## Radar Charts: Performance Comparison ### Overview The image presents two radar charts comparing the performance of different language models across various benchmarks and domains. Chart (a) focuses on benchmarks like GSM8K, MATH, and others, while chart (b) assesses performance across domains such as Prealgebra, Number Theory, and Algebra. The charts display the performance of six models: Qwen2.5-32B, Qwen2.5-32B-IT, ORZ-32B, SimpleRL-32B, Baseline-32B, and SwS-32B. ### Components/Axes **General Chart Elements:** * Each chart is a radar plot with performance scores plotted along radial axes. * The radial axes range from approximately 0% to 100%, with concentric dotted circles indicating 40%, 60%, 80%, and 100%. * A legend is positioned between the two charts, listing the models and their corresponding line styles and colors. **Chart (a): Performance across Benchmarks** * **Title:** (a) Performance across Benchmarks * **Benchmarks (Categories):** GSM8K, MATH, Minerva Math, Olympiad Bench, GaoKao 2023, AMC23, AIME @32 * **Axis Labels and Values:** * GSM8K: 96.3 * MATH: 89.4 * Minerva Math: 47.1 * Olympiad Bench: 60.5 * GaoKao 2023: 80.3 * AMC23: 90.0 * AIME @32: 31.2 **Chart (b): Performance across Domains** * **Title:** (b) Performance across Domains * **Domains (Categories):** Prealgebra, Number Theory, Intermediate Algebra, Algebra, Geometry, Counting & Probability, Precalculus * **Axis Labels and Values:** * Prealgebra: 96.3 * Number Theory: 66.5 * Intermediate Algebra: 84.1 * Algebra: 76.6 * Geometry: 60.8 * Counting & Probability: 57.1 * Precalculus: 72.3 **Legend (Located between the two charts):** * Qwen2.5-32B: Gray dashed line * Qwen2.5-32B-IT: Blue dashed line * ORZ-32B: Orange dashed line * SimpleRL-32B: Green dashed line * Baseline-32B: Purple dashed line * SwS-32B: Solid red line ### Detailed Analysis **Chart (a): Performance across Benchmarks** * **SwS-32B (Red solid line):** This model generally outperforms the others across most benchmarks. * GSM8K: ~96.3 * MATH: ~89.4 * Minerva Math: ~47.1 * Olympiad Bench: ~60.5 * GaoKao 2023: ~80.3 * AMC23: ~90.0 * AIME @32: ~31.2 * **Qwen2.5-32B (Gray dashed line):** Shows relatively lower performance, especially on AIME @32 and Minerva Math. * GSM8K: ~96.3 * MATH: ~40 * Minerva Math: ~10 * Olympiad Bench: ~30 * GaoKao 2023: ~40 * AMC23: ~40 * AIME @32: ~10 * **Qwen2.5-32B-IT (Blue dashed line):** Performance is generally better than Qwen2.5-32B but lower than SwS-32B. * GSM8K: ~96.3 * MATH: ~80 * Minerva Math: ~40 * Olympiad Bench: ~50 * GaoKao 2023: ~70 * AMC23: ~80 * AIME @32: ~20 * **ORZ-32B (Orange dashed line):** Similar performance to Qwen2.5-32B-IT. * GSM8K: ~96.3 * MATH: ~80 * Minerva Math: ~40 * Olympiad Bench: ~50 * GaoKao 2023: ~70 * AMC23: ~80 * AIME @32: ~20 * **SimpleRL-32B (Green dashed line):** Performance is close to ORZ-32B and Qwen2.5-32B-IT. * GSM8K: ~96.3 * MATH: ~80 * Minerva Math: ~40 * Olympiad Bench: ~50 * GaoKao 2023: ~70 * AMC23: ~80 * AIME @32: ~20 * **Baseline-32B (Purple dashed