\n ## Line Chart: Model Accuracy on Math Problems ### Overview This line chart compares the accuracy of four large language models – Baichuan2-13B, LLaMA2-13B, Qwen-14B, and InternLM2-Math-20B – across a series of 31 different math problem types. The y-axis represents accuracy (ranging from 0 to 100), and the x-axis lists the math problem types. Each model's performance is represented by a distinct colored line. ### Components/Axes * **Y-axis Title:** Accuracy * **X-axis Title:** Math Problem Types (listed along the bottom) * **Legend:** Located at the top-left corner, identifying each line with its corresponding model: * Baichuan2-13B (Blue) * LLaMA2-13B (Orange) * Qwen-14B (Green) * InternLM2-Math-20B (Red) * **Math Problem Types (X-axis labels):** 1. Arithmetic & subtract 2. Complete similarity 3. Counting principles 4. Combining like terms 5. Distance between two points 6. Domain & range of functions 7. Estimates & rounding 8. Exponents & radicals 9. Fractions & percentages 10. Interpreting graphs 11. Linear equations 12. Make predictions 13. One-variable equations 14. One-variable inequalities 15. Perimeter & area 16. Probability of composite events 17. Probability of simple events 18. Proportional relationships 19. Rational & irrational numbers 20. Square roots & cube roots 21. Systems of equations 22. Two-variable equations 23. Two-variable inequalities 24. Absolute value 25. Center & variable 26. Mean, median, opposite 27. Polynomials 28. Polygon angles 29. Transform equations 30. Variable expressions 31. Volume ### Detailed Analysis Here's a breakdown of each model's performance, noting trends and approximate accuracy values. Accuracy values are approximate due to the chart's resolution. * **Baichuan2-13B (Blue):** The line fluctuates significantly. Starts around 60, dips to ~30, rises to ~95, then declines to ~40. Notable peaks around problem types 10, 16, and 27. Generally performs well on problems 10-17, but struggles with problems 1-9 and 28-31. * **LLaMA2-13B (Orange):** Shows a generally increasing trend initially, peaking around 85-90 for problems 10-16. Then declines, with significant dips around problems 21, 24, and 31, falling to around 20-30. Starts around 65, peaks around 88, and ends around 30. * **Qwen-14B (Green):** The most volatile line, with large swings in accuracy. Starts around 60, drops to near 0 for problem type 6, then rises to over 95 for problem type 10. Continues to fluctuate wildly, ending around 50. Demonstrates high accuracy on problems 10-12, but very low accuracy on problems 6, 20, and 26. * **InternLM2-Math-20B (Red):** The most consistently high-performing model. Starts around 70, rises to a peak of approximately 98 around problem type 10, and remains relatively high (between 60 and 90) throughout the chart. Experiences a dip around problem type 26, falling to ~50, but recovers quickly. **Specific Data Points (Approximate):** | Problem Type | Baichuan2-13B | LLaMA2-13B | Qwen-14B | InternLM2-Math-20B | |---|---|---|---|---| | 1 | 60 | 65 | 60 | 70 | | 6 | 40 | 50 | 0 | 60 | | 10 | 95 | 88 | 98 | 98 | | 16 | 85 | 90 | 95 | 90 | | 21 | 50 | 25 | 60 | 75 | | 26 | 40 | 60 | 0 | 50 | | 31 | 30 | 30 | 50 | 70 | ### Key Observations * InternLM2-Math-20B consistently outperforms the other models across most problem types. * Qwen-14B exhibits the highest variability in accuracy, suggesting it may be more sensitive to the specific problem type. * LLaMA2-13B shows a clear upward trend initially, followed by a decline, indicating it may struggle with more complex problems. * Baichuan2-13B's performance is moderate and fluctuates considerably. * Problem types 10-16 generally yield higher accuracy scores for all models. * Problem types 6, 20, 26, and 31 consistently result in lower accuracy scores. ### Interpretation The data suggests that InternLM2-Math-20B is the most robust and accurate model for solving a diverse range of math problems. The significant differences in performance across problem types highlight the challenges in developing general-purpose math solvers. The volatility observed in Qwen-14B's performance could be due to its training data or architecture, making it more prone to errors on certain types of problems. The initial success of LLaMA2-13B followed by a decline suggests a potential limitation in its ability to generalize to more complex mathematical concepts. The consistent performance of InternLM2-Math-20B likely stems from its specialized training on mathematical data. The lower accuracy on problem types 6, 20, 26, and 31 could indicate these areas require further research and development in language model-based math solving. The chart provides valuable insights into the strengths and weaknesses of each model, guiding future research efforts towards improving their mathematical reasoning capabilities.