\n ## Bar Chart: Accuracy on MATH-500 ### Overview This bar chart displays the accuracy of several language models on the MATH-500 dataset, broken down by the number of characters in the input. The x-axis represents the different models, and the y-axis represents the accuracy percentage. Each model has a set of bars, one for each character length. ### Components/Axes * **Title:** Accuracy on MATH-500 (positioned at the top-center) * **X-axis Label:** Model Name (bottom-center) * Models: Qwen-2.5-MATH-7B, GPT-4o-mini, Qwen-2.5-MATH-1.5B, DS-R1-Distill-Qwen-7B, DS-math-7b-instruct * **Y-axis Label:** Accuracy (left-center) * Scale: 30 to 75, with increments of 10. * **Legend:** (top-right) * 0 characters (Red) * 10 characters (Brown) * 25 characters (Yellow) * 40 characters (Light Blue) * 55 characters (Blue) * 70 characters (Dark Blue) ### Detailed Analysis The chart consists of five groups of bars, one for each model. Within each group, there are six bars representing the accuracy for different character lengths. **Qwen-2.5-MATH-7B:** * 0 characters: Approximately 73% accuracy. * 10 characters: Approximately 74% accuracy. * 25 characters: Approximately 74.5% accuracy. * 40 characters: Approximately 74% accuracy. * 55 characters: Approximately 73% accuracy. * 70 characters: Approximately 72% accuracy. *Trend: Relatively stable accuracy across character lengths, with a slight peak at 25 characters.* **GPT-4o-mini:** * 0 characters: Approximately 72% accuracy. * 10 characters: Approximately 73% accuracy. * 25 characters: Approximately 73.5% accuracy. * 40 characters: Approximately 73% accuracy. * 55 characters: Approximately 71% accuracy. * 70 characters: Approximately 68% accuracy. *Trend: Accuracy generally decreases with increasing character length.* **Qwen-2.5-MATH-1.5B:** * 0 characters: Approximately 65% accuracy. * 10 characters: Approximately 66% accuracy. * 25 characters: Approximately 67% accuracy. * 40 characters: Approximately 67% accuracy. * 55 characters: Approximately 65% accuracy. * 70 characters: Approximately 64% accuracy. *Trend: Relatively stable accuracy across character lengths.* **DS-R1-Distill-Qwen-7B:** * 0 characters: Approximately 55% accuracy. * 10 characters: Approximately 56% accuracy. * 25 characters: Approximately 56% accuracy. * 40 characters: Approximately 55% accuracy. * 55 characters: Approximately 53% accuracy. * 70 characters: Approximately 52% accuracy. *Trend: Accuracy decreases with increasing character length.* **DS-math-7b-instruct:** * 0 characters: Approximately 40% accuracy. * 10 characters: Approximately 40% accuracy. * 25 characters: Approximately 41% accuracy. * 40 characters: Approximately 41% accuracy. * 55 characters: Approximately 40% accuracy. * 70 characters: Approximately 40% accuracy. *Trend: Relatively stable accuracy across character lengths.* ### Key Observations * Qwen-2.5-MATH-7B and GPT-4o-mini consistently achieve the highest accuracy scores across most character lengths. * The accuracy of GPT-4o-mini decreases noticeably as the character length increases. * DS-math-7b-instruct consistently has the lowest accuracy scores. * The impact of character length on accuracy varies between models. Some models are relatively unaffected, while others show a clear decline in performance with longer inputs. ### Interpretation The chart demonstrates the performance of different language models on a mathematical reasoning task (MATH-500) as a function of input length. The varying performance suggests that the models have different capacities for handling longer and more complex inputs. The decrease in accuracy for GPT-4o-mini with increasing character length could indicate a limitation in its context window or its ability to process longer sequences effectively. The consistently lower performance of DS-math-7b-instruct suggests that it may be less capable in mathematical reasoning compared to the other models tested. The relatively stable performance of Qwen-2.5-MATH-7B across different character lengths suggests a robust ability to handle varying input complexities. This data is valuable for understanding the strengths and weaknesses of each model and for selecting the most appropriate model for a given task based on the expected input length and complexity.