line):** Performance is close to ORZ-32B and Qwen2.5-32B-IT. * GSM8K: ~96.3 * MATH: ~80 * Minerva Math: ~40 * Olympiad Bench: ~50 * GaoKao 2023: ~70 * AMC23: ~80 * AIME @32: ~20 **Chart (b): Performance across Domains** * **SwS-32B (Red solid line):** Again, this model shows the highest performance across all domains. * Prealgebra: ~96.3 * Number Theory: ~66.5 * Intermediate Algebra: ~84.1 * Algebra: ~76.6 * Geometry: ~60.8 * Counting & Probability: ~57.1 * Precalculus: ~72.3 * **Qwen2.5-32B (Gray dashed line):** Shows the lowest performance across all domains. * Prealgebra: ~96.3 * Number Theory: ~30 * Intermediate Algebra: ~50 * Algebra: ~40 * Geometry: ~30 * Counting & Probability: ~20 * Precalculus: ~40 * **Qwen2.5-32B-IT (Blue dashed line):** Performance is generally better than Qwen2.5-32B but lower than SwS-32B. * Prealgebra: ~96.3 * Number Theory: ~60 * Intermediate Algebra: ~80 * Algebra: ~70 * Geometry: ~50 * Counting & Probability: ~40 * Precalculus: ~60 * **ORZ-32B (Orange dashed line):** Similar performance to Qwen2.5-32B-IT. * Prealgebra: ~96.3 * Number Theory: ~60 * Intermediate Algebra: ~80 * Algebra: ~70 * Geometry: ~50 * Counting & Probability: ~40 * Precalculus: ~60 * **SimpleRL-32B (Green dashed line):** Performance is close to ORZ-32B and Qwen2.5-32B-IT. * Prealgebra: ~96.3 * Number Theory: ~60 * Intermediate Algebra: ~80 * Algebra: ~70 * Geometry: ~50 * Counting & Probability: ~40 * Precalculus: ~60 * **Baseline-32B (Purple dashed line):** Performance is close to ORZ-32B and Qwen2.5-32B-IT. * Prealgebra: ~96.3 * Number Theory: ~60 * Intermediate Algebra: ~80 * Algebra: ~70 * Geometry: ~50 * Counting & Probability: ~40 * Precalculus: ~60 ### Key Observations * **SwS-32B Dominance:** The SwS-32B model consistently achieves the highest performance across both benchmarks and domains. * **Qwen2.5-32B Underperformance:** The Qwen2.5-32B model generally exhibits the lowest performance compared to the other models. * **Benchmark Variability:** Performance varies significantly across different benchmarks, particularly for models other than SwS-32B. For example, performance on AIME @32 is notably lower for most models. * **Domain Consistency:** The relative performance of models across different domains is more consistent compared to the benchmarks. ### Interpretation The radar charts provide a clear visual comparison of the performance of different language models on various mathematical tasks. The SwS-32B model's superior performance suggests it may have architectural or training advantages that make it more effective in these domains. The Qwen2.5-32B model's lower scores indicate potential areas for improvement. The variability in performance across benchmarks highlights the diverse challenges posed by different problem types, while the consistency across domains suggests a more uniform level of competence in those areas. These insights can guide future research and development efforts to enhance the capabilities of language models in mathematical reasoning.

