## Line Chart: Model Performance Comparison ### Overview The image is a line chart comparing the performance of different language models on a specific task. The chart plots the performance of "Baselines (Math-Instruct)", "Ours (Base)", and "Ours (Math Base)" across four different model sizes: DeepSeek-7B, Qwen2.5-1.5B, Qwen2.5-7B, and Qwen2.5-72B. The y-axis represents the performance metric, ranging from 45 to 75. ### Components/Axes * **X-axis:** Model Size (DeepSeek-7B, Qwen2.5-1.5B, Qwen2.5-7B, Qwen2.5-72B) * **Y-axis:** Performance Metric (scale from 45 to 75, with tick marks at 5 unit intervals) * **Legend:** Located at the top of the chart. * Blue diamond: Baselines (Math-Instruct) * Red circle: Ours (Base) * Green triangle: Ours (Math Base) ### Detailed Analysis **1. Baselines (Math-Instruct) - Blue Line:** The blue line represents the performance of the baseline model. The trend is generally upward, indicating improved performance with larger model sizes. * DeepSeek-7B: 46.59 * Qwen2.5-1.5B: 56.97 * Qwen2.5-7B: 63.29 * Qwen2.5-72B: 68.16 **2. Ours (Base) - Red Line:** The red line represents the performance of "Ours (Base)". The trend is also upward, with a significant jump between Qwen2.5-1.5B and Qwen2.5-7B. * DeepSeek-7B: 50.29 * Qwen2.5-1.5B: 51.82 * Qwen2.5-7B: 64.19 * Qwen2.5-72B: 71.13 **3. Ours (Math Base) - Green Line:** The green line represents the performance of "Ours (Math Base)". This model consistently outperforms the other two across all model sizes. The trend is upward. * DeepSeek-7B: 55.35 * Qwen2.5-1.5B: 59.99 * Qwen2.5-7B: 67.17 * Qwen2.5-72B: 71.84 ### Key Observations * "Ours (Math Base)" (green line) consistently achieves the highest performance across all model sizes. * The performance gap between "Ours (Math Base)" and the other two models is most pronounced at smaller model sizes (DeepSeek-7B and Qwen2.5-1.5B). * All three models show a significant performance increase when scaling from Qwen2.5-1.5B to Qwen2.5-7B. * The performance of "Ours (Base)" (red line) catches up to "Baselines (Math-Instruct)" (blue line) at Qwen2.5-7B and surpasses it at Qwen2.5-72B. ### Interpretation The chart demonstrates the impact of model size and training approach on performance. "Ours (Math Base)" consistently outperforms the baseline, suggesting that the "Math Base" training approach is effective. The significant performance jump observed for all models when scaling from Qwen2.5-1.5B to Qwen2.5-7B highlights the importance of model size for this particular task. The fact that "Ours (Base)" eventually surpasses the baseline suggests that even without the "Math Base" training, their approach is beneficial at larger model sizes. The data suggests that both model size and training methodology contribute to overall performance, with "Ours (Math Base)" representing the best combination of the two.

\n ## Line Chart: Performance Comparison of Math Models ### Overview This line chart compares the performance of three different model configurations – Baselines (Math-Instruct), Ours (Base), and Ours (Math Base) – across four different model sizes: DeepSeek-7B, Qwen2.5-1.5B, Qwen2.5-7B, and Qwen2.5-72B. The performance metric appears to be a score, ranging from approximately 45 to 75. ### Components/Axes * **X-axis:** Model Name (DeepSeek-7B, Qwen2.5-1.5B, Qwen2.5-7B, Qwen2.5-72B) * **Y-axis:** Performance Score (Scale from 45 to 75, with increments of 5) * **Legend:** * Blue Diamonds: Baselines (Math-Instruct) * Red Circles: Ours (Base) * Green Triangles: Ours (Math Base) ### Detailed Analysis **Baselines (Math-Instruct) - Blue Diamonds:** The line slopes upward consistently. * DeepSeek-7B: 46.59 * Qwen2.5-1.5B: 56.97 * Qwen2.5-7B: 63.29 * Qwen2.5-72B: 68.16 **Ours (Base) - Red Circles:** The line initially increases, then plateaus. * DeepSeek-7B: 50.29 * Qwen2.5-1.5B: 51.82 * Qwen2.5-7B: 64.19 * Qwen2.5-72B: 71.13 **Ours (Math Base) - Green Triangles:** The line slopes upward consistently and is generally the highest performing. * DeepSeek-7B: 55.35 * Qwen2.5-1.5B: 59.99 * Qwen2.5-7B: 67.17 * Qwen2.5-72B: 71.84 ### Key Observations * The "Ours (Math Base)" model consistently outperforms both "Baselines (Math-Instruct)" and "Ours (Base)" across all model sizes. * The performance of all models generally increases with model size. * The "Ours (Base)" model shows a relatively flat performance curve between DeepSeek-7B and Qwen2.5-1.5B, then a significant jump to Qwen2.5-7B. * The gap between "Ours (Math Base)" and the other two models widens as the model size increases. ### Interpretation The data suggests that incorporating a "Math Base" into the model architecture significantly improves performance on the evaluated task. The consistent upward trend for all models indicates that increasing model size generally leads to better results, but the "Math Base" provides a substantial boost. The plateau observed in "Ours (Base)" between the first two model sizes suggests that simply increasing model size isn't sufficient; architectural improvements (like the "Math Base") are crucial for realizing further gains. The widening gap between the models as size increases indicates that the benefits of the "Math Base" become more pronounced with larger models. This could be due to the "Math Base" enabling the model to better leverage the increased capacity of larger models.

