Stepwise Intrinsic Rewards for Reasoning in Large Language Models

Abstract

Reinforcement learning (RL) has become a widely used paradigm for improving the reasoning abilities of large language models (LLMs) and Vision-language models (VLMs). Sparse binary outcome rewards, however, score only final correctness and cannot identify which intermediate steps contributed to it; in multimodal tasks, they may also reward answers driven by linguistic priors rather than visual evidence. Process reward models (PRMs) densify supervision but usually require process annotations, auxiliary models, or inference-time search. In this paper, we introduce Stepwise Marginal Information Gain (MIG), an intrinsic process reward computed from the policy itself. MIG measures how each structured reasoning prefix changes the length-normalized, teacher-forced log-likelihood of the reference answer. A monotonic historical watermark rewards only new likelihood maxima, avoiding duplicate credit after sub-record detours. We combine this signal with outcome and format rewards and a gated self-distillation objective that retains only structurally valid and correct trajectories. For VLMs, a real-versus-blank likelihood gate down-weights rewards when answers remain predictable without the image. Across eight task-specific benchmarks, the full method exceeds outcome-only GRPO in every single-run comparison. In broad-data transfer, it improves average accuracy by up to 4.8 points over binary-reward training and gains 12.6 points on MathVerse. At 7B, it exceeds an external PRM-BoN@16 baseline by 12.9 points on vision-language transfer without inference-time reranking. These results support policy-derived stepwise credit as an annotation-free alternative to explicit process reward modeling.