## Line Chart: Model Accuracy Comparison ### Overview The image is a line chart comparing the accuracy of three language models: MetaMath-13B, LLaMA2-70B, and GPT-4, across a series of mathematical problems. The x-axis represents different problem types (labeled in Chinese), and the y-axis represents accuracy, ranging from 0 to 80. ### Components/Axes * **Title:** None visible. * **X-axis:** Represents different mathematical problem types, labeled in Chinese. The labels are closely spaced and difficult to read individually. * **Y-axis:** "Accuracy", ranging from 0 to 80 in increments of 20. Horizontal gridlines are present at each increment. * **Legend:** Located at the top of the chart. * Blue line: MetaMath-13B * Orange line: LLaMA2-70B * Green line: GPT-4 ### Detailed Analysis The chart displays the accuracy of each model across a range of mathematical problems. The x-axis labels are in Chinese, representing different problem types. Here's a breakdown of each model's performance: * **MetaMath-13B (Blue):** Generally shows the lowest accuracy among the three models. The accuracy fluctuates significantly across different problem types, ranging from approximately 0 to 60. * **LLaMA2-70B (Orange):** Shows a moderate level of accuracy, generally higher than MetaMath-13B but lower than GPT-4. The accuracy also fluctuates, ranging from approximately 5 to 65. * **GPT-4 (Green):** Consistently demonstrates the highest accuracy across most problem types. The accuracy fluctuates, ranging from approximately 30 to 90. Here are some approximate data points for each model at the beginning and end of the chart: * **MetaMath-13B:** * First data point: Accuracy ~40 * Last data point: Accuracy ~10 * **LLaMA2-70B:** * First data point: Accuracy ~45 * Last data point: Accuracy ~55 * **GPT-4:** * First data point: Accuracy ~50 * Last data point: Accuracy ~90 Here is a transcription of the x-axis labels, along with their English translations: | Chinese Label | Approximate English Translation | |---|---| | 全等 | Congruence | | 等腰三角形 | Isosceles triangle | | 等边三角形 | Equilateral triangle | | 平行四边形 | Parallelogram | | 弧长 | Arc length | | 圆锥 | Cone | | 函数与一次函数 | Function and linear function | | 函数与二次函数 | Function and quadratic function | | 反比例函数 | Inverse proportional function | | 整式的加减 | Addition and subtraction of polynomials | | 一元一次方程 | Linear equation in one variable | | 平方根 | Square root | | 用平方根解一元二次方程 | Solving quadratic equations in one variable using square roots | | 用公式法解一元二次方程 | Solving quadratic equations in one variable using the quadratic formula | | 用因式分解法解一元二次方程 | Solving quadratic equations in one variable by factoring | | 一元二次方程的应用 | Application of quadratic equations in one variable | | 一元一次不等式 | Linear inequality in one variable | | 一元一次不等式的应用 | Application of linear inequalities in one variable | | 随机事件与概率 | Random events and probability | ### Key Observations * GPT-4 consistently outperforms MetaMath-13B and LLaMA2-70B across the majority of problem types. * MetaMath-13B generally has the lowest accuracy. * All three models exhibit significant fluctuations in accuracy depending on the problem type. * The performance gap between GPT-4 and the other two models is substantial. ### Interpretation The data suggests that GPT-4 is significantly more proficient at solving the mathematical problems represented on the x-axis compared to MetaMath-13B and LLaMA2-70B. The fluctuations in accuracy across different problem types indicate that each model has strengths and weaknesses in specific areas of mathematics. The consistent underperformance of MetaMath-13B suggests it may require further training or optimization to achieve comparable accuracy to the other models. The chart highlights the varying capabilities of different language models in tackling mathematical reasoning tasks.