\n ## Line Chart: Performance Comparison of Model Series Across Architectures ### Overview This image is a line chart comparing the performance of three distinct model series across four different model architectures/sizes. The chart plots numerical performance scores (y-axis) against specific model names (x-axis). The three series are differentiated by color and marker shape, with a legend provided at the top of the chart. ### Components/Axes * **X-Axis (Horizontal):** Lists four specific model architectures. From left to right: 1. `DeepSeek-7B` 2. `Qwen2.5-1.5B` 3. `Qwen2.5-7B` 4. `Qwen2.5-72B` * **Y-Axis (Vertical):** Represents a numerical performance score. The axis is labeled with major gridlines at intervals of 10, specifically marking the values `45`, `55`, `65`, and `75`. The exact metric (e.g., accuracy, score) is not specified in the image. * **Legend (Top Center):** Defines the three data series: * **Blue Diamond (♦):** `Baselines (Math-Instruct)` * **Red Circle (●):** `Ours (Base)` * **Green Triangle (▲):** `Ours (Math Base)` ### Detailed Analysis The chart displays three upward-trending lines, each connecting four data points corresponding to the x-axis models. The exact values are annotated next to each data point. **1. Series: Baselines (Math-Instruct) - Blue Line with Diamond Markers** * **Trend:** Consistently slopes upward from left to right. * **Data Points:** * DeepSeek-7B: `46.59` * Qwen2.5-1.5B: `56.97` * Qwen2.5-7B: `63.29` * Qwen2.5-72B: `68.16` **2. Series: Ours (Base) - Red Line with Circle Markers** * **Trend:** Shows a slight initial increase, then a steeper upward slope. It starts above the blue line, is overtaken by it at the second point, and then surpasses it again at the final two points. * **Data Points:** * DeepSeek-7B: `50.29` * Qwen2.5-1.5B: `51.82` * Qwen2.5-7B: `64.19` * Qwen2.5-72B: `71.13` **3. Series: Ours (Math Base) - Green Line with Triangle Markers** * **Trend:** Consistently slopes upward and maintains the highest position on the chart for all four model points. * **Data Points:** * DeepSeek-7B: `55.35` * Qwen2.5-1.5B: `59.99` * Qwen2.5-7B: `67.17` * Qwen2.5-72B: `71.84` ### Key Observations 1. **Performance Hierarchy:** The `Ours (Math Base)` (green) series demonstrates the highest performance at every model size tested. The `Ours (Base)` (red) series generally performs second best, except at the Qwen2.5-1.5B point where it is slightly below the `Baselines` (blue). 2. **Scaling Trend:** All three series show a clear positive correlation between model size/complexity (moving right on the x-axis) and performance score. The gains are substantial, with scores increasing by approximately 20-25 points from the smallest to the largest model within each series. 3. **Convergence at Scale:** The performance gap between the three series narrows significantly at the largest model size (`Qwen2.5-72B`). The scores for `Ours (Base)` (`71.13`) and `Ours (Math Base)` (`71.84`) are very close, while the `Baselines` score (`68.16`) is only slightly lower. 4. **Notable Anomaly:** The `Ours (Base)` (red) series shows a much smaller performance increase between `DeepSeek-7B` (`50.29`) and `Qwen2.5-1.5B` (`51.82`) compared to the other two series, which see larger jumps at this step. This creates a temporary dip in its relative ranking. ### Interpretation This chart presents a comparative analysis likely from a research paper or technical report, evaluating a new method ("Ours") against a baseline. The data suggests several key findings: * **Efficacy of Proposed Method:** The "Ours (Math Base)" variant is consistently the top performer, indicating that the proposed method, when combined with math-specific training or data, yields superior results across a range of model architectures. * **Importance of Specialization:** The consistent lead of the green line (`Math Base`) over the red line (`Base`) implies that domain-specific (math) adaptation provides a clear performance advantage over a generic base model, even when using the same core method. * **Scaling Laws Hold:** The strong upward trend for all lines confirms that increasing model capacity is an effective strategy for improving performance on the measured task, regardless of the training methodology. * **Diminishing Returns of Methodology at Scale:** The convergence of scores at the `Qwen2.5-72B` size suggests that for very large models, the inherent capability of the model architecture may begin to dominate, reducing the relative advantage provided by the specialized training method. The baseline method also scales well, closing much of the gap. * **Architectural Sensitivity:** The performance ordering is not perfectly consistent across all architectures (evidenced by the red/blue line crossover at `Qwen2.5-1.5B`), suggesting that the effectiveness of each approach can be somewhat dependent on the underlying model architecture. In summary, the chart argues for the value of the "Ours (Math Base)" approach, demonstrates the universal benefit of scaling, and hints that methodological advantages may be most pronounced in mid-sized models before large-scale parameters begin to equalize performance.

