RL for Language Models

In this work, we reveal that Large Language Models (LLMs) possess intrinsic behavioral plasticity-akin to chameleons adapting their coloration to environmental cues-that can be exposed through token-conditional generation and stabilized via reinforcement learning. Specifically, by conditioning generation on carefully selected token prefixes sampled from responses exhibiting desired behaviors, LLMs seamlessly adapt their behavioral modes at inference time (e.g., switching from step-by-step reasoning to direct answering) without retraining. Based on this insight, we propose Token-Conditioned Reinforcement Learning (ToCoRL), a principled framework that leverages RL to internalize this chameleon-like plasticity, transforming transient inference-time adaptations into stable and learnable behavioral patterns. ToCoRL guides exploration with token-conditional generation and keep enhancing exploitation, enabling emergence of appropriate behaviors. Extensive experiments show that ToCoRL enables precise behavioral control without capability degradation. Notably, we show that large reasoning models, while performing strongly on complex mathematics, can be effectively adapted to excel at factual question answering, which was a capability previously hindered by their step-by-step reasoning patterns.

Large language models are increasingly trained as heterogeneous systems spanning multiple domains, expert partitions, and agentic pipelines, yet prevalent proximal objectives operate at a single scale and lack a principled mechanism for coupling token-level, trajectory-level, and higher-level hierarchical stability control. To bridge this gap, we derive the Aggregational Policy Censoring Objective (APC-Obj), the first exact unconstrained reformulation of sample-based TV-TRPO, establishing that clipping-based surrogate design and trust-region optimization are dual formulations of the same problem. Building on this foundation, we develop Fiber Bundle Gating (FBG), an algebraic framework that organizes sampled RL data as a fiber bundle and decomposes ratio gating into a base-level gate on trajectory aggregates and a fiber-level gate on per-token residuals, with provable first-order agreement with the true RL objective near on-policy. From APC-Obj and FBG we derive Fibration Policy Optimization (or simply, FiberPO), a concrete objective whose Jacobian is block-diagonal over trajectories, reduces to identity at on-policy, and provides better update direction thus improving token efficiency. The compositional nature of the framework extends beyond the trajectory-token case: fibrations compose algebraically into a Fibration Gating Hierarchy (FGH) that scales the same gating mechanism to arbitrary hierarchical depth without new primitives, as demonstrated by FiberPO-Domain, a four-level instantiation with independent trust-region budgets at the domain, prompt group, trajectory, and token levels. Together, these results connect the trust-region theory, a compositional algebraic structure, and practical multi-scale stability control into a unified framework for LLM policy optimization.

Large language models (LLMs) with reasoning abilities have demonstrated growing promise for tackling complex scientific problems. Yet such tasks are inherently domain-specific, unbounded and open-ended, demanding exploration across vast and flexible solution spaces. Existing approaches, whether purely learning-based or reliant on carefully designed workflows, often suffer from limited exploration efficiency and poor generalization. To overcome these challenges, we present HELIX -- a Hierarchical Evolutionary reinforcement Learning framework with In-context eXperiences. HELIX introduces two key novelties: (i) a diverse yet high-quality pool of candidate solutions that broadens exploration through in-context learning, and (ii) reinforcement learning for iterative policy refinement that progressively elevates solution quality. This synergy enables the discovery of more advanced solutions. On the circle packing task, HELIX achieves state-of-the-art result with a sum of radii of 2.63598308 using only a 14B model. Across standard machine learning benchmarks, HELIX further surpasses GPT-4o with a carefully engineered pipeline, delivering an average F1 improvement of 5.95 points on the Adult and Bank Marketing datasets.

Large Language Models (LLMs) have demonstrated strong general capabilities, yet their deployment in finance remains challenging due to dense domain-specific terminology, stringent numerical reasoning requirements, and low tolerance for factual errors. We conduct a controlled empirical study showing that in specialized vertical domains, performance is largely determined by the quality and difficulty/verifiability profile of post-training data. We introduce ODA-Fin-SFT-318k, constructed via multi-stage distillation and verification to produce high-quality Chain-of-Thought supervision, and ODA-Fin-RL-12k, curated for hard-but-verifiable tasks that balance reward precision and task diversity. Using standard SFT and RL pipelines, we show that high-quality CoT distillation establishes a robust foundation during SFT, while difficulty- and verifiability-aware sampling improves RL generalization. Evaluated on nine benchmarks spanning general financial tasks, sentiment analysis, and numerical reasoning, our ODA-Fin-RL-8B consistently surpasses open-source state-of-the-art (SOTA) financial LLMs of comparable size. We release our ODA-Fin-SFT-318k and ODA-Fin-RL-12k datasets, along with trained models to advance data-centric financial AI research.

