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Facts Don't Speak Louder than Words: The Behavioral Essence of Long-CoT Distillation

NeurIPS 2026 · Large language models › Reasoning and chain of thought · approach: Chain-of-thought training and analysis

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Shows that Long-CoT distillation works nearly as well on incorrect reasoning traces and restricted prompt sets, proposes a Behavioral Hypothesis, and finds cross-entropy beats plain-p loss on complex CoTs.

Problem

Long-CoT distillation relies on rejection sampling for correct traces over diverse prompts, but the mechanism behind its gains is poorly understood.

Approach

Fine-tuning on incorrect reasoning traces, or on a small restricted or already-solved prompt set, gives nearly the same gains as correct diverse data, supporting a Behavioral Hypothesis that distillation mainly teaches reasoning behaviors rather than facts; the best SFT loss depends on CoT complexity (-p for simple, -log p for complex).

Key results

• Negative-trajectory SFT reaches 97.7% of the absolute math accuracy of positive-trajectory SFT (Accneg/Accpos) and keeps 94.7% of the relative gain.
• On the Complex CoT tier, -p loss drops Qwen2.5-7B average accuracy to 17.0 vs 46.4 for -log p, while on Simple CoT -p leads (37.4 vs 22.8 on Qwen3-4B-Base).
• Training on 500 unique prompts sampled 128 times each matches the accuracy of 16K prompts sampled 4 times each under a fixed trajectory budget.

Surprising findings

• Training only on incorrect trajectories yields nearly the same math gains as correct ones, and models still improve on training prompts despite flawed facts.
• Plain -p loss, which is claimed superior in prior work, collapses on complex long CoTs, with -p-trained models generating over 20K tokens on average.

Limitations

• Experiments are limited to small-to-medium models (1.7B-14B) and do not test frontier-scale models or teachers.
• Incorrect trajectories are filtered only by final-answer exact match, so they are mostly near-correct and do not represent a full taxonomy of error types.
• Evaluated mainly on math with a limited set of non-math benchmarks.

Experimental setup

Datasets: DAPO-Math-17K NuminaMath-CoT GURU (science QA subset)

Benchmarks: AIME 2024 AMC23 Minerva Math OlympiadBench MATH GPQA-Diamond MMLU-Pro LiveCodeBench-v2 AIME 2026 LiveCodeBench-v6 SuperGLUE

Metrics: avg@16 accuracy pass@16 average response token length linear CKA

Baselines: SFT on correct trajectories (-log p) SFT on correct trajectories (-p) base models

Builds on: rejection sampling plain-p probability loss (Wu et al.)

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• SCOUT: Teaching Pre-trained Language Models to Enhance Reasoning via Flow Chain-of-Thought (NeurIPS 2025 · similarity 0.93)
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