## Line Charts: Accuracy vs. DTR for AIME 25 and GPQA-D ### Overview The image contains two line charts comparing the accuracy (Pass@1) against DTR (Decoding Temperature Ratio) for two datasets: AIME 25 and GPQA-D. Each chart displays three data series representing "Low", "Medium", and "High" levels, presumably of some experimental parameter. The charts show how accuracy changes with DTR for each level. ### Components/Axes **Chart 1: AIME 25** * **Title:** AIME 25 * **X-axis:** DTR (Decoding Temperature Ratio) * Scale: Approximately 0.125 to 0.200, with increments of 0.025. * Markers: 0.125, 0.150, 0.175, 0.200 * **Y-axis:** Accuracy (Pass@1) * Scale: Approximately 0.45 to 0.90, with increments of 0.15. * Markers: 0.45, 0.60, 0.75, 0.90 * **Data Series:** * **Low (Blue):** Starts around (0.125, 0.45) and increases to approximately (0.200, 0.60). * **Medium (Green):** Starts around (0.150, 0.73) and increases to approximately (0.200, 0.85). * **High (Red):** Starts around (0.125, 0.90) and remains relatively constant around 0.90. * **Correlation Coefficients (r):** * Low (Blue): r = 0.937, located near the top-right of the blue line. * Medium (Green): r = 0.849, located near the top-right of the green line. * High (Red): r = 0.769, located near the top-right of the red line. **Chart 2: GPQA-D** * **Title:** GPQA-D * **X-axis:** DTR (Decoding Temperature Ratio) * Scale: Approximately 0.12 to 0.21, with increments of 0.03. * Markers: 0.12, 0.15, 0.18, 0.21 * **Y-axis:** Accuracy (Pass@1) * Scale: Approximately 0.64 to 0.76, with increments of 0.04. * Markers: 0.64, 0.68, 0.72, 0.76 * **Data Series:** * **Low (Blue):** Starts around (0.18, 0.64) and increases slightly to approximately (0.21, 0.65). * **Medium (Green):** Starts around (0.15, 0.70) and remains relatively constant around 0.70. * **High (Red):** Starts around (0.12, 0.76) and remains relatively constant around 0.77. * **Correlation Coefficients (r):** * Low (Blue): r = 0.986, located near the top-right of the blue line. * Medium (Green): r = 0.871, located near the top-right of the green line. * High (Red): r = 0.839, located near the top-right of the red line. **Legend:** * Located at the bottom center of the image. * Low: Blue line with circle markers. * Medium: Green line with circle markers. * High: Red line with circle markers. ### Detailed Analysis **AIME 25 Chart:** * **Low (Blue):** The accuracy increases steadily with DTR, starting from approximately 0.45 at DTR 0.125 to about 0.60 at DTR 0.200. * **Medium (Green):** The accuracy increases from approximately 0.73 at DTR 0.150 to about 0.85 at DTR 0.200. * **High (Red):** The accuracy starts at approximately 0.90 at DTR 0.125 and remains relatively constant around 0.90 as DTR increases. **GPQA-D Chart:** * **Low (Blue):** The accuracy increases slightly with DTR, starting from approximately 0.64 at DTR 0.18 to about 0.65 at DTR 0.21. * **Medium (Green):** The accuracy remains relatively constant around 0.70 as DTR increases from 0.15 to 0.18. * **High (Red):** The accuracy remains relatively constant around 0.77 as DTR increases from 0.12 to 0.15. ### Key Observations * For AIME 25, the "High" level consistently yields the highest accuracy, while "Low" yields the lowest. Accuracy generally increases with DTR for "Low" and "Medium" levels. * For GPQA-D, the "High" level also yields the highest accuracy, while "Low" yields the lowest. The accuracy changes are less pronounced with DTR compared to AIME 25. * The correlation coefficients (r) are generally high, indicating a strong positive relationship between DTR and accuracy, especially for the "Low" level in both datasets. ### Interpretation The charts suggest that the Decoding Temperature Ratio (DTR) has a varying impact on accuracy depending on the dataset (AIME 25 vs. GPQA-D) and the level of the experimental parameter ("Low", "Medium", "High"). For AIME 25, increasing DTR seems to improve accuracy for "Low" and "Medium" levels, while "High" remains consistently high. For GPQA-D, the impact of DTR is less significant, with accuracy remaining relatively stable across different DTR values. The high correlation coefficients indicate a strong positive relationship between DTR and accuracy, particularly for the "Low" level, suggesting that increasing DTR can be beneficial in certain scenarios. The "High" level consistently achieves the highest accuracy, implying that this setting is optimal for both datasets.

