A MONOTONIC PROGRESS CONSTRAINT FOR LONG-HORIZON REASONING IN LARGE LANGUAGE MODELS.

Large language models frequently lose coherence and accumulate logical errors over extended reasoning sequences. This work introduces a monotonic progress constraint,The method is training-free, model-agnostic, and adds negligible computational overhead. On long-chain deductive tasks in mid-sized models, it achieves up to 13× improvement in stability and coherence compared to standard autoregressive decoding, with near-zero error accumulation over thousands of steps. This simple structural prior provides a practical solution for reliable multi-step reasoning in LLMs.