We study post-training linear autoregressive models with outcome and process rewards. Given a context $\boldsymbol{x}$, the model must predict the response $\boldsymbol{y} \in Y^N$, a sequence of length $N$ that satisfies a $γ$ margin condition, an extension of the standard separability to sequences. We prove that on test samples where the base model achieves a non-trivial likelihood $α$, a variant of policy gradient (PG) can achieve likelihood $1 - \varepsilon$ with an essentially minimax optimal number of reward queries $\tilde{O}((α^{-1} + \varepsilon^{-1})/γ^2)$. However, a barrier arises for going beyond the support of the base model. We prove that the overall expected error after post-training with outcome rewards is governed by a property of the base model called the Likelihood Quantile (LQ), and that variants of PG, while minimax optimal, may require a number of reward queries exponential in $N$ to go beyond this support, regardless of the pre-training algorithm. To overcome this barrier, we study post-training with a process reward model, and demonstrate how PG variants in this setting avoid the curse of dimensionality in $N$ via dependence on a token-level LQ. Along the way, we prove that under the margin condition, SGD with adaptive learning rate (LR) achieves a near optimal test error for statistical learning, and PG with adaptive LR achieves a near optimal number of mistakes for online learning while being computationally efficient whenever possible, both of which may be of independent interest.

Reinforcement learning (RL) for large language models (LLMs) has shown strong performance in single-turn tasks, but extending it to multi-turn interaction remains challenging due to sparse rewards and poor per-turn credit assignment. In emotional support dialogues, responses shape future user states, so matched-state step-wise comparison is unavailable, while trajectory-level supervision is insufficient. We propose MICA (Multi-granularity Intertemporal Credit Assignment), a critic-free RL framework for multi-turn emotional support tasks. MICA derives both immediate and delayed credit from a shared potential function over the user's structured support state. Incremental Distance Reward measures the per-turn decrease in residual distance to the target state, while its Monte Carlo return captures delayed effects. After scope-specific normalization, the two signals form a mixed advantage for stable per-turn optimization without matched-state comparisons, rollout trees, or a learned critic. On EMPA, EQ-Bench, and EmoBench with Qwen2.5-7B-Instruct and Qwen3-8B/14B/32B, MICA consistently outperforms GRPO and REINFORCE++, achieving up to +42.5 on EMPA, while adding no rollout cost and remaining robust to reward judges. These results show that turn-aware credit assignment enables effective and practical multi-turn RL for interactive LLMs.

Reinforcement learning is a framework for learning to act sequentially in an unknown environment. We propose a natural approach for modeling policy structure in policy gradients. The key idea is to optimize for a subset of future rewards: smaller subsets represent simpler policies, which can be learned more reliably because their empirical gradient estimates are more accurate. Our approach allows for modeling and comparison of different policy classes, including full planning, greedy, K-step lookahead, and segment policies. We evaluate the policies empirically on multiple persona-alignment conversational problems. Different policies excel in different problems, reflecting their different characteristics and highlighting the importance of our studied policy class.

Large language models (LLMs) benefit substantially from supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR) in reasoning tasks. However, these recipes perform poorly in instruction-based molecular optimization, where each data point typically provides only a single optimized reference molecule and no step-by-step optimization trajectory. We reveal that answer-only SFT on the reference molecules collapses reasoning, and RLVR provides sparse feedback under similarity constraints due to the model's lack of effective exploration, which slows learning and limits optimization. To encourage the exploration of new molecules while balancing the exploitation of the reference molecules, we introduce Reference-guided Policy Optimization (RePO), an optimization approach that learns from reference molecules without requiring trajectory data. At each update, RePO samples candidate molecules with their intermediate reasoning trajectories from the model and trains the model using verifiable rewards that measure property satisfaction under similarity constraints in an RL manner. Meanwhile, it applies reference guidance by keeping the policy's intermediate reasoning trajectory as context and training only the answer in a supervised manner. Together, the RL term promotes exploration, while the guidance term mitigates reward sparsity and stabilizes training by grounding outputs to references when many valid molecular edits exist. Across molecular optimization benchmarks, RePO consistently outperforms SFT and RLVR baselines (e.g., GRPO), achieving improvements on the optimization metric (Success Rate $\times$ Similarity), improving balance across competing objectives, and generalizing better to unseen instruction styles. Our code is publicly available at https://github.com/tmlr-group/RePO.