## Chart: Accuracy vs. DTR for AIME 25 and GPQA-D ### Overview The image presents two line charts comparing the relationship between Accuracy (Pass@1) and DTR (Decoding-Time Ratio) for two datasets: AIME 25 and GPQA-D. Each chart displays three lines representing different levels of complexity: Low, Medium, and High. The charts aim to demonstrate how accuracy changes with varying decoding times for each dataset and complexity level. ### Components/Axes * **X-axis:** DTR (Decoding-Time Ratio). Scale ranges from approximately 0.125 to 0.21. * **Y-axis:** Accuracy (Pass@1). Scale ranges from approximately 0.4 to 0.95. * **Datasets:** AIME 25 (left chart), GPQA-D (right chart). * **Complexity Levels (Legend):** * Low (Light Blue, dashed line with circle markers) * Medium (Green, dashed line with circle markers) * High (Red, dashed line with circle markers) * **Legend Position:** Bottom-center of the image. ### Detailed Analysis or Content Details **AIME 25 (Left Chart)** * **High (Red):** The line slopes downward slightly, starting at approximately 0.91 at DTR 0.125 and ending at approximately 0.88 at DTR 0.20. A value of approximately 0.769 is annotated near DTR 0.15. * **Medium (Green):** The line shows an upward trend, starting at approximately 0.74 at DTR 0.125 and reaching approximately 0.84 at DTR 0.20. A value of approximately 0.849 is annotated near DTR 0.175. * **Low (Light Blue):** The line exhibits an upward trend, starting at approximately 0.48 at DTR 0.125 and reaching approximately 0.60 at DTR 0.20. A value of approximately 0.937 is annotated near DTR 0.175. **GPQA-D (Right Chart)** * **High (Red):** The line slopes downward, starting at approximately 0.77 at DTR 0.12 and ending at approximately 0.74 at DTR 0.21. A value of approximately 0.839 is annotated near DTR 0.15. * **Medium (Green):** The line shows an upward trend, starting at approximately 0.69 at DTR 0.12 and reaching approximately 0.72 at DTR 0.21. A value of approximately 0.871 is annotated near DTR 0.18. * **Low (Light Blue):** The line exhibits a relatively flat trend, starting at approximately 0.65 at DTR 0.12 and ending at approximately 0.66 at DTR 0.21. A value of approximately 0.936 is annotated near DTR 0.18. ### Key Observations * In both datasets, the "High" complexity level consistently demonstrates the highest accuracy at lower DTR values. * As DTR increases, the accuracy of the "High" complexity level tends to decrease more rapidly than the other levels. * The "Low" complexity level shows a more gradual increase in accuracy with increasing DTR, and in the GPQA-D dataset, it remains relatively flat. * The annotated values appear to be peak accuracy points for each complexity level within each dataset. ### Interpretation The charts suggest a trade-off between accuracy and decoding time. Higher complexity models (represented by the "High" line) achieve higher accuracy initially but experience a more significant drop in accuracy as decoding time increases. Lower complexity models (represented by the "Low" line) have lower initial accuracy but are more robust to increases in decoding time. The "Medium" complexity level offers a balance between these two extremes. The differences between AIME 25 and GPQA-D indicate that the optimal complexity level and DTR may vary depending on the specific dataset. The annotated values likely represent points where the models achieve a good balance between accuracy and decoding speed for each complexity level. The relatively flat "Low" line in GPQA-D suggests that increasing decoding time does not significantly improve accuracy for this dataset at the lowest complexity level. This could indicate that the dataset is relatively simple or that the low-complexity model has already reached its performance limit.

