Current Large Language Model (LLM) agents struggle with long-horizon reasoning tasks, such as competition-level mathematics, where sustaining precision over hundreds of steps is critical. A primary bottleneck is the reliance on natural language context or summaries to track progress; these linguistic representations are inherently "lossy," introducing semantic drift and accumulating errors that derail the reasoning chain. To address this, we propose Structured Strategy Folding (SSF), a novel paradigm that shifts the agent’s memory mechanism from linguistic description to computational verification. Instead of compressing history into text, SSF "folds" the reasoning trajectory into a sequence of Executable Symbolic States (ESS). Each ESS serves as a verifiable anchor—comprising either executed code artifacts or formally judged symbolic lemmas—generated through a dual-pathway validation mechanism. By interacting with these rigorous state artifacts rather than raw textual history, the agent effectively eliminates ambiguity and prevents error propagation. Experiments on challenging mathematical benchmarks demonstrate that SSF significantly outperforms standard Chain-of-Thought and existing summarization baselines, achieving substantial accuracy improvements while maintaining robust performance over extended reasoning horizons.

Large Language Models (LLMs) as agents often fail to improve in new environments. We identify and characterize a failure mode we call exploration collapse: under reinforcement learning (RL) in environments whose states are unfamiliar to the policy, Pass@k, the probability that at least one of k sampled trajectories succeeds, drops markedly over training even as Pass@1 edges up, revealing increasingly brittle exploration; environments closer to the pretraining distribution show no such decline. We trace this collapse to weak grounding in environment states and dynamics, and study a simple remedy: explicitly teaching the agent to estimate the current state and predict its transitions before optimizing for reward. We instantiate it as SPA, an explore-then-exploit recipe that cold-starts the policy with a Self-Experience supervised finetuning (SFT) stage, collecting the model’s own interaction trajectories and supervising state and next-state prediction, and then runs standard RL. The resulting world model serves as a grounded initialization for RL rather than an inference-time planner. Across unseen environments, SPA consistently and substantially improves over vanilla RL: for example, it raises the Sokoban success rate from 25.6% to 59.8% on Qwen2.5-1.5B-Instruct, letting sub-3B models surpass a 20B baseline on these tasks. Controlled studies indicate that the gains track four factors: grounded state representations, explicit transition modeling, self-experience trajectories from a sufficiently strong exploration policy, and adequate coverage of transition data.

Reward models (RMs) play a central role throughout the language model (LM) pipeline, particularly in non-verifiable domains. However, the dominant LLM-as-a-Judge paradigm relies on the strong reasoning capabilities of large models, while alternative approaches require reference responses or explicit rubrics, limiting flexibility and broader accessibility. In this work, we propose FLIP (FLipped Inference for Prompt reconstruction), a reference-free and rubric-free reward modeling approach that reformulates reward modeling through backward inference: inferring the instruction that would most plausibly produce a given response. The similarity between the inferred and the original instructions is then used as the reward signal. Evaluations across four domains using 13 small language models show that FLIP outperforms LLM-as-a-Judge baselines by an average of 79.6%. Moreover, FLIP substantially improves downstream performance in extrinsic evaluations under test-time scaling via parallel sampling and GRPO training. We further find that FLIP is particularly effective for longer outputs and robust to common forms of reward hacking. By explicitly exploiting the validation–generation gap, FLIP enables reliable reward modeling in downscaled regimes where judgment methods fail.

LLM training increasingly relies on teacher-generated supervision, from synthetic responses to reasoning traces and tool-use demonstrations. Current practice often chooses the highest-performing teacher to generate student training data, implicitly treating teacher test performance as a proxy for teaching quality. We show that this assumption can fail: even when multiple teachers provide correct answers to the same question, the answer from the strongest teacher is not necessarily the best supervision for a given student. To address this gap, we propose Student-Centric Answer Sampling (SCAS), a framework that selects from verified teacher-generated answers according to their estimated student-centric learning cost. Motivated by a token-wise gradient decomposition, we derive an efficient forward-only proxy for this cost and use it to guide answer selection during training. Experiments across 30 teacher models, 6 student base models, and 8 tasks show that SCAS consistently improves student performance, suggesting that effective distillation should prioritize supervision matched to the current student rather than teacher strength alone.