## Line Chart: Model Accuracy on Mathematical Problems ### Overview This image presents a line chart comparing the accuracy of three large language models – MetaMath-13B, LLaMA2-70B, and GPT-4 – across a series of mathematical problems. The x-axis represents different mathematical problem sets, labeled in Chinese characters, and the y-axis represents the accuracy achieved by each model, ranging from 0 to 80. ### Components/Axes * **Y-axis Title:** "Accuracy" * **X-axis Labels:** A series of mathematical problem sets labeled in Chinese. The labels are densely packed and appear to represent different mathematical topics or difficulty levels. * **Legend:** Located at the top-center of the chart. * Blue Line: MetaMath-13B * Orange Line: LLaMA2-70B * Green Line: GPT-4 * **Gridlines:** Horizontal gridlines are present to aid in reading accuracy values. ### Detailed Analysis The chart displays the accuracy of each model as a line plotted against the problem sets. **MetaMath-13B (Blue Line):** The line fluctuates significantly. It starts at approximately 75, drops to around 10, then oscillates between approximately 15 and 40 for the majority of the problem sets. Towards the end, it declines to around 10. * Initial Accuracy: ~75 * Lowest Accuracy: ~8 * Highest Accuracy (excluding initial point): ~40 * Final Accuracy: ~10 **LLaMA2-70B (Orange Line):** This line also exhibits considerable fluctuation. It begins at around 25, rises to a peak of approximately 65, then generally oscillates between 20 and 55. It ends at around 45. * Initial Accuracy: ~25 * Lowest Accuracy: ~15 * Highest Accuracy: ~65 * Final Accuracy: ~45 **GPT-4 (Green Line):** This line demonstrates the most consistent and generally highest accuracy. It starts at approximately 45, rises to a peak of around 85, and remains largely above 60 throughout the chart. It ends at approximately 85. * Initial Accuracy: ~45 * Lowest Accuracy: ~60 * Highest Accuracy: ~85 * Final Accuracy: ~85 **X-Axis Labels (Chinese):** The x-axis labels are in Chinese. A rough transliteration and potential meaning (based on common mathematical terms) is provided below. Note that this is an approximation. 1. 全面微积分 (Quánmiàn wēijífēn) - Comprehensive Calculus 2. 初等代数 (Chūděng dàishù) - Elementary Algebra 3. 高等代数 (Gāoděng dàishù) - Advanced Algebra 4. 三角学 (Sānjiǎoxué) - Trigonometry 5. 概率与统计 (Gàilǜ yǔ tǒngjì) - Probability and Statistics 6. 求和 (Qiúhé) - Summation 7. 反常积分 (Fǎncháng jīfēn) - Improper Integral 8. 反三角函数 (Fǎn sānjiǎo hánshù) - Inverse Trigonometric Functions 9. 极限 (Jìxiàn) - Limits 10. 导数 (Dǎoshù) - Derivatives 11. 积分 (Jīfēn) - Integrals 12. 级数 (Jíshù) - Series 13. 微分方程 (Wēifēn fāngchéng) - Differential Equations 14. 线性代数 (Xiànxìng dàishù) - Linear Algebra 15. 平面几何 (Píngmiàn jǐhè) - Plane Geometry 16. 立体几何 (Lìtǐ jǐhè) - Solid Geometry 17. 一元二次方程 (Yīyuán èrcì fāngchéng) - Quadratic Equation 18. 一元三次方程 (Yīyuán sān cì fāngchéng) - Cubic Equation 19. 概率 (Gàilǜ) - Probability 20. 期望 (Qīwàng) - Expectation 21. 方差 (Fāngchā) - Variance 22. 偏导数 (Piāndǎoshù) - Partial Derivatives 23. 向量 (Xiàngliàng) - Vectors ### Key Observations * GPT-4 consistently outperforms both MetaMath-13B and LLaMA2-70B across all problem sets. * MetaMath-13B exhibits the most volatile performance, with large swings in accuracy. * LLaMA2-70B shows moderate performance, generally falling between MetaMath-13B and GPT-4. * The problem sets appear to vary in difficulty, as evidenced by the fluctuations in accuracy for all models. ### Interpretation The data strongly suggests that GPT-4 possesses superior mathematical reasoning capabilities compared to MetaMath-13B and LLaMA2-70B. The consistent high accuracy of GPT-4 indicates a robust understanding of mathematical concepts and problem-solving skills. The significant fluctuations in accuracy for MetaMath-13B suggest that its performance is highly sensitive to the specific type of mathematical problem presented. LLaMA2-70B provides a middle ground, demonstrating better performance than MetaMath-13B but still lagging behind GPT-4. The Chinese labels on the x-axis indicate that the models were evaluated on a diverse range of mathematical topics, including calculus, algebra, trigonometry, probability, and geometry. The varying accuracy levels across these topics suggest that the models may have different strengths and weaknesses in specific areas of mathematics. The chart provides valuable insights into the mathematical reasoning abilities of these large language models and highlights the potential for further research and development in this field.