## Scatter Plot with Trend Lines: AIME 25 and GPQA-D Accuracy vs. DTR ### Overview The image displays two side-by-side scatter plots with overlaid trend lines, comparing model accuracy (Pass@1) against a metric labeled "DTR" for two different datasets or tasks: "AIME 25" (left) and "GPQA-D" (right). Each plot contains three data series, categorized by difficulty level (Low, Medium, High), distinguished by color. The plots show a positive correlation between DTR and accuracy for each series, with varying strengths. ### Components/Axes * **Titles:** * Left Chart: "AIME 25" (centered at the top). * Right Chart: "GPQA-D" (centered at the top). * **Y-Axis (Both Charts):** Labeled "Accuracy (Pass@1)". The scale is linear. * AIME 25 Range: Approximately 0.40 to 0.95. Major tick marks at 0.45, 0.60, 0.75, 0.90. * GPQA-D Range: Approximately 0.62 to 0.78. Major tick marks at 0.64, 0.68, 0.72, 0.76. * **X-Axis (Both Charts):** Labeled "DTR". The scale is linear. * AIME 25 Range: Approximately 0.11 to 0.21. Major tick marks at 0.125, 0.150, 0.175, 0.200. * GPQA-D Range: Approximately 0.11 to 0.22. Major tick marks at 0.12, 0.15, 0.18, 0.21. * **Legend:** Positioned at the bottom center of the entire figure, below both charts. * **Low:** Blue line with circle markers. * **Medium:** Green line with circle markers. * **High:** Red line with circle markers. * **Data Series & Trend Lines:** Each series consists of individual data points (circles) and a dashed trend line with a shaded confidence interval. A Pearson correlation coefficient (`r`) is displayed near each trend line. ### Detailed Analysis #### **AIME 25 Chart (Left)** * **High (Red) Series:** * **Placement:** Top-left quadrant of the chart. * **Trend:** Strong positive slope. Points cluster tightly around the trend line. * **Data Range:** DTR from ~0.115 to ~0.140. Accuracy from ~0.89 to ~0.93. * **Correlation:** `r = 0.769` (displayed in red text near the series). * **Medium (Green) Series:** * **Placement:** Center of the chart, spanning from lower-left to upper-right. * **Trend:** Positive slope, less steep than the High series. * **Data Range:** DTR from ~0.140 to ~0.185. Accuracy from ~0.68 to ~0.85. * **Correlation:** `r = 0.949` (displayed in green text near the series). * **Low (Blue) Series:** * **Placement:** Bottom-right quadrant of the chart. * **Trend:** Positive slope, similar steepness to the Medium series. * **Data Range:** DTR from ~0.155 to ~0.205. Accuracy from ~0.40 to ~0.60. * **Correlation:** `r = 0.937` (displayed in blue text near the series). #### **GPQA-D Chart (Right)** * **High (Red) Series:** * **Placement:** Top-left quadrant of the chart. * **Trend:** Positive slope. * **Data Range:** DTR from ~0.120 to ~0.145. Accuracy from ~0.76 to ~0.78. * **Correlation:** `r = 0.839` (displayed in red text near the series). * **Medium (Green) Series:** * **Placement:** Center of the chart. * **Trend:** Positive slope. * **Data Range:** DTR from ~0.150 to ~0.190. Accuracy from ~0.69 to ~0.71. * **Correlation:** `r = 0.871` (displayed in green text near the series). * **Low (Blue) Series:** * **Placement:** Bottom-right quadrant of the chart. * **Trend:** Positive slope. * **Data Range:** DTR from ~0.185 to ~0.220. Accuracy from ~0.64 to ~0.65. * **Correlation:** `r = 0.981` (displayed in blue text near the series). ### Key Observations 1. **Consistent Positive Correlation:** For both datasets (AIME 25 and GPQA-D) and across all difficulty levels (Low, Medium, High), accuracy increases as DTR increases. All correlation coefficients (`r`) are positive and strong (ranging from 0.769 to 0.981). 2. **Difficulty Stratification:** There is a clear vertical separation by difficulty. For any given DTR value, the "High" difficulty series has the highest accuracy, followed by "Medium," then "Low." This ordering is perfectly maintained in both charts. 3. **DTR Range by Difficulty:** There is a clear horizontal separation by difficulty. The "High" difficulty series operates at the lowest DTR values, "Medium" in the middle, and "Low" at the highest DTR values. This suggests DTR might be inversely related to task difficulty. 4. **Dataset Comparison:** The AIME 25 dataset shows a much wider range of accuracy values (approx. 0.40-0.93) compared to GPQA-D (approx. 0.64-0.78). The slopes of the trend lines also appear steeper in the AIME 25 plot. 5. **Correlation Strength:** The "Low" difficulty series shows the strongest correlation in both datasets (`r=0.937` for AIME 25, `r=0.981` for GPQA-D). ### Interpretation The data demonstrates a robust, positive relationship between the DTR metric and model accuracy (Pass@1) across two distinct benchmarks. The consistent stratification by difficulty level is the most salient finding. * **What the data suggests:** Higher DTR values are associated with better performance. However, the tasks where the model achieves high accuracy (the "High" difficulty series) are inherently associated with *lower* DTR values. This presents an interesting paradox: the model performs best on hard tasks, but those hard tasks are characterized by low DTR. This could imply that DTR measures something like "data transformation rate" or "difficulty transformation ratio," where a lower value indicates a more challenging, less transformed, or more "raw" problem setup that the model is surprisingly adept at solving. * **Relationship between elements:** The three difficulty tiers form parallel, non-overlapping bands across the DTR-accuracy space. This indicates that difficulty level is a primary confounding variable; analyzing the effect of DTR on accuracy without controlling for difficulty would be misleading. The strong correlations within each band show that DTR is still a meaningful predictor of performance *within* a given difficulty class. * **Notable Anomalies/Trends:** The perfect ordering of difficulty bands and their distinct DTR ranges is striking. It suggests the "DTR" metric is intrinsically linked to the problem difficulty definition used for these benchmarks. The near-perfect correlation (`r=0.981`) for the Low/GPQA-D series indicates an almost linear relationship in that specific regime. The wider accuracy spread in AIME 25 might indicate it is a more discriminating benchmark or that the model's performance is more variable on its problem set.

