## Line Chart: Model Accuracy on Math Problems ### Overview The image is a line chart comparing the accuracy of four different language models (Yi-6B, ChatGLM3-6B, LLaMA2-7B, and DeepSeekMath-7B) on a series of math problems. The x-axis represents different math problem types (in Chinese), and the y-axis represents the accuracy score. ### Components/Axes * **Title:** There is no explicit title on the chart. * **X-axis:** Represents different math problem types, labeled in Chinese. The labels are densely packed and rotated for readability. * **Y-axis:** Represents "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: Yi-6B * Orange line: ChatGLM3-6B * Green line: LLaMA2-7B * Red line: DeepSeekMath-7B ### Detailed Analysis **X-Axis Labels (Math Problem Types - Chinese with approximate English Translation):** The x-axis labels are in Chinese. Here's a transcription and approximate translation: 1. 全等三角形 (Quán děng sānjiǎoxíng) - Congruent triangles 2. 等腰三角形 (Děng yāo sānjiǎoxíng) - Isosceles triangle 3. 勾股定理 (Gōu gǔ dìnglǐ) - Pythagorean theorem 4. 平行四边形 (Píngxíng sìbiānxíng) - Parallelogram 5. 函数与一次方程 (Hánshù yǔ yīcì fāngchéng) - Function and linear equation 6. 反比例函数 (Fǎn bǐlì hánshù) - Inverse proportional function 7. 圆 (Yuán) - Circle 8. 弧长与扇形 (Hú cháng yǔ shànxíng) - Arc length and sector 9. 圆锥 (Yuánzhuī) - Cone 10. 点与坐标 (Diǎn yǔ zuòbiāo) - Point and coordinates 11. 函数与一次函数 (Hánshù yǔ yīcì hánshù) - Function and linear function 12. 一次函数 (Yīcì hánshù) - Linear function 13. 关系式 (Guānxì shì) - Relation 14. 求一次函数 (Qiú yīcì hánshù) - Finding a linear function 15. 一元一次方程 (Yī yuán yīcì fāngchéng) - Linear equation in one variable 16. 二次函数 (Èrcì hánshù) - Quadratic function 17. 整式的运算 (Zhěng shì de yùsuàn) - Operations with polynomials 18. 平方根 (Píngfāng gēn) - Square root 19. 一元二次方程 (Yī yuán èrcì fāngchéng) - Quadratic equation in one variable 20. 一元一次不等式 (Yī yuán yīcì bù děngshì) - Linear inequality in one variable 21. 解一元一次方程 (Jiě yī yuán yīcì fāngchéng) - Solving linear equations in one variable 22. 解不等式 (Jiě bù děngshì) - Solving inequalities 23. 分式方程 (Fēnshì fāngchéng) - Fractional equation 24. 整式的加减 (Zhěng shì de jiājiǎn) - Addition and subtraction of polynomials 25. 二次根式 (Èrcì gēnshì) - Quadratic radical 26. 平方根与算术平方根 (Píngfāng gēn yǔ suànshù píngfāng gēn) - Square root and arithmetic square root 27. 一元二次方程的根 (Yī yuán èrcì fāngchéng de gēn) - Roots of a quadratic equation in one variable 28. 概率与频率 (Gàilǜ yǔ pínlǜ) - Probability and frequency 29. 随机事件与概率 (Suíjī shìjiàn yǔ gàilǜ) - Random events and probability **Data Series Analysis:** * **Yi-6B (Blue):** The accuracy fluctuates, generally staying between 20 and 60. It shows some peaks and valleys, but no clear upward or downward trend. * Approximate values: Ranges from ~5 to ~55. * **ChatGLM3-6B (Orange):** This model shows more variance in accuracy. It has some high peaks, reaching above 80, but also drops to near 0 on some problem types. * Approximate values: Ranges from ~0 to ~90. * **LLaMA2-7B (Green):** This model generally has lower accuracy compared to the others, often staying below 40. It also exhibits significant fluctuations. * Approximate values: Ranges from ~5 to ~70. * **DeepSeekMath-7B (Red):** This model generally performs the best, with accuracy frequently above 50 and reaching peaks near 90. It also has some dips, but not as severe as ChatGLM3-6B. * Approximate values: Ranges from ~10 to ~90. ### Key Observations * DeepSeekMath-7B generally outperforms the other models across most problem types. * ChatGLM3-6B has the highest variance in performance, with both high peaks and low dips. * LLaMA2-7B tends to have the lowest accuracy among the four models. * All models show significant fluctuations in accuracy depending on the specific math problem type. ### Interpretation The chart demonstrates the varying capabilities of different language models in solving different types of math problems. DeepSeekMath-7B appears to be the most robust model for this specific set of problems, while LLaMA2-7B struggles. The fluctuations in accuracy across problem types suggest that each model has strengths and weaknesses in specific mathematical domains. The performance differences could be attributed to the models' architectures, training data, or specific optimizations for mathematical reasoning. The fact that all models exhibit variance indicates that mathematical reasoning remains a challenging task for these language models, and performance is highly dependent on the specific problem type.

