[2603.19987] Breaking the Capability Ceiling of LLM Post-Training by Reintroducing Markov States

Computer Science > Machine Learning arXiv:2603.19987 (cs) [Submitted on 20 Mar 2026] Title:Breaking the Capability Ceiling of LLM Post-Training by Reintroducing Markov States Authors:Yurun Yuan, Tengyang Xie View a PDF of the paper titled Breaking the Capability Ceiling of LLM Post-Training by Reintroducing Markov States, by Yurun Yuan and 1 other authors View PDF HTML (experimental) Abstract:Reinforcement learning (RL) has become a standard paradigm for post-training and aligning Large Language Models (LLMs), yet recent evidence suggests it faces a persistent "capability ceiling": unlike classical RL systems that discover novel strategies, RL for LLMs often acts as a mere refiner of patterns already latent in pre-trained weights. In this work, we identify a fundamental structural bottleneck: while classical RL relies on compact, informative Markov states, current LLM post-training formulations are tethered to an ever-expanding history of actions. We revisit a classical principle long central to RL yet absent from LLM post-training: explicit Markov states. Theoretically, we provide rigorous guarantees demonstrating that leveraging estimated Markov states can significantly reduce sample complexity. Empirically, we show that introducing Markov states consistently breaks the performance boundaries of standard RL post-training across a suite of complex logic puzzles. Our findings suggest that moving beyond "history-as-state" modeling in favor of structured Markovian representa...