Reliable deployment of large language models (LLMs) requires accurate uncertainty estimation. Existing methods are predominantly answer-first, producing confidence only after generating an answer, which measure the correctness of a specific response and limits practical usability. We study a confidence-first paradigm, where the model outputs its confidence before answering, interpreting this score as the model's probability of answering the question correctly under its current policy. We propose CoCA(Co-optimized Confidence and Answers), a GRPO reinforcement learning framework that jointly optimizes confidence calibration and answer accuracy via segmented credit assignment. By assigning separate rewards and group-relative advantages to confidence and answer segments, CoCA enables stable joint optimization and avoids reward hacking. Experiments across math, code, and factual QA benchmarks show improved calibration and uncertainty discrimination while preserving answer quality, thereby enabling a broader range of downstream applications.

Proximal constraints are fundamental to the stability of the Large Language Model reinforcement learning. While the canonical clipping mechanism in PPO serves as an efficient surrogate for trust regions, we identify a critical bottleneck: fixed bounds strictly constrain the upward update margin of low-probability actions, disproportionately suppressing high-advantage tail strategies and inducing rapid entropy collapse. To address this, we introduce Band-constrained Policy Optimization (BandPO). BandPO replaces canonical clipping with Band, a unified theoretical operator that projects trust regions defined by f-divergences into dynamic, probability-aware clipping intervals. Theoretical analysis confirms that Band effectively resolves this exploration bottleneck. We formulate this mapping as a convex optimization problem, guaranteeing a globally optimal numerical solution while deriving closed-form solutions for specific divergences. Extensive experiments across diverse models and datasets demonstrate that BandPO consistently outperforms canonical clipping and Clip-Higher, while robustly mitigating entropy collapse.

Large language models (LLMs) typically receive diverse natural language (NL) feedback through interaction with the environment. However, current reinforcement learning (RL) algorithms rely solely on scalar rewards, leaving the rich information in NL feedback underutilized and leading to inefficient exploration. In this work, we propose GOLF, an RL framework that explicitly exploits group-level language feedback to guide targeted exploration through actionable refinements. GOLF aggregates two complementary feedback sources: (i) external critiques that pinpoint errors or propose targeted fixes, and (ii) intra-group attempts that supply alternative partial ideas and diverse failure patterns. These group-level feedbacks are aggregated to produce high-quality refinements, which are adaptively injected into training as off-policy scaffolds to provide targeted guidance in sparse-reward regions. Meanwhile, GOLF jointly optimizes generation and refinement within a unified RL loop, creating a virtuous cycle that continuously improves both capabilities. Experiments on both verifiable and non-verifiable benchmarks show that GOLF achieves superior performance and exploration efficiency, achieving 2.2$\times$ improvements in sample efficiency compared to RL methods trained solely on scalar rewards. Code is available at https://github.com/LuckyyySTA/GOLF.

Reinforcement Learning from AI Feedback (RLAIF) enables language models to improve by training on their own preference judgments, yet no theoretical account explains why this self-improvement seemingly works for value learning. We propose the latent value hypothesis, that pretraining on internet-scale data encodes human values as directions in representation space, and constitutional prompts elicit these latent values into preference judgments. We formalize this intuition under a linear model where the constitution acts as a projection operator selecting value-relevant directions. Our analysis yields several results. RLAIF improves alignment when the constitution-activated direction correlates with true values better than the model's default generation direction thus explaining the generation-judgment gap; the ceiling on RLAIF quality is determined by how well representations encode values, which scales with model capacity; and adversarial constitutions exist that can activate anti-social value directions encoded from harmful pretraining data. Our account unifies scattered empirical findings including the refusal direction, low-rank safety subspaces, and RLAIF scaling behavior.

