Title: Shape of Thought: When Distribution Can Matter More than Correctness in Reasoning Tasks
Primary area: foundation or frontier models, including LLMs
Keywords: LLM, Reasoning, Synthetic Data, Chain of Thought

Abstract: We present the surprising finding that a language model's reasoning capabilities can be improved by training on synthetic datasets of chain-of-thought (CoT) traces from more capable models, even when all of those traces lead to an incorrect final answer. Our experiments show this approach can yield better performance on reasoning tasks than training on human-annotated datasets. We hypothesize that two key factors explain this phenomenon: first, the distribution of synthetic data is inherently closer to the language model's own distribution, making it more amenable to learning. Second, these "incorrect" traces are often only partially flawed and contain valid reasoning steps from which the model can learn. To further test the first hypothesis, we use a language model to paraphrase human-annotated traces -- shifting their distribution closer to the model's own distribution -- and show that this improves performance. For the second hypothesis, we introduce increasingly flawed CoT traces and study to what extent models are tolerant to these flaws. We demonstrate our findings across the MATH, GSM8K, and Countdown datasets using various language models ranging from 1.5B to 9B across Qwen, Llama, and Gemma models. Our study shows that curating datasets that are closer to the model's distribution is a critical aspect to consider. We also show that a correct final answer is not always a reliable indicator of a faithful reasoning process.

TL;DR: Training on synthetic CoT traces, even with wrong final answers, improves reasoning due to aligning with the model's distribution and leveraging partial reasoning steps, outperforming human-annotated data.