## Line Chart: Model Accuracy on Math Problems ### Overview This line chart compares the accuracy of four different language models (Yi-6B, ChatGLM3-6B, LLaMA2-7B, and DeepSeekMath-7B) across a series of math problems. The x-axis represents the math problem categories, and the y-axis represents the accuracy score, ranging from 0 to 80. ### Components/Axes * **Y-axis Title:** Accuracy * **X-axis Labels:** The x-axis labels are in Chinese characters. A rough translation (using online tools) suggests they represent different categories of math problems, including: * 全面提升 (Comprehensive Improvement) * 数学应用 (Math Application) * 初中数学 (Junior High Math) * 高等数学 (Higher Math) * 微积分 (Calculus) * 线性代数 (Linear Algebra) * 概率统计 (Probability and Statistics) * 复分析 (Complex Analysis) * 多元微积分 (Multivariable Calculus) * 一元微积分 (Single Variable Calculus) * 几何 (Geometry) * 微积分应用 (Calculus Application) * 因果推理 (Causal Reasoning) * 随机过程 (Stochastic Processes) * 随机事件概率 (Probability of Random Events) * **Legend:** Located at the top of the chart, the legend identifies each line by model name and color: * Yi-6B (Light Blue) * ChatGLM3-6B (Orange) * LLaMA2-7B (Green) * DeepSeekMath-7B (Red) ### Detailed Analysis The chart displays accuracy as a function of problem category. I will describe each line's trend and then extract approximate data points. * **Yi-6B (Light Blue):** This line fluctuates significantly, starting around 40, peaking around 70, and then dropping to around 20 before rising again. * 全面提升: ~42 * 数学应用: ~50 * 初中数学: ~65 * 高等数学: ~55 * 微积分: ~45 * 线性代数: ~30 * 概率统计: ~25 * 复分析: ~35 * 多元微积分: ~40 * 一元微积分: ~50 * 几何: ~45 * 微积分应用: ~60 * 因果推理: ~50 * 随机过程: ~30 * 随机事件概率: ~40 * **ChatGLM3-6B (Orange):** This line generally shows higher accuracy than Yi-6B, with peaks around 85 and a more stable performance. * 全面提升: ~60 * 数学应用: ~70 * 初中数学: ~85 * 高等数学: ~75 * 微积分: ~65 * 线性代数: ~50 * 概率统计: ~40 * 复分析: ~55 * 多元微积分: ~60 * 一元微积分: ~70 * 几何: ~65 * 微积分应用: ~80 * 因果推理: ~70 * 随机过程: ~50 * 随机事件概率: ~60 * **LLaMA2-7B (Green):** This line consistently shows the lowest accuracy, generally below 30, with minimal fluctuation. * 全面提升: ~10 * 数学应用: ~15 * 初中数学: ~20 * 高等数学: ~15 * 微积分: ~10 * 线性代数: ~10 * 概率统计: ~15 * 复分析: ~20 * 多元微积分: ~15 * 一元微积分: ~20 * 几何: ~15 * 微积分应用: ~25 * 因果推理: ~15 * 随机过程: ~10 * 随机事件概率: ~15 * **DeepSeekMath-7B (Red):** This line exhibits the highest accuracy overall, with peaks exceeding 80 and generally stable performance. * 全面提升: ~50 * 数学应用: ~75 * 初中数学: ~85 * 高等数学: ~80 * 微积分: ~70 * 线性代数: ~60 * 概率统计: ~50 * 复分析: ~65 * 多元微积分: ~70 * 一元微积分: ~75 * 几何: ~70 * 微积分应用: ~85 * 因果推理: ~75 * 随机过程: ~60 * 随机事件概率: ~70 ### Key Observations * DeepSeekMath-7B consistently outperforms the other models across all problem categories. * LLaMA2-7B consistently performs the worst. * ChatGLM3-6B generally performs better than Yi-6B, but with more variability. * The accuracy scores vary significantly depending on the problem category. "初中数学" (Junior High Math) and "微积分应用" (Calculus Application) seem to be categories where the models achieve higher accuracy. ### Interpretation The data suggests that DeepSeekMath-7B is the most capable model for solving the presented math problems, while LLaMA2-7B struggles significantly. The varying accuracy across different problem categories indicates that the models' strengths and weaknesses are problem-specific. The higher accuracy on "初中数学" and "微积分应用" might be due to these problems being more common in the training data or being inherently simpler. The chart highlights the importance of model selection based on the specific task and the need for further research to improve the performance of language models on complex math problems. The Chinese labels suggest the evaluation dataset is tailored towards a Chinese-speaking audience or curriculum. The large differences in performance between the models suggest that the architecture and training data play a significant role in mathematical reasoning capabilities.