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced the reasoning capabilities of Large Language Models (LLMs) by optimizing them against factual outcomes. However, this paradigm falters in long-context scenarios, as its reliance on internal parametric knowledge is ill-suited for tasks requiring contextual grounding--the ability to find and reason over externally provided information. We identify a key reason for this failure: a reward based solely on the final answer is too sparse to effectively guide the model for identifying relevant evidence. We formally prove that the outcome-only reward leads to significant vanishing gradients for the context grounding process, rendering learning intractable. To overcome this bottleneck, we introduce LongRLVR to augment the sparse answer reward with a dense and verifiable context reward. This auxiliary signal directly incentivizes the model for selecting the correct grounding information, providing a robust learning gradient that solves the underlying optimization challenge. We validate our method on challenging long-context benchmarks using Qwen and LLaMA models. LongRLVR consistently and significantly outperforms the standard RLVR across all models and benchmarks, e.g., boosting a 14B model's scores on RULER-QA from 73.17 to 88.90 and on LongBench v2 from 39.8 to 46.5. Our work demonstrates that explicitly rewarding the grounding process is a critical and effective strategy for unlocking the full reasoning potential of LLMs in long-context applications. Our code is available at https://github.com/real-absolute-AI/LongRLVR.

Asynchronous execution is essential for scaling reinforcement learning (RL) to modern large model workloads, including large language models and AI agents, but it can fundamentally alter RL optimization behavior. While prior work on asynchronous RL focuses on training throughput and distributional correction, we show that naively applying asynchrony to policy-gradient updates can induce qualitatively different training dynamics and lead to severe training instability. Through systematic empirical and theoretical analysis, we identify a key signature of this instability: asynchronous training exhibits persistently high cosine similarity between consecutive policy gradients, in contrast to the near-orthogonal updates observed under synchronized training. This stale-aligned gradient effect amplifies correlated updates and increases the risk of overshooting and divergence. Motivated by this observation, we propose GRADIENT ALIGNMENT CONTROL(GAC), a simple dynamics-aware stabilization method that regulates asynchronous RL progress along stale-aligned directions via gradient projection. We establish convergence guarantees under bounded staleness and demonstrate empirically that GAC recovers stable, on-policy training dynamics and matches synchronized baselines even at high staleness.

Large Language Models (LLMs) often fail to generate correct code on the first attempt, which requires using generated unit tests as verifiers to validate the solutions. Despite the success of recent verification methods, they remain constrained by a "scaling-by-quantity" paradigm. This brute-force approach suffers from a critical limitation: it yields diminishing returns in fault detection while causing severe test redundancy. To address this, we propose MIST-RL (Mutation-based Incremental Suite Testing via Reinforcement Learning), a framework that shifts the focus to "scaling-by-utility". We formulate test generation as a sequential decision process optimized via Group Relative Policy Optimization (GRPO). Specifically, we introduce a novel incremental mutation reward combined with dynamic penalties, which incentivizes the model to discover new faults while it suppresses functionally equivalent assertions. Experiments on HumanEval+ and MBPP+ demonstrate that MIST-RL outperforms state-of-the-art baselines. It achieves a +28.5% higher mutation score while reducing the number of test cases by 19.3%. Furthermore, we show that these compact, high-utility tests serve as superior verifiers, which improves downstream code reranking accuracy on HumanEval+ by 3.05% over the SOTA baseline with 10 candidate samples. The source code and data are provided in the supplementary material.

Large language model alignment via reinforcement learning depends critically on reward function quality. However, static, domain-specific reward models are often costly to train and exhibit poor generalization in out-of-distribution scenarios encountered during RL iterations. We present RLAR (Reinforcement Learning from Agent Rewards), an agent-driven framework that dynamically assigns tailored reward functions to individual queries. Specifically, RLAR transforms reward acquisition into a dynamic tool synthesis and invocation task. It leverages LLM agents to autonomously retrieve optimal reward models from the Internet and synthesize programmatic verifiers through code generation. This allows the reward system to self-evolve with the shifting data distributions during training. Experimental results demonstrate that RLAR yields consistent performance gains ranging from 10 to 60 across mathematics, coding, translation, and dialogue tasks. On RewardBench-V2, RLAR significantly outperforms static baselines and approaches the performance upper bound, demonstrating superior generalization through dynamic reward orchestration. The data and code are available on this link: https://github.com/ZhuoerFeng/RLAR.