This image displays two radar charts, labeled (a) and (b), comparing the performance of six different models across various benchmarks and domains. Both charts share a common legend. The radial axes represent performance percentages, ranging from 0% at the center to 100% at the outermost circle, with intermediate markers at 20%, 40%, 60%, and 80%. The legend, located in the top right quadrant of the overall image, to the right of chart (a) and above chart (b), defines the models and their corresponding line styles and colors: * `--` (dashed, dark gray): Qwen2.5-32B * `- -` (dashed, light blue): Qwen2.5-32B-IT * `- -` (dashed, orange): ORZ-32B * `- -` (dashed, green): SimpleRL-32B * `- -` (dashed, purple): Baseline-32B * `—` (solid, red): SwS-32B The SwS-32B model's performance is highlighted by a light red shaded area, indicating it generally achieves the highest scores, forming the outer boundary of this shaded region. Numerical values are explicitly labeled only for the SwS-32B model at each axis point. For other models, performance values are estimated based on their proximity to the radial grid lines. --- ### (a) Performance across Benchmarks This radar chart, titled "(a) Performance across Benchmarks," evaluates models against seven distinct benchmarks, with "GSM8K" appearing as a central contextual label. **Radial Axes (Benchmarks) and SwS-32B Performance (clockwise from top):** * GSM8K: 96.3 * MATH 500: 89.4 * Minerva Math: 47.1 * Olympiad Bench: 60.5 * GaoKao 2023: 80.3 * AMC23: 90.0 * AIME @32: 31.2 **Data Series (Model Performance) and Trends:** * **SwS-32B** (solid red line, light red shaded area): * **Trend:** This model consistently demonstrates the highest performance across all benchmarks, forming the outermost boundary of the shaded region. Its performance is particularly strong on GSM8K, AMC23, and MATH 500, while its lowest scores are on AIME @32 and Minerva Math. * **Performance Values:** GSM8K: 96.3, MATH 500: 89.4, Minerva Math: 47.1, Olympiad Bench: 60.5, GaoKao 2023: 80.3, AMC23: 90.0, AIME @32: 31.2. * **Qwen2.5-32B** (dashed dark gray line): * **Trend:** This model generally exhibits the lowest performance among all models, with noticeable dips on Olympiad Bench and AIME @32. * **Estimated Performance Values:** GSM8K: ~85%, MATH 500: ~75%, Minerva Math: ~35%, Olympiad Bench: ~30%, GaoKao 2023: ~55%, AMC23: ~65%, AIME @32: ~20%. * **Qwen2.5-32B-IT** (dashed light blue line): * **Trend:** This model shows moderate performance, generally above Qwen2.5-32B but below SwS-32B and other models on most benchmarks. * **Estimated Performance Values:** GSM8K: ~90%, MATH 500: ~80%, Minerva Math: ~40%, Olympiad Bench: ~45%, GaoKao 2023: ~70%, AMC23: ~80%, AIME @32: ~25%. * **ORZ-32B** (dashed orange line): * **Trend:** This model's performance is competitive, often similar to Baseline-32B and SimpleRL-32B, but generally below SwS-32B. It shows a relatively strong performance on Olympiad Bench compared to the Qwen2.5 models. * **Estimated Performance Values:** GSM8K: ~88%, MATH 500: ~78%, Minerva Math: ~42%, Olympiad Bench: ~50%, GaoKao 2023: ~75%, AMC23: ~85%, AIME @32: ~28%. * **SimpleRL-32B** (dashed green line): * **Trend:** This model performs strongly, often very close to SwS-32B, particularly on GSM8K and MATH 500. It has a noticeable dip on Minerva Math and Olympiad Bench compared to its other scores. * **Estimated Performance Values:** GSM8K: ~95%, MATH 500: ~88%, Minerva Math: ~38%, Olympiad Bench: ~48%, GaoKao 2023: ~78%, AMC23: ~88%, AIME @32: ~29%. * **Baseline-32B** (dashed purple line): * **Trend:** This model shows consistently good performance, often ranking second or third among the models, generally above ORZ-32B and Qwen2.5 models, but below SwS-32B. It performs relatively well on AIME @32. * **Estimated Performance Values:** GSM8K: ~92%, MATH 500: ~85%, Minerva Math: ~45%, Olympiad Bench: ~55%, GaoKao 2023: ~79%, AMC23: ~89%, AIME @32: ~30%. --- ### (b) Performance across Domains This radar chart, titled "(b) Performance