## Line Chart: AIME-24 Accuracy vs Normalized (binned) Length of Thoughts ### Overview The image is a line chart showing the relationship between AIME-24 accuracy (in percentage) and the normalized (binned) length of thoughts, measured by the number of tokens. The x-axis represents the normalized number of tokens, ranging from 0.0 to 1.0. The y-axis represents the accuracy percentage, ranging from 40% to 54%. The chart displays a single data series, showing how accuracy changes with the length of thoughts. The background is shaded with a light blue gradient. ### Components/Axes * **Title:** AIME-24 Accuracy vs Normalized (binned) Length of Thoughts * **X-axis:** * Label: Normalized (0-1) Number of Tokens * Scale: 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 * **Y-axis:** * Label: Accuracy (%) * Scale: 40, 42, 44, 46, 48, 50, 52, 54 * **Data Series:** A single line in teal color. ### Detailed Analysis The teal line represents the AIME-24 accuracy at different normalized lengths of thoughts. * **Trend:** The line initially shows a slight increase in accuracy from 0.0 to 0.2, then a significant increase from 0.2 to 0.4, followed by a decrease from 0.4 to 0.8. * **Data Points:** * At 0.0 normalized tokens, the accuracy is approximately 51.4%. * At 0.2 normalized tokens, the accuracy is approximately 51.2%. * At 0.4 normalized tokens, the accuracy peaks at approximately 54.8%. * At 0.6 normalized tokens, the accuracy is approximately 52.5%. * At 0.8 normalized tokens, the accuracy drops to approximately 39.3%. ### Key Observations * The highest accuracy is achieved when the normalized length of thoughts is around 0.4. * Accuracy decreases significantly as the normalized length of thoughts increases from 0.4 to 0.8. * The accuracy is relatively stable between 0.0 and 0.2 normalized tokens. ### Interpretation The chart suggests that there is an optimal length of "thought" (as measured by normalized token count) for maximizing AIME-24 accuracy. Shorter lengths (0.0-0.2) yield moderate accuracy, while lengths around 0.4 yield the highest accuracy. However, longer lengths (0.6-0.8) lead to a substantial drop in accuracy. This could indicate that overly verbose or complex "thoughts" are detrimental to the model's performance. The "binned" nature of the x-axis suggests that the token counts have been grouped into ranges, which could smooth out some of the finer variations in the data.