## Line Chart: Accuracy Comparison of Three AI Models Across Mathematical Topics ### Overview This image is a line chart comparing the accuracy performance of three large language models (LLMs) across a wide range of mathematical topics. The chart plots "Accuracy" on the y-axis against 40 distinct mathematical categories on the x-axis. The three models compared are MetaMath-13B, LLaMA2-70B, and GPT-4. The data reveals significant variability in performance both between models and across different mathematical domains. ### Components/Axes * **Chart Type:** Multi-line chart with markers. * **Y-Axis:** * **Label:** "Accuracy" (written vertically on the left side). * **Scale:** Linear scale from 0 to approximately 95. * **Major Grid Lines:** Horizontal dashed lines at intervals of 20 (0, 20, 40, 60, 80). * **X-Axis:** * **Label:** None explicitly stated. The axis consists of 40 categorical labels representing mathematical topics. * **Labels (Transcribed from Chinese, with English translation):** 1. 全等三角形 - Congruent Triangles 2. 等腰三角形 - Isosceles Triangles 3. 等边三角形 - Equilateral Triangles 4. 平行四边形 - Parallelograms 5. 圆周角 - Inscribed Angle 6. 圆心角 - Central Angle 7. 弧长和扇形面积 - Arc Length and Sector Area 8. 点线面位置关系 - Positional Relationships of Points, Lines, and Planes 9. 函数与一元一次方程 - Functions and Linear Equations in One Variable 10. 函数与一元二次方程 - Functions and Quadratic Equations in One Variable 11. 函数与二元一次方程组 - Functions and Systems of Linear Equations in Two Variables 12. 求一次函数解析式 - Finding the Analytic Expression of a Linear Function 13. 二次函数的性质 - Properties of Quadratic Functions 14. 正比例函数的应用 - Application of Direct Proportional Functions 15. 反比例函数的定义 - Definition of Inverse Proportional Functions 16. 反比例函数的性质 - Properties of Inverse Proportional Functions 17. 反比例函数的应用 - Application of Inverse Proportional Functions 18. 有理数的乘方 - Exponentiation of Rational Numbers 19. 代数式求值 - Evaluating Algebraic Expressions 20. 同底数幂的乘法 - Multiplication of Powers with the Same Base 21. 约分与通分 - Reduction and Reduction to a Common Denominator 22. 十字相乘法 - Cross Multiplication Method 23. 提公因式法 - Factoring by Taking out the Common Factor 24. 分组分解法 - Factoring by Grouping 25. 整式的乘法 - Multiplication of Polynomials 26. 整式的加减 - Addition and Subtraction of Polynomials 27. 二次根式的性质 - Properties of Quadratic Radicals 28. 平方根与算术平方根 - Square Root and Arithmetic Square Root 29. 一元一次方程的根应用 - Application of Roots of Linear Equations in One Variable 30. 解一元二次方程 - Solving Quadratic Equations in One Variable 31. 一元二次方程的根应用 - Application of Roots of Quadratic Equations in One Variable 32. 解一元一次不等式 - Solving Linear Inequalities in One Variable 33. 解一元一次不等式组 - Solving Systems of Linear Inequalities in One Variable 34. 解二元一次方程组 - Solving Systems of Linear Equations in Two Variables 35. 分式方程的应用 - Application of Fractional Equations 36. 数据的收集与整理 - Data Collection and Organization 37. 数据的集中趋势 - Central Tendency of Data 38. 概率的求法 - Methods of Calculating Probability 39. 