## Line Chart: Model Accuracy on Math Problems ### Overview The image is a line chart comparing the accuracy of four different language models (Baichuan2-13B, LLaMA2-13B, Qwen-14B, and InternLM2-Math-20B) on a variety of mathematical problem types. The x-axis represents the problem types, and the y-axis represents the accuracy score. ### Components/Axes * **Title:** (None visible) * **X-axis:** Mathematical problem types (listed below in "Content Details") * **Y-axis:** Accuracy, ranging from 0 to 100, with gridlines at intervals of 20. * **Legend:** Located at the top of the chart. * Blue: Baichuan2-13B * Orange: LLaMA2-13B * Green: Qwen-14B * Red: InternLM2-Math-20B ### Content Details **X-Axis Categories (Problem Types):** 1. Add & subtract 2. Arithmetic sequences 3. Congruence & similarity 4. Consumer math 5. Counting principle 6. Distance between two points 7. Domain & range of functions 8. Equivalent expressions 9. Estimate metric measurements 10. Exponents & scientific notation 11. Financial literacy 12. Fractions & decimals 13. Geometric sequences 14. Interpret functions 15. Linear equations 16. Linear functions 17. Make predictions 18. Multiply 19. Nonlinear functions 20. One-variable statistics 21. Percents 22. Perimeter & area 23. Prime factorization 24. Prime or composite 25. Probability of compound events 26. Probability of simple & opposite events 27. Proportional relationships 28. Quadrants 29. Rational & irrational numbers 30. Scale drawings 31. Square roots & cube roots 32. Surface area & volume 33. Systems of equations 34. Triangle 35. Two-variable statistics 36. Absolute value 37. Axes 38. Center & variability 39. Factors 40. Independent & dependent events 41. Mean, median, mode & range 42. Opposite integers 43. Outlier 44. Polygons 45. Polyhedra 46. Radical exprs 47. Square 48. Transformations 49. Trapezoids 50. Variable exprs **Data Series Trends and Approximate Values:** * **Baichuan2-13B (Blue):** The line fluctuates, generally staying between 60 and 80 accuracy, with a peak near 100 around problem 47 (Square). * Problem 1 (Add & subtract): ~70 * Problem 10 (Exponents & scientific notation): ~72 * Problem 20 (One-variable statistics): ~75 * Problem 30 (Scale drawings): ~80 * Problem 40 (Independent & dependent events): ~60 * Problem 47 (Square): ~98 * Problem 50 (Variable exprs): ~78 * **LLaMA2-13B (Orange):** The line fluctuates significantly, with lows around 20 and highs near 90. * Problem 1 (Add & subtract): ~60 * Problem 10 (Exponents & scientific notation): ~65 * Problem 20 (One-variable statistics): ~70 * Problem 30 (Scale drawings): ~50 * Problem 40 (Independent & dependent events): ~40 * Problem 47 (Square): ~50 * Problem 50 (Variable exprs): ~68 * **Qwen-14B (Green):** The line generally stays between 20 and 60 accuracy, with some peaks and valleys. * Problem 1 (Add & subtract): ~58 * Problem 10 (Exponents & scientific notation): ~42 * Problem 20 (One-variable statistics): ~48 * Problem 30 (Scale drawings): ~40 * Problem 40 (Independent & dependent events): ~35 * Problem 47 (Square): ~70 * Problem 50 (Variable exprs): ~40 * **InternLM2-Math-20B (Red):** The line fluctuates significantly, with lows around 20 and highs near 100. * Problem 1 (Add & subtract): ~70 * Problem 10 (Exponents & scientific notation): ~75 * Problem 20 (One-variable statistics): ~70 * Problem 30 (Scale drawings): ~80 * Problem 40 (Independent & dependent events): ~50 * Problem 47 (Square): ~80 * Problem 50 (Variable exprs): ~68 ### Key Observations * InternLM2-Math-20B and Baichuan2-13B generally perform better than LLaMA2-13B and Qwen-14B across most problem types. * All models show significant variation in accuracy depending on the problem type. * There are specific problem types where certain models excel or struggle. For example, Qwen-14B has particularly low accuracy on some problem types. * Baichuan2-13B has a peak accuracy on "Square" problems. ### Interpretation The chart illustrates the varying strengths and weaknesses of different language models when applied to mathematical problem-solving. The performance differences highlight the impact of model architecture, training data, and fine-tuning strategies on mathematical reasoning capabilities. The significant fluctuations in accuracy across different problem types suggest that each model has specific areas of expertise and difficulty. The data suggests that no single model consistently outperforms the others across all mathematical domains, indicating the need for specialized models or ensemble approaches for comprehensive mathematical problem-solving. The "Square" problem type being a high point for Baichuan2-13B could indicate a specific emphasis or strength in that area during training.