## Line Chart: Accuracy of Four AI Models Across Mathematical Topics ### Overview This image is a line chart comparing the performance (accuracy) of four different large language models (LLMs) on a wide range of mathematical topics. The chart displays the accuracy percentage for each model across approximately 50 distinct mathematical concepts, primarily from middle school and high school curricula. The data is presented as four interconnected line series, each with markers at data points. ### Components/Axes * **Chart Type:** Multi-series line chart with markers. * **Legend:** Positioned at the top center of the chart area. It defines four data series: * **Yi-6B:** Blue line with circular markers. * **ChatGLM3-6B:** Orange line with circular markers. * **LLaMA2-7B:** Green line with circular markers. * **DeepSeekMath-7B:** Red line with circular markers. * **Y-Axis (Vertical):** * **Label:** "Accuracy" (written vertically). * **Scale:** Linear scale from 0 to approximately 90. * **Major Gridlines:** Horizontal dashed lines at intervals of 20 (0, 20, 40, 60, 80). * **X-Axis (Horizontal):** * **Label:** Not explicitly labeled with a title, but contains category labels for mathematical topics. * **Category Labels:** A dense series of labels written in Chinese, rotated at a 45-degree angle for readability. These represent the specific mathematical topics tested. * **Language:** The primary language of the axis labels is **Chinese**. An English translation is provided below for each label. ### Detailed Analysis The chart plots accuracy values for each model on each topic. Below is a reconstruction of the data, reading the approximate values from the chart. Values are estimated to the nearest 5% due to visual interpretation. **X-Axis Categories (Chinese -> 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. 点与圆的位置关系 -> Positional Relationship between a Point and a Circle 9. 函数与一元一次方程 -> Function and Linear Equation in One Variable 10. 函数与一元一次不等式 -> Function and Linear Inequality in One Variable 11. 函数与二元一次方程组 -> Function and System of Linear Equations in Two Variables 12. 求一次函数的解析式 -> Finding the Analytic Expression of a Linear Function 13. 二次函数的定义 -> Definition of Quadratic Function 14. 反比例函数的定义 -> Definition of Inverse Proportional Function 15. 反比例函数的性质 -> Properties of Inverse Proportional Function 16. 有理数的乘方 -> Exponentiation of Rational Numbers 17. 点的坐标与象限 -> Coordinates of a Point and Quadrants 18. 同底数幂的乘法 -> Multiplication of Powers with the Same Base 19. 约分与通分 -> Reduction and Reduction to a Common Denominator 20. 十字相乘法 -> Cross Multiplication Method 21. 提公因式法 -> Factoring by Common Factor 22. 流水问题 -> Flow/Current Problems (Word Problems) 23. 鸡兔同笼 -> Chicken and Rabbit in the Same Cage (Classic Problem) 24. 整式的乘法与加减 -> Multiplication and Addition/Subtraction of Polynomials 25. 平方差公式 -> Difference of Squares Formula 26. 完全平方公式 -> Perfect Square Formula 27. 二次根式的乘除 -> Multiplication and Division of Quadratic Radicals 28. 二次根式的加减 -> Addition and Subtraction of Quadratic Radicals 29. 二次根式的化简 -> Simplification of Quadratic Radicals 30. 二次根式的运算 -> Operations with Quadratic Radicals 31. 一元二次方程的根 -> Roots of a Quadratic Equation in One Variable 32. 解一元二次方程 -> Solving Quadratic Equations in One Variable 33. 一元二次方程的应用 -> Application of Quadratic Equations in One Variable 34. 一元二次不等式的解法 -> Solving Quadratic Inequalities in One Variable 35. 解一元二次不等式 -> Solving Quadratic Inequalities in One Variable (Repeated/Variant) 36. 分式方程的应用 -> Application of Fractional Equations 37. 数据的波动中的极差 -> Range in Data Fluctuation 38. 数据的波动中的方差 -> Variance in Data Fluctuation 39. 频率的求解概率 -> Solving Probability using Frequency 40. 随机事件与概率 -> Random Events and Probability **Data Series Trends & Approximate Values:** * **Trend Verification:** * **DeepSeekMath-7B (Red):** Generally the highest-performing series, with frequent peaks above 70% and several above 80%. It shows high volatility, with sharp drops on some topics (e.g., near 0% on "Chicken and Rabbit" problem). * **ChatGLM3-6B (Orange):** Often the second-highest, closely following the red line. It has the single highest peak on the chart (approx. 