随机事件与概率 - Random Events and Probability 40. (The 40th label is partially cut off but appears to be a continuation of the probability topic). * **Legend:** * **Position:** Top center, above the plot area. * **Items:** * **MetaMath-13B:** Blue line with circular markers. * **LLaMA2-70B:** Orange line with circular markers. * **GPT-4:** Green line with circular markers. ### Detailed Analysis **Trend Verification & Data Point Extraction (Approximate Values):** The chart shows high volatility for all models. Below is an analysis of each series' trend and key points. * **GPT-4 (Green Line):** * **Overall Trend:** Consistently the highest-performing model, with accuracy mostly ranging between 60 and 95. It shows a jagged, "sawtooth" pattern with sharp peaks and valleys but maintains a high baseline. * **Key Data Points (Approximate):** * Peaks near or above 90: "函数与一元二次方程" (~90), "反比例函数的性质" (~90), "同底数幂的乘法" (~90), "整式的乘法" (~90), "解一元二次方程" (~90), "分式方程的应用" (~90), "概率的求法" (~95). * Notable Valleys (still relatively high): "等腰三角形" (~70), "圆心角" (~50), "反比例函数的定义" (~30), "十字相乘法" (~35), "整式的加减" (~35), "平方根与算术平方根" (~50), "解一元一次不等式组" (~25). * **LLaMA2-70B (Orange Line):** * **Overall Trend:** Occupies the middle ground, with accuracy generally between 10 and 70. Its performance is also volatile but sits systematically below GPT-4 and often above MetaMath-13B. * **Key Data Points (Approximate):** * Peaks: "函数与一元二次方程" (~60), "反比例函数的性质" (~65), "同底数幂的乘法" (~55), "整式的乘法" (~70), "解一元二次方程" (~65), "分式方程的应用" (~60). * Valleys: "等腰三角形" (~20), "圆心角" (~5), "反比例函数的定义" (~15), "十字相乘法" (~10), "整式的加减" (~10), "平方根与算术平方根" (~20), "解一元一次不等式组" (~15). * **MetaMath-13B (Blue Line):** * **Overall Trend:** Generally the lowest-performing model, with accuracy mostly between 0 and 55. It exhibits the most extreme volatility, with several points dropping to near 0 and a few spikes that approach or briefly surpass LLaMA2-70B. * **Key Data Points (Approximate):** * Notable Spikes: "平行四边形" (~55), "函数与一元一次方程" (~45), "求一次函数解析式" (~35), "整式的乘法" (~50), "解一元二次方程" (~60). * Valleys at or near 0: "函数与二元一次方程组", "反比例函数的定义", "约分与通分", "整式的加减", "解一元一次不等式组". ### Key Observations 1. **Performance Hierarchy:** A clear and consistent hierarchy is visible: GPT-4 > LLaMA2-70B > MetaMath-13B across almost all topics. 2. **Topic Difficulty Correlation:** All three models show synchronized dips and peaks on certain topics, suggesting some mathematical areas are universally more challenging (e.g., "圆心角" - Central Angle, "反比例函数的定义" - Definition of Inverse Proportional Functions, "整式的加减" - Addition/Subtraction of Polynomials). 3. **Model-Specific Strengths:** MetaMath-13B shows surprising competence in specific geometry ("平行四边形" - Parallelograms) and algebra ("解一元二次方程" - Solving Quadratic Equations) topics, where its accuracy spikes significantly. 4. **Volatility:** The performance of all models is highly topic-dependent. No model demonstrates flat, consistent accuracy; mastery is domain-specific. 5. **Zero-Performance Points:** MetaMath-13B has multiple data points at or near 0% accuracy, indicating complete failure on those specific topics for the evaluated test set. ### Interpretation This chart provides a granular diagnostic of LLM capabilities in mathematics, moving beyond aggregate scores. The data suggests: * **Generalization vs. Specialization:** GPT-4 demonstrates robust generalization across a wide mathematical curriculum. In contrast, MetaMath-13B, despite its smaller size and specialized training, shows a "spiky" profile—it excels in narrow domains but fails completely in others, indicating potential gaps in its training data or reasoning generalization. * **The "Curriculum" of Difficulty:** The synchronized performance dips reveal an implicit hierarchy of difficulty within middle/high school mathematics as perceived by these models. Foundational topics like definitions ("反比例函数的定义") and basic operations ("整式的加减") prove surprisingly