## Line Charts: AIME 25 and GPQA-D Performance Analysis ### Overview The image contains two side-by-side line charts comparing accuracy (Pass@1) against DTR (Dynamic Task Rate) for three difficulty levels: Low, Medium, and High. Each chart represents a different evaluation framework ("AIME 25" and "GPQA-D"). The charts use color-coded lines with correlation coefficients (r-values) indicating relationships between DTR and accuracy. ### Components/Axes - **Y-Axis**: Accuracy (Pass@1) ranging from 0.45 to 0.90 (AIME 25) and 0.64 to 0.76 (GPQA-D). - **X-Axis**: DTR (Dynamic Task Rate) ranging from 0.125 to 0.200 (AIME 25) and 0.12 to 0.21 (GPQA-D). - **Legend**: Located at the bottom, with: - **Blue**: Low difficulty - **Green**: Medium difficulty - **Red**: High difficulty - **Correlation Coefficients (r)**: - AIME 25: High (0.769), Medium (0.849), Low (0.937) - GPQA-D: High (0.839), Medium (0.871), Low (0.980) ### Detailed Analysis #### AIME 25 Chart - **High Difficulty (Red)**: - Accuracy starts at ~0.90 (DTR=0.125) and decreases slightly to ~0.89 (DTR=0.200). - Correlation (r=0.769) indicates a moderate positive relationship. - **Medium Difficulty (Green)**: - Accuracy rises from ~0.70 (DTR=0.15) to ~0.75 (DTR=0.175). - Correlation (r=0.849) suggests a stronger linear relationship. - **Low Difficulty (Blue)**: - Accuracy increases from ~0.45 (DTR=0.125) to ~0.60 (DTR=0.200). - Correlation (r=0.937) shows the strongest linear trend. #### GPQA-D Chart - **High Difficulty (Red)**: - Accuracy remains stable (~0.76 at DTR=0.12 to ~0.76 at DTR=0.21). - Correlation (r=0.839) indicates a moderate relationship. - **Medium Difficulty (Green)**: - Accuracy fluctuates between ~0.68 (DTR=0.15) and ~0.72 (DTR=0.18). - Correlation (r=0.871) reflects a slightly stronger trend than High difficulty. - **Low Difficulty (Blue)**: - Accuracy rises from ~0.64 (DTR=0.12) to ~0.68 (DTR=0.21). - Correlation (r=0.980) demonstrates the strongest linear dependency. ### Key Observations 1. **Difficulty-Accuracy Tradeoff**: - High difficulty consistently achieves the highest accuracy but shows the weakest correlation with DTR. - Low difficulty has the lowest accuracy but the strongest correlation with DTR. 2. **Trend Variability**: - High difficulty lines are relatively flat, suggesting robustness to DTR changes. - Low difficulty lines exhibit steep slopes, indicating sensitivity to DTR adjustments. 3. **Framework Differences**: - GPQA-D generally shows higher accuracy across all difficulty levels compared to AIME 25. - GPQA-D's Low difficulty line has the highest r-value (0.980), suggesting near-perfect linear alignment. ### Interpretation The data reveals a critical insight: **higher difficulty tasks prioritize accuracy over adaptability**, maintaining performance despite DTR variations (low r-values). Conversely, **lower difficulty tasks are more adaptive** to DTR changes but struggle with baseline accuracy. This suggests that evaluation frameworks like AIME 25 and GPQA-D may emphasize different aspects of task performance—robustness vs. sensitivity. The near-perfect correlation (r=0.980) in GPQA-D's Low difficulty line implies that DTR adjustments could be a reliable lever for tuning performance in simpler tasks, whereas harder tasks require alternative optimization strategies.