across Domains," evaluates models across seven distinct mathematical domains, with "Prealgebra" appearing as a central contextual label. **Radial Axes (Domains) and SwS-32B Performance (clockwise from top):** * Prealgebra: 96.3 * Intermediate Algebra: 84.1 * Algebra: 76.6 * Geometry: 60.8 * Counting & Probability: 57.1 * Precalculus: 72.3 * Number Theory: 66.5 **Data Series (Model Performance) and Trends:** * **SwS-32B** (solid red line, light red shaded area): * **Trend:** This model consistently demonstrates the highest performance across all domains, forming the outermost boundary of the shaded region. Its performance is particularly strong on Prealgebra and Intermediate Algebra, while its lowest scores are on Counting & Probability and Geometry. * **Performance Values:** Prealgebra: 96.3, Intermediate Algebra: 84.1, Algebra: 76.6, Geometry: 60.8, Counting & Probability: 57.1, Precalculus: 72.3, Number Theory: 66.5. * **Qwen2.5-32B** (dashed dark gray line): * **Trend:** This model generally exhibits the lowest performance among all models across most domains, with significant dips on Geometry and Counting & Probability. * **Estimated Performance Values:** Prealgebra: ~85%, Intermediate Algebra: ~70%, Algebra: ~60%, Geometry: ~40%, Counting & Probability: ~35%, Precalculus: ~50%, Number Theory: ~45%. * **Qwen2.5-32B-IT** (dashed light blue line): * **Trend:** This model shows moderate performance, generally above Qwen2.5-32B but below SwS-32B and other models on most domains. * **Estimated Performance Values:** Prealgebra: ~90%, Intermediate Algebra: ~75%, Algebra: ~65%, Geometry: ~50%, Counting & Probability: ~45%, Precalculus: ~60%, Number Theory: ~55%. * **ORZ-32B** (dashed orange line): * **Trend:** This model's performance is competitive, often similar to Baseline-32B and SimpleRL-32B, but generally below SwS-32B. It shows a relatively strong performance on Geometry and Counting & Probability compared to the Qwen2.5 models. * **Estimated Performance Values:** Prealgebra: ~88%, Intermediate Algebra: ~78%, Algebra: ~70%, Geometry: ~55%, Counting & Probability: ~50%, Precalculus: ~65%, Number Theory: ~60%. * **SimpleRL-32B** (dashed green line): * **Trend:** This model performs strongly, often very close to SwS-32B, particularly on Prealgebra and Intermediate Algebra. It has a noticeable dip on Geometry and Counting & Probability compared to its other scores, but still performs better than most other non-SwS models. * **Estimated Performance Values:** Prealgebra: ~95%, Intermediate Algebra: ~82%, Algebra: ~75%, Geometry: ~58%, Counting & Probability: ~55%, Precalculus: ~70%, Number Theory: ~65%. * **Baseline-32B** (dashed purple line): * **Trend:** This model shows consistently good performance, often ranking second or third among the models, generally above ORZ-32B and Qwen2.5 models, but below SwS-32B. It performs relatively well across all domains, with its lowest scores on Counting & Probability and Geometry. * **Estimated Performance Values:** Prealgebra: ~92%, Intermediate Algebra: ~80%, Algebra: ~72%, Geometry: ~59%, Counting & Probability: ~56%, Precalculus: ~71%, Number Theory: ~66%.

## Radar Charts: Performance Comparison of Language Models ### Overview The image presents two radar charts comparing the performance of several language models across different benchmarks and domains. Chart (a) shows performance across benchmarks (GSM8K, AIME@32, AMC23, GaoKao 2023, Olympiad Bench, MATH 500, Minerva Math, Precalculus), while chart (b) displays performance across mathematical domains (Prealgebra, Number Theory, Counting & Probability, Geometry, Algebra, Intermediate Algebra). The models being compared are Qwen2.5-32B, Qwen2.5-32B-IT, ORZ-32B, SimpleRL-32B, Baseline-32B, and SwS-32B. ### Components/Axes Both charts share the following components: * **Radial Axes:** Representing different benchmarks/domains. The axes are labeled with the benchmark/domain names. * **Concentric Circles:** Representing performance levels, ranging from 