Industrial advertising question answering (QA) is a high-stakes task in which hallucinated content, particularly fabricated URLs, can lead to financial loss, compliance violations, and legal risk. Although Retrieval-Augmented Generation (RAG) is widely adopted, deploying it in production remains challenging because industrial knowledge is inherently relational, frequently updated, and insufficiently aligned with generation objectives. We propose a reinforced co-adaptation framework that jointly optimizes retrieval and generation through two components: (1) Graph-aware Retrieval (GraphRAG), which models entity-relation structure over a high-citation knowledge subgraph for multi-hop, domain-specific evidence selection; and (2) evidence-constrained reinforcement learning via Group Relative Policy Optimization (GRPO) with multi-dimensional rewards covering faithfulness, style compliance, safety, and URL validity. Experiments on an internal advertising QA dataset show consistent gains across expert-judged dimensions including accuracy, completeness, and safety, while reducing the hallucination rate by 72%. A two-week online A/B test demonstrates a 28.6% increase in like rate, a 46.2% decrease in dislike rate, and a 92.7% reduction in URL hallucination. The system has been running in production for over half a year and has served millions of QA interactions.

Despite the strong performance of Large Language Models (LLMs) on complex instruction-following tasks, precise control of output length remains a persistent challenge. Existing methods primarily attempt to enforce length constraints by externally imposing length signals or optimization objectives, while largely overlooking the underlying limitation: the model's intrinsic deficit in length cognition. To address this, we propose LARFT (Length-Aware Reinforcement Fine-Tuning), a training framework that aligns the model's length cognition with its action. Specifically, LARFT integrates length-oriented reinforcement learning with a hindsight length awareness. By transforming on-policy data into hindsight self-awareness tasks where the model learns to identify the actual length of its own generation, LARFT jointly optimizes the model's internal representation of length information and refines its policy to satisfy length constraints, thereby achieving precise and reliable length instruction following. Extensive experiments across four base models demonstrate that LARFT outperforms existing baselines, achieving an average improvement of +20.92 points across three length instruction following benchmarks with only a marginal decline of -1.45 points on four general capability benchmarks.

Reinforcement learning (RL) has become a central post-training paradigm for large language models (LLMs), but its performance is highly sensitive to the quality of training problems. This sensitivity stems from the non-stationarity of RL: rollouts are generated by an evolving policy, and learning is shaped by exploration and reward feedback, unlike supervised fine-tuning (SFT) with fixed trajectories. As a result, prior work often relies on manual curation or simple heuristic filters (e.g., accuracy), which can admit incorrect or low-utility problems. We propose GradAlign, a gradient-aligned data selection method for LLM reinforcement learning that uses a small, trusted validation set to prioritize training problems whose policy gradients align with validation gradients, yielding an adaptive curriculum. We evaluate GradAlign across three challenging data regimes: unreliable reward signals, distribution imbalance, and low-utility training corpus, showing that GradAlign consistently outperforms existing baselines, underscoring the importance of directional gradient signals in navigating non-stationary policy optimization and yielding more stable training and improved final performance. We release our implementation at https://github.com/StigLidu/GradAlign

Existing alignment paradigms remain limited in capturing the pluralistic nature of human values. Overton Pluralism (OP) addresses this gap by generating responses with diverse perspectives from a single query. This paper introduces OP-GRPO (Overton Pluralistic Group Relative Policy Optimization), a reinforcement learning framework for implicit Overton Pluralism that enables a single LLM to produce pluralistic responses without explicit prompting or modular orchestration. Our workflow consists of two main steps: 1) Similarity estimator training, which fine-tunes a Sentence Transformer for OP tasks to provide a more accurate coverage evaluation of the given responses; and 2) OP-GRPO training, which incorporates this similarity estimator into a carefully designed dual-reward system to ensure both broad coverage of genuine human perspectives and the uniqueness of each perspective, thereby promoting diversity. Empirical results demonstrate that OP-GRPO achieves a "Small models, Big perspective coverage" effect: our trained Qwen2.5-3B-Instruct surpasses the GPT-OSS (20B) baseline with a 37.4% relative accuracy gain on the Natural Language Inference (NLI) benchmark. It also outperforms a modular-architecture baseline with a 19.1% relative improvement. Evaluations with GPT-5.4 as the LLM judge and OP-Benchmark further confirm the robustness of our approach.

