shape-of-thought

name	shape-of-thought
title	Shape of Thought: When Distribution Matters More Than Correctness
version	0.0.2
engine	skillxiv-v0.0.2-claude-opus-4.6
license	MIT
url	https://arxiv.org/abs/2512.22255
keywords	["training-data","reasoning","distribution-alignment","synthetic-data"]
description	Demonstrate that synthetic CoT traces with incorrect final answers outperform human-written correct solutions for supervised fine-tuning. Distribution proximity between training data and student model's natural output matters more than correctness—validating human traces with model-like distributions improves performance, providing practical guidance for dataset curation.

Overview

Challenges conventional wisdom that training data quality depends primarily on correctness.

Core Technique

Distribution Proximity Hypothesis:

# Human traces (H): correct but distribution-mismatched
# Model traces correct (G): correct and distribution-matched
# Model traces incorrect (W): incorrect but distribution-matched

# W outperforms H despite incorrectness
# because distribution proximity enables faster learning

When to Use

Use when: Curating reasoning datasets, SFT training, synthetic data selection.

References

• Distribution alignment vs correctness
• Partial correctness in synthetic data
• Dataset curation guidance