MinPath: Learning Efficient LLM Reasoning via Minimal Dependency Paths

Large language models increasingly rely on long Chain-of-Thought (CoT) to solve complex reasoning tasks, but the resulting CoT often contains repeated checks, abandoned branches, and unused planning that increase inference cost without supporting the final answer. Existing efficient reasoning methods address this through length budgets, token-level importance, confidence signals, or a stronger teacher model, treating CoT compression mainly as a text-shortening problem rather than as a question of which steps the answer actually depends on. We propose MinPath, a training framework that treats CoT compression as a graph problem. The raw CoT is represented as a Typed Reasoning Graph, where the Minimal Dependency Path supporting the target conclusion is extracted, and the resulting MinPath is used for fine-tuning. Across four reasoning models on GSM8K, MATH-500, and AIME24, MinPath reduces generated tokens by 33.9\% on average with nearly unchanged precision (accuracy even improved in 41.7\% of all experiments) and outperforms five compression baselines in every evaluated setting.