Best-of-N is a widely used inference strategy for complex reasoning, whose effectiveness depends on whether sampled candidates can cover diverse and high-quality reasoning paths. However, post-trained reasoning models often suffer from \emph{exploration collapse}, where independent rollouts repeatedly follow similar reasoning paths and limit the gains from increasing the rollout budget. Existing methods alleviate this issue by promoting broader exploration, but do not explicitly guide exploration toward continuations that make meaningful progress, resulting in limited exploration efficiency. To address this, we propose \emph{\underline{S}tate-conditioned \underline{P}rogress-guided \underline{S}teering} (SPS), a training-free latent steering framework. Specifically, SPS constructs a state-conditioned Direction Bank containing multiple progress-guided steering vectors for different prefix-state regions. During online inference, SPS retrieves a suitable steering vector based on the current prefix state and applies it at high-uncertainty transitions to guide the next reasoning step toward meaningful progress. Extensive experiments across multiple model scales and benchmarks demonstrate that SPS consistently outperforms strong baselines. Further analyses validate the effectiveness of its key designs and offer valuable insights for future research. The code is available at https://github.com/rattlesnakey/SPS.
Reinforcement learning (RL) has emerged as a promising paradigm for training reasoning-oriented models by leveraging rule-based reward signals. However, RL training typically tends to improve single-sample success rates (i.e., Pass@1) while offering limited exploration of diverse reasoning trajectories, which is crucial for multi-sample performance (i.e., Pass@k). Our preliminary analysis reveals that this limitation stems from a fundamental squeezing effect, whereby probability mass is excessively concentrated on a narrow subset of high-reward trajectories, restricting genuine exploration and constraining attainable performance under RL training. To address this issue, in this work, we propose Steering Probability Squeezing (SPS), a training paradigm that interleaves conventional RL with inverse reinforcement learning (IRL). SPS treats on-policy rollouts as demonstrations and employs IRL to explicitly reshape the induced trajectory distribution, thereby enhancing exploration without introducing external supervision. Experiments on five commonly used reasoning benchmarks demonstrate that SPS can enable better exploration and improve Pass@k. Beyond algorithmic contributions, we provide an analysis of RL learning dynamics and identify an empirical upper bound on Pass@k, shedding light on intrinsic exploration limits in RL-based reasoning models. Our findings suggest that alternating between RL and IRL offers an effective pathway toward extending the exploration capacity of reasoning-oriented large language models.
Strong reasoning depends not only on model knowledge but also on how effectively cognitive behaviors are deployed during generation. Existing methods often rely on explicit behavior-level control, making them insufficiently adaptive when failures and required corrections vary across reasoning states, tasks, and models. To this end, we propose Latent Reward Steering (LRS), an adaptive inference-time framework that promotes cognitive behaviors by optimizing the sparse-autoencoder (SAE) latent states that implicitly carry them. Rather than relying on predefined cognitive behaviors or steering directions derived from them, LRS trains a latent reward model on reasoning traces by final answer correctness to estimate the quality of intermediate latent states. During inference, reward gradients provide state-specific correction directions for fragile latent states, while a reward and confidence gate restricts intervention to states the reward signal flags as fragile. Experiments on multiple reasoning LLM backbones and benchmarks show that \ours consistently improves performance over various baselines, and post-hoc analyses further indicate that \ours implicitly promotes good cognitive behaviors that fix the original reasoning errors. Code is available at: https://github.com/jiakanglee/Latent-Reward-Steering.
Large language models show strong reasoning ability, but their internal reasoning process can remain unstable in complex multi-step settings, where early hidden-state errors may propagate to incorrect predictions. We propose ReLAR, a reinforcement-guided latent refinement framework that iteratively updates hidden representations before decoding. ReLAR maintains a compact latent reasoning state and uses learned depth and action controllers to adaptively determine both the number and direction of refinement steps. The controllers are trained with a policy gradient objective based on step-wise likelihood improvement, enabling efficient input-dependent reasoning without explicit chain-of-thought generation. Experiments on medical, mathematical, multi-hop reasoning, and open-ended generation benchmarks show that ReLAR improves accuracy, generation quality, and reasoning stability with substantially lower inference overhead than explicit reasoning baselines.