Shape of Thought: When Distribution Matters More than Correctness in Reasoning Tasks

TL;DR

Training language models on synthetic, distribution-matched chain-of-thought traces—even if incorrect—can enhance reasoning performance more effectively than using human-annotated data, due to better alignment with the model's own distribution.

Contribution

This paper demonstrates that synthetic, distribution-matched reasoning traces improve model reasoning more than human data, highlighting the importance of data distribution in training.

Findings

Synthetic data closer to model distribution enhances reasoning.

Partially flawed reasoning traces still provide valuable learning signals.

Distribution alignment improves performance across multiple reasoning tasks.

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 various reasoning domains like math, algorithmic reasoning and code generation using MATH, GSM8K, Countdown and MBPP datasets on 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.