0% to 100%. The circles are marked at 20% intervals (20%, 40%, 60%, 80%, 100%). * **Lines:** Each line represents the performance of a specific language model. * **Legend:** Located in the top-left corner of each chart, identifying each line with a specific color and model name. **Chart (a) - Performance across Benchmarks:** * Benchmarks: GSM8K, AIME@32, AMC23, GaoKao 2023, Olympiad Bench, MATH 500, Minerva Math, Precalculus. **Chart (b) - Performance across Domains:** * Domains: Prealgebra, Number Theory, Counting & Probability, Geometry, Algebra, Intermediate Algebra. ### Detailed Analysis or Content Details **Chart (a) - Performance across Benchmarks:** * **Qwen2.5-32B (Purple):** Shows generally high performance, peaking at approximately 96.3% on GSM8K, and maintaining relatively high scores across all benchmarks. The line is mostly above 80% except for Minerva Math (around 47.1%) and Precalculus (around 72.3%). * **Qwen2.5-32B-IT (Orange):** Similar to Qwen2.5-32B, with a peak of around 96.3% on GSM8K. It shows slightly lower performance on AIME@32 (around 31.2%) and AMC23 (around 90.0%). * **ORZ-32B (Green):** Demonstrates strong performance, peaking at approximately 96.3% on GSM8K. It shows a dip on Minerva Math (around 47.1%). * **SimpleRL-32B (Blue):** Generally lower performance than the other models, with a peak of around 80.3% on GaoKao 2023. It shows the lowest performance on Minerva Math (around 31.2%). * **Baseline-32B (Red):** Moderate performance, peaking at around 89.4% on MATH 500. It shows lower performance on AIME@32 (around 31.2%). * **SwS-32B (Teal):** Performance is variable, peaking at around 80.3% on GaoKao 2023. It shows a low score on Minerva Math (around 47.1%). **Chart (b) - Performance across Domains:** * **Qwen2.5-32B (Purple):** Highest performance, peaking at 96.3% on Prealgebra. Maintains high scores across most domains, with a slight dip to around 76.6% on Algebra. * **Qwen2.5-32B-IT (Orange):** Similar to Qwen2.5-32B, peaking at 96.3% on Prealgebra. * **ORZ-32B (Green):** Strong performance, peaking at 96.3% on Prealgebra. * **SimpleRL-32B (Blue):** Lower performance, peaking at 84.1% on Intermediate Algebra. * **Baseline-32B (Red):** Moderate performance, peaking at 84.1% on Intermediate Algebra. * **SwS-32B (Teal):** Variable performance, peaking at 84.1% on Intermediate Algebra. ### Key Observations * **Qwen2.5-32B and Qwen2.5-32B-IT consistently outperform other models** across most benchmarks and domains. * **SimpleRL-32B generally exhibits the lowest performance.** * **Minerva Math consistently presents a challenge** for most models, resulting in lower scores in Chart (a). * **Intermediate Algebra is a strong suit** for several models in Chart (b). * The shapes of the radar charts are similar for Qwen2.5-32B, Qwen2.5-32B-IT, and ORZ-32B, indicating similar performance profiles. ### Interpretation The data suggests that Qwen2.5-32B and its IT variant are the most capable language models among those tested, demonstrating superior performance across a wide range of benchmarks and mathematical domains. The consistent underperformance of SimpleRL-32B indicates potential limitations in its architecture or training data. The lower scores on Minerva Math suggest that this benchmark presents a unique challenge, potentially requiring specialized knowledge or reasoning abilities. The high scores on Intermediate Algebra for several models suggest a strong foundation in fundamental algebraic concepts. The radar chart format effectively visualizes the relative strengths and weaknesses of each model across different tasks. The area enclosed by each line represents the overall performance of the model, with larger areas indicating better overall performance. The deviations from the circular shape highlight specific areas where a model excels or struggles. The charts allow for a quick and intuitive comparison of model capabilities, facilitating informed decision-making in selecting the most appropriate model for a given task.