90% on "Function and Linear Equation"). It also experiences significant drops. * **Yi-6B (Blue):** Typically performs in the middle range, between 20% and 60%. It has a notable low point (approx. 5%) on "Solving Quadratic Inequalities". * **LLaMA2-7B (Green):** Generally the lowest-performing series, frequently below 40%. It has several very low points (below 10%) on topics like "Congruent Triangles" and "Chicken and Rabbit" problem. * **Sample Data Points (First 10 Topics):** | Topic (English) | Yi-6B (Blue) | ChatGLM3-6B (Orange) | LLaMA2-7B (Green) | DeepSeekMath-7B (Red) | | :--- | :--- | :--- | :--- | :--- | | Congruent Triangles | ~40% | ~50% | ~40% | ~55% | | Isosceles Triangles | ~35% | ~20% | ~25% | ~70% | | Equilateral Triangles | ~35% | ~45% | ~10% | ~65% | | Parallelograms | ~50% | ~60% | ~20% | ~75% | | Inscribed Angle | ~30% | ~55% | ~15% | ~70% | | Central Angle | ~5% | ~0% | ~5% | ~30% | | Arc Length/Sector Area | ~30% | ~30% | ~15% | ~30% | | Point & Circle Relation | ~25% | ~40% | ~20% | ~55% | | Function & Linear Eq. | ~50% | ~90% | ~65% | ~85% | | Function & Linear Ineq. | ~45% | ~55% | ~35% | ~70% | ### Key Observations 1. **High Variability:** Performance for all models is extremely topic-dependent. No model is consistently superior across all mathematical domains. 2. **Model Hierarchy:** A rough performance hierarchy is visible: DeepSeekMath-7B (Red) ≥ ChatGLM3-6B (Orange) > Yi-6B (Blue) > LLaMA2-7B (Green). However, this order flips on specific topics. 3. **Notable Outliers:** * **High Peaks:** ChatGLM3-6B achieves ~90% on "Function and Linear Equation". DeepSeekMath-7B peaks near 85% on several topics. * **Severe Drops:** Multiple models score near 0% on "Chicken and Rabbit in the Same Cage" (Topic 23). LLaMA2-7B scores very low (~5%) on "Congruent Triangles". Yi-6B drops to ~5% on "Solving Quadratic Inequalities". 4. **Topic Difficulty:** Some topics appear universally challenging (e.g., "Chicken and Rabbit", "Central Angle"), where all models score below 40%. Others, like "Function and Linear Equation", see high scores from multiple models. 5. **Specialization:** DeepSeekMath-7B shows particular strength in algebraic and function-related topics (e.g., topics 9-15, 31-35). LLaMA2-7B struggles significantly with geometry topics (e.g., topics 1-8). ### Interpretation This chart provides a granular comparison of mathematical reasoning capabilities across four LLMs. The data suggests that: * **Model Architecture and Training Data Matter:** The superior performance of DeepSeekMath-7B, likely a model fine-tuned for mathematics, indicates that specialized training can yield significant gains in specific domains like math problem-solving. * **Mathematical Reasoning is Not Monolithic:** The extreme volatility in scores shows that "math ability" in AI is not a single skill. Proficiency in algebra does not guarantee proficiency in geometry or word problems. Models have distinct strengths and weaknesses. * **Classic Problems Remain a Challenge:** The near-zero scores on the "Chicken and Rabbit" problem—a classic logic puzzle—highlight a potential weakness in handling certain types of structured, non-computational word problems, even for otherwise strong models. * **Benchmarking Value:** For developers or researchers, this chart is valuable for identifying which model might be best suited for a specific educational application (e.g., a geometry tutor vs. an algebra solver). It also pinpoints specific areas (like "Central Angle" or "Chicken and Rabbit" problems) where all current models need improvement, guiding future research and fine-tuning efforts. In essence, the chart moves beyond a single "accuracy" score to reveal the complex, topic-dependent landscape of AI mathematical reasoning, emphasizing that model selection should be guided by the specific task at hand.

