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This paper introduces an uncertainty-guided progressive contraction framework to compress reasoning supervision for large language models, addressing the diminishing returns of scaling post-training corpora. By constructing Monte Carlo reasoning trees to expose process-level uncertainty and progressively contracting both supervision and optimization based on teacher-informed pools and learner states, the method significantly reduces training budgets. Experiments demonstrate that this approach achieves substantial reductions in training exposure (over 450x less) while maintaining or improving reasoning performance across diverse benchmarks and LLM families.
Reasoning supervision can be compressed over 450x with uncertainty-guided contraction, boosting LLM efficiency without sacrificing capability.
Large language models have achieved remarkable advances in complex reasoning. However, scaling reasoning post-training with ever-larger corpora can substantially increase training cost without proportional performance gains. In this study, we therefore ask: how far can reasoning supervision be compressed without sacrificing capability? To this end, we propose an uncertainty-guided progressive contraction framework that concentrates supervision and optimization on the reasoning trajectories most valuable for learning. Specifically, rather than treating a teacher-generated chain-of-thought (CoT) as a single realized path, we construct uncertainty-profiled reasoning supervision by building Monte Carlo reasoning trees around intermediate reasoning states to expose process-level uncertainty. This uncertainty first contracts the original corpus into a compact teacher-informed pool. A second, learner-aware contraction then performs online routing during SFT, concentrating optimization according to the student's evolving learning state. Together, the two stages progressively contract both supervision and optimization, substantially reducing the student training budget. Experiments across diverse reasoning benchmarks and LLM families show that our method uses as little as 0.22% of the optimization budget of full-data SFT, over 450x less training exposure, while maintaining or improving reasoning performance. Notably, our framework generalizes well across heterogeneous student families, black-box teachers, and weak-to-strong transfer. This indicates that it is not only a way to accelerate training but can also enhance reasoning capability.
