## Chart: Accuracy vs Ratio ### Overview The image is a line chart comparing the accuracy (%) of different models (Full, Random, Bottom, Top) against the ratio (%) on the R1-Qwen | MATH500 dataset. The x-axis represents the ratio (%), and the y-axis represents the accuracy (%). ### Components/Axes * **Title:** R1-Qwen | MATH500 * **X-axis:** Ratio (%) with markers at 2, 4, 6, 8, 10, 20, 30, 40, 50 * **Y-axis:** Accuracy (%) with markers at 82, 84, 86, 88, 90, 92, 94 * **Legend:** Located in the top-right corner. * Full (Gray dashed line with 'x' markers) * Random (Green line with triangle markers) * Bottom (Blue line with square markers) * Top (Red line with circle markers) ### Detailed Analysis * **Full (Gray dashed line with 'x' markers):** The accuracy remains almost constant at approximately 94.5% across all ratios. * Ratio 2%: ~94.5% * Ratio 50%: ~94.5% * **Random (Green line with triangle markers):** The accuracy initially increases slightly, then decreases and plateaus. * Ratio 2%: ~82% * Ratio 6%: ~82% * Ratio 10%: ~82% * Ratio 20%: ~81% * Ratio 30%: ~81% * Ratio 50%: ~85% * **Bottom (Blue line with square markers):** The accuracy increases steadily with the ratio. * Ratio 2%: ~81.5% * Ratio 6%: ~82.5% * Ratio 10%: ~82.5% * Ratio 20%: ~83% * Ratio 30%: ~84% * Ratio 50%: ~86% * **Top (Red line with circle markers):** The accuracy increases rapidly initially, then plateaus at higher ratios. * Ratio 2%: ~81.5% * Ratio 4%: ~88.5% * Ratio 6%: ~91.5% * Ratio 8%: ~92.5% * Ratio 10%: ~93% * Ratio 20%: ~94% * Ratio 30%: ~94.5% * Ratio 50%: ~94.5% ### Key Observations * The "Full" model consistently achieves the highest accuracy, remaining almost constant across all ratios. * The "Top" model shows a significant initial increase in accuracy, eventually reaching a similar level to the "Full" model. * The "Bottom" model's accuracy increases steadily but remains lower than the "Full" and "Top" models. * The "Random" model performs the worst, with its accuracy fluctuating and remaining the lowest among all models. ### Interpretation The chart compares the performance of different models based on accuracy versus ratio. The "Full" model serves as a benchmark, demonstrating the highest achievable accuracy. The "Top" model quickly approaches this benchmark, suggesting it is an efficient strategy. The "Bottom" model shows a gradual improvement, indicating it benefits from higher ratios but is less effective overall. The "Random" model's poor performance suggests that random selection is not a viable strategy for this task. The data suggests that focusing on the "Top" elements is a more effective approach than random selection or focusing on the "Bottom" elements.

\n ## Line Chart: R1-Qwen | MATH500 Accuracy vs. Ratio ### Overview This line chart displays the accuracy of different sampling methods (Full, Random, Bottom, Top) on the MATH500 dataset, as a function of the ratio of data used. The x-axis represents the ratio of data used (in percentage), and the y-axis represents the accuracy (in percentage). ### Components/Axes * **Title:** R1-Qwen | MATH500 * **X-axis Label:** Ratio (%) * **Y-axis Label:** Accuracy (%) * **Legend:** * Full (represented by a grey dashed line with 'x' markers) * Random (represented by a green solid line with triangle markers) * Bottom (represented by a blue solid line with square markers) * Top (represented by a red solid line with circle markers) * **X-axis Markers:** 2, 4, 6, 8, 10, 20, 30, 40, 50 * **Y-axis Markers:** 80, 82, 84, 86, 88, 90, 92, 94 ### Detailed Analysis * **Top (Red Line):** The Top line starts at approximately 82% accuracy at a ratio of 2%, then rapidly increases to approximately 94% accuracy at a ratio of 10%. It plateaus around 94-95% accuracy from a ratio of 10% to 50%. * **Bottom (Blue Line):** The Bottom line starts at approximately 82% accuracy at a ratio of 2%. It gradually increases to approximately 86% accuracy at a ratio of 50%, with a relatively linear trend. * **Full (Grey Dashed Line):** The Full line remains relatively constant at approximately 94% accuracy across all ratios, from 2% to 50%. * **Random (Green Line):** The Random line starts at approximately 82% accuracy at a ratio of 2%. It initially fluctuates around 82-83% until a ratio of 10%, then