## Line Chart: Model Accuracy Across Tasks ### Overview The image is a line chart comparing the accuracy of four AI models (Yi-6B, ChatGLM3-6B, LLaMA2-7B, DeepSeekMath-7B) across 30+ tasks represented by Chinese characters on the x-axis. The y-axis measures accuracy from 0 to 100. Each model is represented by a distinct color: blue (Yi-6B), orange (ChatGLM3-6B), green (LLaMA2-7B), and red (DeepSeekMath-7B). The chart shows significant variability in performance across tasks, with sharp peaks and troughs for all models. ### Components/Axes - **X-axis**: Labeled with Chinese characters (e.g., "全等三角形", "等腰三角形", "平行四边形", etc.), representing 30+ distinct tasks or categories. - **Y-axis**: Labeled "Accuracy" with a scale from 0 to 100 in increments of 20. - **Legend**: Positioned at the top-right, mapping colors to models: - Blue: Yi-6B - Orange: ChatGLM3-6B - Green: LLaMA2-7B - Red: DeepSeekMath-7B ### Detailed Analysis 1. **Yi-6B (Blue)**: - Stable but lower performance overall, with peaks around 60 and troughs near 20. - Notable spikes in tasks like "等腰三角形" (~70) and "平行四边形" (~50). - Lowest point: ~5 on "等腰三角形". 2. **ChatGLM3-6B (Orange)**: - Highest peak: ~90 on "等腰三角形". - Sharp declines in tasks like "等腰三角形" (~10) and "平行四边形" (~20). - Moderate performance (~40–60) on most tasks. 3. **LLaMA2-7B (Green)**: - Peaks around 70 (e.g., "等腰三角形", "平行四边形"). - Troughs near 10 on tasks like "等腰三角形". - Consistent mid-range performance (~30–50) on most tasks. 4. **DeepSeekMath-7B (Red)**: - Highest peaks: ~80 on "等腰三角形" and "平行四边形". - Sharp declines to ~20 on tasks like "等腰三角形". - Strong performance in math-related tasks (e.g., "等腰三角形" ~70). ### Key Observations - **Task-Specific Performance**: Models excel in specific tasks (e.g., DeepSeekMath-7B in math, ChatGLM3-6B in geometry). - **Volatility**: All models show extreme fluctuations, with some tasks causing accuracy to drop to near 0. - **Stability**: Yi-6B is the most consistent, though with lower overall accuracy. - **Outliers**: ChatGLM3-6B’s ~90 peak on "等腰三角形" and DeepSeekMath-7B’s ~80 on "平行四边形" stand out. ### Interpretation The data suggests that no single model dominates across all tasks. DeepSeekMath-7B and ChatGLM3-6B show task-specific strengths, likely due to specialized training data. Yi-6B’s stability implies robustness but limited specialization. The extreme variability highlights the importance of model selection based on task requirements. Anomalies like ChatGLM3-6B’s near-zero performance on "等腰三角形" suggest potential overfitting or data mismatch for certain tasks.