## Radar Charts: AI Model Performance Across Mathematical Benchmarks and Domains ### Overview The image displays two radar charts (spider plots) comparing the performance of six different 32-billion-parameter AI models. The charts are labeled (a) and (b), with a shared legend positioned at the top-center between them. The charts use a circular grid with concentric rings representing performance percentages (40%, 60%, 80%, 100%). Each model is represented by a distinct line style and color, plotting its score across multiple axes radiating from the center. ### Components/Axes * **Legend (Top-Center):** Lists six models with corresponding line styles and colors: * `Qwen2.5-32B`: Gray, dashed line (`---`) * `Qwen2.5-32B-IT`: Light blue, dashed line (`---`) * `ORZ-32B`: Orange, dashed line (`---`) * `SimpleRL-32B`: Green, dashed line (`---`) * `Baseline-32B`: Purple, dashed line (`---`) * `SwS-32B`: Red, solid line (`—`) * **Chart (a) - Performance across Benchmarks:** * **Axes (7 total, clockwise from top):** GSM8K, MATH 500, Minerva Math, Olympiad Bench, GaoKao 2023, AMC23, AIME @32. * **Scale:** Concentric rings marked at 40%, 60%, 80%, and 100% (outermost). * **Chart (b) - Performance across Domains:** * **Axes (7 total, clockwise from top):** Prealgebra, Intermediate Algebra, Algebra, Geometry, Counting & Probability, Precalculus, Number Theory. * **Scale:** Identical concentric ring scale as chart (a). ### Detailed Analysis **Chart (a) - Performance across Benchmarks:** * **SwS-32B (Red, Solid Line):** Consistently forms the outermost polygon, indicating top performance across all benchmarks. Specific labeled scores (red text) are: GSM8K: 96.3, MATH 500: 89.4, Minerva Math: 47.1, Olympiad Bench: 60.5, GaoKao 2023: 80.3, AMC23: 90.6, AIME @32: 31.2. * **Other Models:** Generally form nested polygons inside the SwS-32B line. The gray dashed line (`Qwen2.5-32B`) is often the innermost, indicating the lowest performance on most benchmarks shown. The purple (`Baseline-32B`) and green (`SimpleRL-32B`) lines are frequently the next closest to the red line. * **Trend Verification:** All models show a similar *relative* performance pattern across benchmarks. They score highest on GSM8K and AMC23, moderately on MATH 500 and GaoKao 2023, and lowest on the more specialized Olympiad Bench, Minerva Math, and AIME @32. The red line's shape is a scaled-up version of the others. **Chart (b) - Performance across Domains:** * **SwS-32B (Red, Solid Line):** Again forms the outermost polygon. Specific labeled scores (red text) are: Prealgebra: 96.3, Intermediate Algebra: 84.1, Algebra: 76.6, Geometry: 60.8, Counting & Probability: 57.1, Precalculus: 72.3, Number Theory: 66.5. * **Other Models:** The nesting pattern is similar to chart (a). The gray dashed line (`Qwen2.5-32B`) is again the innermost. The purple (`Baseline-32B`) line is notably strong in Precalculus and Number Theory, nearly matching the red line on those axes. * **Trend Verification:** All models perform best in Prealgebra and Intermediate Algebra. Performance generally decreases for more advanced domains like Geometry, Counting & Probability, and Number Theory. The red line maintains a consistent lead across all domains. ### Key Observations 1. **Dominant Model:** The `SwS-32B` model (red solid line) demonstrates superior performance across every benchmark and every mathematical domain presented in these charts. 2. **Performance Hierarchy:** A clear and consistent hierarchy is visible: `SwS-32B` > `Baseline-32B`/`SimpleRL-32B` > `ORZ-32B` > `Qwen2.5-32B-IT` > `Qwen2.5-32B`. The exact order between `Baseline-32B` and `SimpleRL-32B` varies slightly by axis. 3. **Benchmark Difficulty:** The AIME @32 and Minerva Math benchmarks appear to be the most challenging, as all models score below 50% on them (with SwS-32B at 31.2 and 47.1, respectively). 4. **Domain Strength:** All models show relative strength in foundational algebra topics (Prealgebra, Intermediate Algebra) and relative weakness in combinatorial and geometric topics (Counting & Probability, Geometry). ### Interpretation These radar charts provide a multidimensional comparison of AI model capabilities in mathematics. The data suggests that the training or architectural approach used for `SwS-32B` yields significant and consistent improvements over the other compared models (`Qwen2.5-32B`, `ORZ-32B`, `SimpleRL-32B`, and a `Baseline-32B`). The fact that the performance *pattern* (the shape of the polygon) is similar across all models indicates that the relative difficulty of these mathematical tasks is consistent; the models differ in their overall capability level, not in their specialized strengths/weaknesses. The charts effectively argue that `SwS-32B` is a state-of-the-art model for mathematical reasoning within this 32B parameter class. The inclusion of both broad benchmarks (like GSM8K) and specialized domains (like Number Theory) shows that its advantage is comprehensive. For a researcher or user, this visualization implies that choosing `SwS-32B` would likely lead to better performance on a wide range of mathematical problems, from grade-school arithmetic to competition-level algebra and calculus. The clear visual gap between the red line and the others is a powerful indicator of a meaningful performance leap.