decreases to approximately 81% at a ratio of 20%. It then increases to approximately 85% at a ratio of 50%. Here's a more detailed breakdown of the data points (approximate values): | Ratio (%) | Top (Red) | Bottom (Blue) | Full (Grey) | Random (Green) | |---|---|---|---|---| | 2 | 82 | 82 | 94 | 82 | | 4 | 88 | 83 | 94 | 82 | | 6 | 91 | 83 | 94 | 82 | | 8 | 92.5 | 83.5 | 94 | 82.5 | | 10 | 94 | 84 | 94 | 82 | | 20 | 94 | 84.5 | 94 | 81 | | 30 | 94 | 85 | 94 | 82 | | 40 | 94 | 85 | 94 | 84 | | 50 | 94 | 86 | 94 | 85 | ### Key Observations * The "Top" sampling method achieves the highest accuracy, especially at lower ratios. * The "Full" method maintains a consistently high accuracy across all ratios. * The "Random" method exhibits the most variability in accuracy. * The "Bottom" method shows a steady, but relatively slow, increase in accuracy. * The "Top" method demonstrates diminishing returns after a ratio of 10%, as accuracy plateaus. ### Interpretation The data suggests that selecting the "top" performing samples (presumably based on some criteria) is highly effective for achieving high accuracy on the MATH500 dataset, particularly when only a small portion of the data is available. The "Full" method provides a baseline of high accuracy, but doesn't offer significant improvement over the "Top" method. The "Random" method is the least consistent, indicating that random sampling is not an optimal strategy for this task. The "Bottom" method shows some improvement with increasing data ratio, but remains significantly lower in accuracy than the "Top" and "Full" methods. The plateauing of the "Top" method after a ratio of 10% suggests that the most informative samples are identified early on, and adding more data beyond that point doesn't yield substantial gains. This could indicate that the MATH500 dataset has a hierarchical structure, where a small subset of samples contains the majority of the relevant information. The difference between the "Top" and "Full" methods suggests that the full dataset contains some noise or less informative samples.

## Line Chart: R1-Qwen | MATH500 ### Overview This is a line chart comparing the performance (accuracy) of four different data selection strategies ("Full", "Bottom", "Random", "Top") on the MATH500 benchmark as the ratio of training data used increases. The chart demonstrates how accuracy changes with the percentage of data utilized. ### Components/Axes * **Title:** "R1-Qwen | MATH500" (Top center) * **Y-Axis:** Label is "Accuracy (%)". Scale runs from 80 to 94 in increments of 2. * **X-Axis:** Label is "Ratio (%)". The scale is non-linear, with marked points at 2, 4, 6, 8, 10, 20, 30, 40, and 50. * **Legend:** Located in the top-right corner of the chart area. It defines four data series: * **Full:** Gray dashed line with 'x' markers. * **Bottom:** Blue solid line with square markers. * **Random:** Green solid line with triangle markers. * **Top:** Red solid line with circle markers. ### Detailed Analysis **Data Series and Trends:** 1. **Full (Gray, 'x' markers):** * **Trend:** Perfectly horizontal line, indicating constant performance. * **Data Points:** Accuracy is consistently at **94%** for all data ratios from 2% to 50%. 2. **Top (Red, circle markers):** * **Trend:** Strong, consistent upward slope. Shows the most significant improvement as more data is added. * **Data Points (Approximate):** * Ratio 2%: ~82% * Ratio 4%: ~88% * Ratio 6%: ~90% * Ratio 8%: ~92% * Ratio 10%: ~93% * Ratio 20%: ~93.5% * Ratio 30%: ~94% * Ratio 40%: ~94% * Ratio 50%: ~94% 3. **Bottom (Blue, square markers):** * **Trend:** Gradual, steady upward slope. Performance improves slowly with more data. * **Data Points (Approximate):** * Ratio 2%: ~82% * Ratio 4%: ~82.2% * Ratio 6%: ~82.5% * Ratio 8%: ~82.5% * Ratio 10%: ~82.5% * Ratio 20%: ~83% * Ratio 30%: ~84% * Ratio 40%: ~85% * Ratio 50%: ~86% 4. **Random (Green, triangle markers):** * **Trend:** Fluctuating, with a slight overall upward trend. It dips in the middle range before recovering. * **Data Points (Approximate):** * Ratio 2%: ~82% * Ratio 4%: ~82% * Ratio 6%: ~82% * Ratio 8%: ~82% * Ratio 10%: ~82% * Ratio 20%: ~81% * Ratio 30%: ~81% * Ratio 40%: ~83% * Ratio 50%: ~85% ### Key Observations * The **"Full"** model sets the performance