difficult, possibly because they require precise, rule-based reasoning that LLMs can find challenging. * **Implications for Use:** For reliable mathematical problem-solving, GPT-4 is the most dependable choice across the board. Using a model like MetaMath-13B would require careful human oversight and knowledge of its specific strengths and weaknesses. The chart acts as a capability map for selecting the right tool for a specific mathematical task. * **Investigative Insight (Peircean):** The chart is an *index* of the models' internal knowledge structures and reasoning flaws. The valleys are not random; they point to specific conceptual hurdles (e.g., handling definitions, certain algebraic manipulations). The spikes in MetaMath-13B suggest its fine-tuning was highly effective for certain problem *types* but did not confer broad mathematical understanding. This visual data argues that "math accuracy" is not a monolithic skill but a constellation of competencies.

## Line Chart: Accuracy Comparison of AI Models on Math Problems ### Overview The chart compares the accuracy of three AI models (MetaMath-13B, LLaMA2-70B, GPT-4) across 40+ math problems. Accuracy is measured on a 0-100% scale, with jagged lines indicating variability. GPT-4 consistently performs best, while MetaMath-13B shows the most erratic results. ### Components/Axes - **Y-Axis**: Accuracy (0-100%, labeled "Accuracy") - **X-Axis**: Math problems (Chinese text, 40+ categories) - **Legend**: - Blue: MetaMath-13B - Orange: LLaMA2-70B - Green: GPT-4 - **Legend Position**: Top-center - **Data Series**: Three colored lines (blue, orange, green) ### Detailed Analysis 1. **GPT-4 (Green Line)**: - **Trend**: Dominates with peaks near 90% and troughs above 60%. - **Key Values**: - Highest accuracy: ~95% (multiple problems) - Lowest accuracy: ~65% (e.g., "反比例函数" problem) - **Stability**: Minimal dips below 60%. 2. **LLaMA2-70B (Orange Line)**: - **Trend**: Volatile, with sharp rises/falling. Matches GPT-4 in ~20% of problems. - **Key Values**: - Peaks: ~70-80% (e.g., "多项式方程") - Troughs: ~10-30% (e.g., "函数与一元一次方程") - **Inconsistency**: Wide swings (e.g., 90% drop from 80% to 10%). 3. **MetaMath-13B (Blue Line)**: - **Trend**: Most erratic, with extreme lows (near 0%) and moderate highs (~60%). - **Key Values**: - Peaks: ~60% (e.g., "函数的单调性") - Troughs: ~0-5% (e.g., "反比例函数", "函数的反演") - **Unpredictability**: Frequent drops to near-zero accuracy. ### Key Observations - **GPT-4 Superiority**: Consistently outperforms others across all problems. - **LLaMA2-70B Variability**: Strong in specific areas (e.g., polynomial equations) but fails catastrophically on others. - **MetaMath-13B Fragility**: Struggles with foundational concepts (e.g., inverse proportionality, function inversion). ### Interpretation The data suggests GPT-4 has robust, generalizable math-solving capabilities, while LLaMA2-70B excels in niche areas but lacks consistency. MetaMath-13B’s performance indicates significant gaps in handling core mathematical principles. The jagged lines for all models imply sensitivity to problem phrasing or complexity. Notably, LLaMA2-70B’s ability to match GPT-4 in select problems hints at potential for targeted improvements, whereas MetaMath-13B requires foundational retraining. The Chinese problem labels (e.g., "反比例函数" = inverse proportionality functions) highlight domain-specific challenges, with MetaMath-13B failing most frequently on advanced topics.