## Radar Charts: Performance Comparison Across Benchmarks and Domains ### Overview Two radar charts compare the performance of five AI models across different benchmarks (left) and academic domains (right). The charts use color-coded lines to represent models, with SwS-32B (red) consistently outperforming others in most categories. ### Components/Axes **Legend (Top-Left of Both Charts):** - Qwen2.5-32B (Gray dashed) - Qwen2.5-32B-IT (Blue dashed) - ORZ-32B (Orange dashed) - SimpleRL-32B (Green dashed) - Baseline-32B (Purple dashed) - SwS-32B (Red solid) **Chart (a) - Performance across Benchmarks:** - **Axes (Clockwise from Top):** 1. GSM8K (96.3) 2. MATH (89.4) 3. AIME@32 (31.2) 4. AMC23 (90.0) 5. GaoKao 2023 (80.3) 6. Olympiad Bench (60.5) 7. Minerva Math (47.1) **Chart (b) - Performance across Domains:** - **Axes (Clockwise from Top):** 1. Prealgebra (96.3) 2. Intermediate Algebra (84.1) 3. Number Theory (66.5) 4. Precalculus (72.3) 5. Counting & Probability (57.1) 6. Geometry (60.8) 7. Algebra (76.6) ### Detailed Analysis **Chart (a) Trends:** - SwS-32B (Red) dominates all benchmarks, peaking at 96.3 (GSM8K) and maintaining >80% in 5/7 categories. - Qwen2.5-32B-IT (Blue) shows strong performance in MATH (89.4) but struggles in Minerva Math (47.1). - Baseline-32B (Purple) has the lowest scores, with 31.2 (AIME@32) and 60.5 (Olympiad Bench). - ORZ-32B (Orange) and SimpleRL-32B (Green) show mid-tier performance, with ORZ-32B excelling in AMC23 (90.0). **Chart (b) Trends:** - SwS-32B maintains dominance, with 96.3 (Prealgebra) and 84.1 (Intermediate Algebra). - Qwen2.5-32B-IT (Blue) performs best in Number Theory (66.5) but weakest in Geometry (60.8). - Baseline-32B (Purple) scores lowest in Counting & Probability (57.1) and Geometry (60.8). - ORZ-32B (Orange) shows consistent mid-range performance (72.3-84.1). ### Key Observations 1. **SwS-32B Superiority:** Red line consistently leads in both charts, suggesting it's optimized for these tasks. 2. **Qwen2.5-32B-IT Variability:** Blue line shows high variance (e.g., 89.4 in MATH vs. 47.1 in Minerva Math). 3. **Baseline-32B Weakness:** Purple line underperforms across all categories, indicating fundamental limitations. 4. **Domain-Specific Gaps:** Minerva Math (47.1) and Geometry (60.8) are weak points for most models. ### Interpretation The data reveals SwS-32B as the most robust model across both benchmarks and academic domains, likely due to specialized training. Qwen2.5-32B-IT's performance suggests it excels in specific areas (e.g., MATH) but lacks generalization. The Baseline-32B's poor results highlight the importance of architectural complexity. Notably, Minerva Math and Geometry represent systemic challenges for current models, possibly due to insufficient training data or task complexity. These insights could guide targeted model improvements or domain-specific adaptations.