ceiling at 94% accuracy. * The **"Top"** selection strategy rapidly approaches the "Full" model's performance, matching it by the 30% data ratio mark. * The **"Bottom"** and **"Random"** strategies perform significantly worse than "Top" at all data ratios. "Random" performs worse than "Bottom" for most of the middle range (10%-30%). * All strategies start at approximately the same accuracy (~82%) when using only 2% of the data. * There is a notable performance dip for the **"Random"** strategy between 10% and 30% data ratio. ### Interpretation This chart illustrates the principle of data quality over quantity for this specific task (MATH500 with R1-Qwen). The "Top" strategy, which presumably selects the highest-quality or most relevant data samples, achieves near-maximum performance using only 30% of the available data. This suggests that a significant portion of the training data may be redundant or less informative for improving accuracy on this benchmark. The poor performance of the "Bottom" (likely lowest-quality data) and "Random" strategies confirms that indiscriminate data addition is inefficient. The dip in the "Random" curve could indicate that adding certain mid-quality data points introduces noise that temporarily hinders model performance before the benefit of increased data volume takes over at higher ratios. The key takeaway is that intelligent data curation ("Top" selection) is a highly effective method for achieving optimal model performance with reduced computational cost, as it avoids processing the full dataset.

## Line Chart: R1-Qwen | MATH500 ### Overview The chart illustrates the relationship between "Ratio (%)" (x-axis) and "Accuracy (%)" (y-axis) across four distinct data series: Full, Bottom, Random, and Top. The y-axis ranges from 80% to 95%, while the x-axis spans from 2% to 50% in increments. The legend is positioned in the upper-right quadrant, with color-coded labels for each series. ### Components/Axes - **X-axis (Ratio %)**: Labeled "Ratio (%)", with markers at 2, 4, 6, 8, 10, 20, 30, 40, and 50. - **Y-axis (Accuracy %)**: Labeled "Accuracy (%)", with markers at 82, 84, 86, 88, 90, 92, and 94. - **Legend**: Located in the upper-right corner, with the following mappings: - **Full**: Gray dashed line (constant value). - **Bottom**: Blue solid line. - **Random**: Green solid line. - **Top**: Red solid line. ### Detailed Analysis 1. **Full (Gray Dashed Line)**: - Maintains a constant accuracy of **94%** across all ratios. - Positioned at the top of the chart, unaffected by ratio changes. 2. **Top (Red Solid Line)**: - Starts at **~82%** at 2% ratio. - Sharp upward trend to **~94%** by 4% ratio. - Plateaus near **94%** for ratios ≥4%. - Key data points: - 2%: ~82% - 4%: ~88% - 8%: ~92% - 10%: ~93% - 20%: ~94% - 30%: ~94% - 40%: ~94% - 50%: ~94% 3. **Bottom (Blue Solid Line)**: - Begins at **~82%** at 2% ratio. - Gradual upward trend to **~86%** at 50% ratio. - Key data points: - 2%: ~82% - 4%: ~82.5% - 8%: ~83% - 10%: ~83.2% - 20%: ~84% - 30%: ~84.5% - 40%: ~85% - 50%: ~86% 4. **Random (Green Solid Line)**: - Stable at **~82%** until 40% ratio. - Sudden jump to **~85%** at 50% ratio. - Key data points: - 2%: ~82% - 4%: ~82.2% - 8%: ~82.1% - 10%: ~82% - 20%: ~81.5% - 30%: ~81.8% - 40%: ~82.5% - 50%: ~85% ### Key Observations - **Top Series**: Dominates performance, achieving near-peak accuracy (94%) after a rapid initial increase. - **Bottom Series**: Shows consistent but slower improvement compared to Top. - **Random Series**: Exhibits minimal variation until a late-stage spike at 50% ratio. - **Full Series**: Represents a theoretical upper bound, unaffected by ratio adjustments. ### Interpretation The chart suggests that the "Top" strategy achieves the highest accuracy, particularly after a 4% ratio threshold, while the "Full" series represents an idealized baseline. The "Random" series underperforms until a late-stage anomaly, and the "Bottom" series demonstrates steady but suboptimal growth. The "Full" line’s constancy implies it may represent a control or reference model, while the "Top" line’s sharp rise indicates a highly effective, ratio-sensitive approach. The "Random" series’ late jump at 50% could signal an outlier or contextual factor not reflected in lower ratios.