend for that specific benchmark. ### Interpretation This data suggests a fundamental trade-off in AI reasoning models between computational cost (thinking length) and performance (accuracy). The relationship is not linear and is highly dependent on the nature of the task (benchmark). * **MathVision** tasks likely involve complex, multi-step reasoning where additional "thinking" directly translates to solving more problems, hence the strong, sustained improvement. * **MathVista** tasks may have a inherent complexity ceiling; after a certain point, throwing more tokens at the problem yields negligible benefit, suggesting the model's reasoning capability or the problem's solvability saturates. * **MMMU** (Massive Multi-discipline Multimodal Understanding) tasks show a reliable, scalable benefit, indicating that broader knowledge integration and reasoning continue to improve with more processing. The key takeaway is that "thinking longer" is a powerful lever for improving AI performance, but its effectiveness is task-dependent. Optimizing for efficiency would require understanding where diminishing returns set in for a given class of problems, as seen starkly in the MathVista plot. The slight dip at 8k tokens in MathVista also hints that scaling behavior can have non-monotonic quirks worth investigating.

## Scatter Plots: Test Time Accuracy vs. Max Thinking Length ### Overview The image contains three scatter plots comparing **Test Time Accuracy (%)** against **Max Thinking Length (k tokens)** for three different systems: **MathVision**, **MathVista**, and **MMU**. Each plot shows a clear upward trend, indicating that longer thinking lengths correlate with higher accuracy. --- ### Components/Axes 1. **X-Axis (Horizontal)**: - Label: **Max Thinking Length (k tokens)** - Values: 1, 2, 4, 8, 16 (logarithmic scale). 2. **Y-Axis (Vertical)**: - Label: **Test Time Accuracy (%)** - Ranges: - MathVision: 16%–36% - MathVista: 66%–71% - MMU: 48%–62% 3. **Legends**: - Positioned at the top of each plot, labeled with the system name (MathVision, MathVista, MMU). - Data points are black dots with percentage labels. --- ### Detailed Analysis #### MathVision - **Data Points**: - 1k tokens: 18.7% - 2k tokens: 22.6% - 4k tokens: 29.0% - 8k tokens: 34.0% - 16k tokens: 36.8% - **Trend**: Gradual increase in accuracy with longer thinking lengths. #### MathVista - **Data Points**: - 1k tokens: 66.7% - 2k tokens: 69.0% - 4k tokens: 70.6% - 8k tokens: 70.9% - 16k tokens: 71.3% - **Trend**: Steeper initial improvement, plateauing near 71% at 16k tokens. #### MMU - **Data Points**: - 1k tokens: 49.2% - 2k tokens: 52.4% - 4k tokens: 56.2% - 8k tokens: 60.1% - 16k tokens: 61.7% - **Trend**: Consistent upward trajectory, but slower growth compared to MathVista. --- ### Key Observations 1. **MathVista** achieves the highest accuracy (71.3% at 16k tokens), outperforming both MathVision and MMU. 2. **MathVision** shows the lowest baseline accuracy (18.7% at 1k tokens) but improves significantly with longer thinking lengths. 3. **MMU** has moderate accuracy (61.7% at 16k tokens) with a steady but gradual improvement. 4. All systems exhibit diminishing returns at higher thinking lengths (e.g., MathVista’s accuracy increases by only 0.4% between 8k and 16k tokens). --- ### Interpretation - **Performance Correlation**: Longer thinking lengths consistently improve accuracy across all systems, suggesting that extended computation time allows for better problem-solving. - **Model Efficiency**: - **MathVista** demonstrates the most efficient scaling, achieving near-peak accuracy (71.3%) with minimal additional gains at 16k tokens. - **MathVision** requires the longest thinking length (16k tokens) to reach its peak (36.8%), indicating potential inefficiencies in its reasoning process. - **MMU** balances moderate accuracy with steady improvement, though it lags behind MathVista in both baseline and peak performance. - **Diminishing Returns**: The flattening trends at higher thinking lengths (e.g., MathVista’s 70.9% → 71.3% increase) suggest a practical limit to the benefits of extended computation. This data highlights the trade-off between computational resources and accuracy, with MathVista emerging as the most effective system for maximizing test time accuracy.