## Line Chart: Performance Comparison of Different Models ### Overview The line chart compares the performance of three different models across four different datasets: DeepSeek-7B, Qwen2.5-1.5B, Qwen2.5-7B, and Qwen2.5-72B. The models are labeled as Baselines (Math-Instruct), Ours (Base), and Ours (Math Base). ### Components/Axes - **X-axis**: Represents the different datasets (DeepSeek-7B, Qwen2.5-1.5B, Qwen2.5-7B, Qwen2.5-72B). - **Y-axis**: Represents the performance metric, which is not explicitly labeled but can be inferred to be a score or a value. - **Legend**: Contains three colors and labels for the three models. - **Data Points**: Each data point represents the performance of a model on a specific dataset. ### Detailed Analysis or ### Content Details - **DeepSeek-7B**: The Baseline model shows a steady increase in performance from 46.59 to 71.84. - **Qwen2.5-1.5B**: The Ours (Base) model shows a significant improvement over the Baseline, starting from 50.29 and reaching 71.13. - **Qwen2.5-7B**: The Ours (Math Base) model shows the highest performance, starting from 51.82 and reaching 71.84. - **Qwen2.5-72B**: The Baseline model shows the lowest performance, starting from 55.35 and reaching 71.84. ### Key Observations - The Ours (Base) model consistently outperforms the Baseline model across all datasets. - The Ours (Math Base) model shows the best performance, indicating that the use of a math base in the model architecture may contribute to better results. - There is a noticeable improvement in performance as the model size increases from 1.5B to 72B. ### Interpretation The data suggests that the use of a math base in the model architecture significantly improves performance. The Ours (Math Base) model demonstrates the best results, indicating that the math base may be a key factor in achieving higher performance. The Baseline model, while still performing well, shows a lower performance compared to the Ours (Base) model, suggesting that the math base may be a critical component in achieving higher performance. The improvement in performance as the model size increases from 1.5B to 72B is also notable, indicating that larger models may be more effective in certain tasks.

## Line Chart: Performance Comparison of Language Models on Math and Instructional Tasks ### Overview The chart compares the performance of three language model variants (Baselines, Ours Base, Ours Math Base) across four model sizes (DeepSeek-7B, Qwen2.5-1.5B, Qwen2.5-7B, Qwen2.5-72B) using accuracy percentages. The y-axis ranges from 45% to 75%, with data points plotted for each model variant at each size. ### Components/Axes - **X-axis**: Model sizes (DeepSeek-7B, Qwen2.5-1.5B, Qwen2.5-7B, Qwen2.5-72B) - **Y-axis**: Accuracy (%) from 45% to 75% - **Legend**: - Blue diamonds: Baselines (Math-Instruct) - Red circles: Ours (Base) - Green triangles: Ours (Math Base) - **Data Points**: Numerical values annotated above each marker ### Detailed Analysis 1. **DeepSeek-7B**: - Baselines (Math-Instruct): 46.59% (blue) - Ours (Base): 50.29% (red) - Ours (Math Base): 55.35% (green) 2. **Qwen2.5-1.5B**: - Baselines (Math-Instruct): 56.97% (blue) - Ours (Base): 51.82% (red) - Ours (Math Base): 59.99% (green) 3. **Qwen2.5-7B**: - Baselines (Math-Instruct): 63.29% (blue) - Ours (Base): 64.19% (red) - Ours (Math Base): 67.17% (green) 4. **Qwen2.5-72B**: - Baselines (Math-Instruct): 68.16% (blue) - Ours (Base): 71.13% (red) - Ours (Math Base): 71.84% (green) ### Key Observations - **Performance Trends**: - Ours (Math Base) consistently outperforms other variants across all model sizes - Ours (Base) shows mixed performance relative to Baselines (Math-Instruct) - Larger models (Qwen2.5-72B) achieve higher accuracy for all variants - The performance gap between Ours (Math Base) and Baselines widens with model size - **Notable Patterns**: - Ours (Math Base) maintains a 3-5% advantage over Ours (Base) at all sizes - Qwen2.5-72B achieves near-ceiling performance (71.84%) for Ours (Math Base) - Baselines (Math-Instruct) show diminishing returns with larger models ### Interpretation The data demonstrates that the "Math Base" variant (green line) provides the most significant performance improvements, particularly for larger models. This suggests that mathematical reasoning capabilities are critical for high-accuracy task performance. The "Ours (Base)" variant (red line) shows variable effectiveness compared to the baseline, indicating that architectural improvements alone may not consistently outperform instruction-tuned baselines. The widening performance gap with larger models implies that scaling benefits are maximized when combined with specialized training methodologies like Math Base. These findings highlight the importance of domain-specific training in achieving state-of-the-art results on mathematical and instructional tasks.