Constraint-Rectified Training for Efficient Chain-of-Thought

TL;DR

This paper introduces CRT, a training framework that enhances the efficiency of Chain-of-Thought reasoning in large language models by reducing redundancy and maintaining accuracy, resulting in more cost-effective and interpretable reasoning processes.

Contribution

CRT provides a stable, interpretable post-training method that effectively balances reasoning length and accuracy, improving efficiency without sacrificing answer quality.

Findings

CRT reduces token usage while maintaining accuracy.

It shortens reasoning traces and reduces internal redundancy.

Enables fine-grained control over explanation length.

Abstract

Chain-of-Thought (CoT) has significantly enhanced the reasoning capabilities of Large Language Models (LLMs), especially when combined with reinforcement learning (RL) based post-training methods. While longer reasoning traces can improve answer quality and unlock abilities such as self-correction, they also incur high inference costs and often introduce redundant steps, known as overthinking. Recent research seeks to develop efficient reasoning strategies that balance reasoning length and accuracy, either through length-aware reward design or prompt-based calibration. However, these heuristic-based approaches may suffer from severe accuracy drop and be very sensitive to hyperparameters. To address these problems, we introduce CRT (Constraint-Rectified Training), a principled post-training framework based on reference-guarded constrained optimization, yielding a more stable and interpretable formulation for efficient reasoning. CRT alternates between minimizing reasoning length and rectifying accuracy only when performance falls below the reference, enabling stable and effective pruning of redundant reasoning. We further extend CRT with a two-stage training scheme that first discovers the shortest reliable reasoning patterns and then refines accuracy under a learnt length budget, preventing the re-emergence of verbose CoT. Our comprehensive evaluation shows that this framework consistently reduces token usage while maintaining answer quality at a robust and reliable level. Further analysis reveals that CRT improves reasoning efficiency not only by shortening responses but also by reducing internal language redundancy, leading to a new evaluation metric. Moreover, CRT-based training naturally yields a sequence of intermediate checkpoints that span a spectrum of explanation lengths while preserving correctness, enabling fine-grained control over reasoning verbosity without retraining.