Large language models (LLMs) have demonstrated impressive performance on reasoning-intensive tasks, but enhancing their reasoning abilities typically relies on either reinforcement learning (RL) with verifiable signals or supervised fine-tuning (SFT) with high-quality long chain-of-thought (CoT) demonstrations, both of which are expensive. In this paper, we study a novel problem of incentivizing the reasoning capacity of LLMs without expensive high-quality demonstrations and reinforcement learning. We investigate whether the reasoning capabilities of LLMs can be effectively incentivized via supervision from significantly weaker models. We further analyze when and why such weak supervision succeeds in eliciting reasoning abilities in stronger models. Our findings show that supervision from significantly weaker reasoners can substantially improve student reasoning performance, recovering close to 94% of the gains of expensive RL at a fraction of the cost. Experiments across diverse benchmarks and model architectures demonstrate that weak reasoners can effectively incentivize reasoning in stronger student models, consistently improving performance across a wide range of reasoning tasks. Our results suggest that this simple weak-to-strong paradigm is a promising and generalizable alternative to costly methods for incentivizing strong reasoning capabilities at inference-time in LLMs. Code is at https://github.com/W2SR-ARR/Code.

We study the post-training of large language models (LLMs) with human preference data. Recently, direct preference optimization and its variants have shown considerable promise in aligning language models, eliminating the need for reward models and online sampling. Despite these benefits, these methods rely on explicit assumptions about the Bradley-Terry (BT) model, which makes them prone to overfitting and results in suboptimal performance, particularly on reasoning-heavy tasks. To address these challenges, we propose a principled preference fine-tuning algorithm called InfoPO, which effectively and efficiently aligns large language models using preference data. InfoPO eliminates the reliance on the BT model and prevents the likelihood of the chosen response from decreasing. Extensive experiments confirm that InfoPO consistently outperforms established baselines on widely used open benchmarks, particularly in reasoning tasks.

Large Language Models (LLMs) require alignment via reinforcement learning (RL) to effectively perform task-specific objectives, such as human preference alignment and enhanced reasoning. While Proximal Policy Optimization (PPO) is widely adopted, its computational overhead, stemming from additional value model requirements, limits applicability. Existing alternatives, like Group Relative Policy Optimization (GRPO), mitigate computational costs but remain sensitive to reward model quality. To address this, we introduce Group Preference Reward Shaping (GPRS), a novel method that leverages preference-based comparisons rather than precise numerical rewards. GPRS requires no extra model components and remains robust across varying reward model sizes and qualities. Extensive experiments demonstrate that GPRS consistently outperforms existing critic-model-free RL algorithms in Reinforcement Learning from Human Feedback (RLHF) and reasoning tasks, providing stable and good alignment performance.

Traditional scaling laws in natural language processing suggest that increasing model size and training data enhances performance. However, recent studies reveal deviations, particularly in large language models, where performance improvements decelerate—a phenomenon known as sub-scaling. This paper revisits these scaling laws by examining the impact of data quality and training strategies on model performance. Through extensive empirical analysis of over 400 models, we identify high data density and non-optimal resource allocation as key factors contributing to sub-scaling. High data density leads to diminishing returns due to redundant information, while optimal resource allocation is crucial for sustained performance improvements. We propose a sub-optimal scaling law that better predicts performance in sub-scaling regimes, highlighting the importance of data quality and diversity.

This paper introduces a novel generalized self-imitation learning GSIL framework, which effectively and efficiently aligns large language models with offline demonstration data. We develop GSIL by deriving a surrogate objective of imitation learning with density ratio estimates, facilitating the use of self-generated data and optimizing the imitation learning objective with simple classification losses. GSIL eliminates the need for complex adversarial training in standard imitation learning, achieving lightweight and efficient fine-tuning for large language models. In addition, GSIL encompasses a family of offline losses parameterized by a general class of convex functions for density ratio estimation and enables a unified view for alignment with demonstration data. Extensive experiments show that GSIL consistently and significantly outperforms baselines in many challenging benchmarks, such as coding (HuamnEval), mathematical reasoning (GSM8K) and instruction-following benchmark (MT-Bench). Code is public available at https://github.com/tengxiao1/GSIL.