LSRL: Process-Supervised GRPO on Latent Recurrent States Improves Mathematical Reasoning

AbstractLatent-recurrent language models solve tasks by iteratively refining hidden states rather than emitting chain-of-thought tokens, yet the opacity of those hidden trajectories hinders credit assignment and limits mathematical reasoning accuracy. We propose Latent-State Supervised Reinforcement Learning (LSRL), a process-supervised variant of Guided Reward Policy Optimization (GRPO) that delivers dense rewards at every latent step. We decode each recurrent depth of a 3.5-billion-parameter Huginn model and score the partial solutions with a GPT-4.1-nano grader aligned to final-answer correctness. Using LoRA adapters, we update the policy on a single NVIDIA L40S GPU with only 500 GSM-8K training problems. Relative to the depth-8 supervised Huginn baseline, LSRL improves absolute accuracy by +4.27 points on GSM-8K and +2.06 points on MathQA. These results demonstrate that rewarding latent steps provides an efficient route to stronger mathematical reasoning in latent-recurrent language models.