Reinforcement learning (RL) has become a key driver of progress in large language models, but scaling RL to long chain-of-thought (CoT) trajectories is increasingly constrained by backpropagation over every generated token. Even with optimized rollout engines, full-token updates can consume a large fraction of total training cost, turning token length into a hidden tax on RL. We introduce Not All Tokens Are Needed (NAT), a unified framework that makes the token budget a first-class optimization primitive. NAT updates the policy using only a selected subset of generated tokens while preserving the learning signal of full-sequence RL. The core idea is an unbiased partial-token policy-gradient estimator via Horvitz-Thompson reweighting, which ensures statistically correct gradients despite subsampling. We instantiate NAT with two simple, plug-and-play token selection schemes: Uniform Random Sampling (URS) and Random Prefix Cutting (RPC), both of which reduce forward and backward compute and memory without modifying the reward computation or rollout pipeline. Across mathematical reasoning benchmarks, NAT matches full-token GRPO performance while using as few as 50% of tokens, providing an efficient and orthogonal pathway to scaling RL beyond the limits imposed by long trajectories. In our experiments, RPC saves 18% peak GPU memory and 29% forward and backward RL training time for Qwen3-8B.

Asynchronous reinforcement learning has become increasingly central to scaling LLM post-training, delivering major throughput gains by decoupling rollout generation from policy updates. However, widely used policy-gradient objectives such as REINFORCE and GRPO suffer under high asynchrony: stale rollouts produce heavy-tailed importance weights, so a small number of trajectories dominate updates and the policy-gradient estimator becomes markedly higher variance. Through systematic analysis on math, reasoning, and tool-use benchmarks, we find that this increasing variance is reliably predicted by collapsing effective sample size (ESS), which prior stabilization methods largely fail to address. Motivated by this diagnosis, we introduce $\textbf{V}$ariance $\textbf{C}$ontrolled $\textbf{P}$olicy $\textbf{O}$ptimization ($\textbf{VCPO}$), a method that (i) dynamically scales the learning rate with ESS to dampen unreliable updates and (ii) applies a closed-form minimum-variance baseline for off-policy settings, without a critic model and adding minimal overhead. Empirically, across math and general reasoning benchmarks, this enables robustly stable asynchronous training compared to previous stabilization and algorithmic methods, even in highly off-policy regimes (128 steps off-policy). In a long-horizon, tool-use task, VCPO matches synchronous performance while delivering a 2.5$\times$ speedup in training time. Code is available at: https://github.com/mit-han-lab/vcpo

Existing Reinforcement Learning with Verifiable Rewards (RLVR) algorithms, such as GRPO, rely on rigid, uniform, and symmetric trust region mechanisms that are fundamentally misaligned with the complex optimization dynamics of Large Language Models (LLMs). In this paper, we identify three critical challenges in these methods: (1) inefficient gradient utilization caused by the binary cutoff of hard clipping, (2) insensitive probability mass arising from uniform ratio constraints that ignore the token distribution, and (3) asymmetric signal reliability stemming from the disparate credit assignment ambiguity between positive and negative samples. To bridge these gaps, we propose Mass-Adaptive Soft Policy Optimization (MASPO), a unified framework designed to harmonize these three dimensions. MASPO integrates a differentiable soft Gaussian gating to maximize gradient utility, a mass-adaptive limiter to balance exploration across the probability spectrum, and an asymmetric risk controller to align update magnitudes with signal confidence. Extensive evaluations demonstrate that MASPO serves as a robust, all-in-one RLVR solution, significantly outperforming baselines. Our code is available at: https://github.com/FlyTune/MASPO-RL.

Large reasoning models (LRMs) excel on complex problems but face a critical barrier to efficiency: reinforcement learning (RL) training requires long rollouts for outcome-based rewards, where autoregressive decoding dominates time and memory usage. While sliding-window cache strategies can bound memory, they disrupt long-context reasoning and degrade performance. We introduce Progressive Thought Encoding, a parameter-efficient fine-tuning method that enables LRMs to reason effectively under fixed-size caches. By progressively encoding intermediate reasoning into fixed-size vector representations, our approach eliminates the need to backpropagate through full-cache rollouts, thereby reducing memory usage, while maintaining constant memory during inference. Experiments on three models, including Qwen2.5-3B-Instruct, Qwen2.5-7B-Instruct, and DeepSeek-R1-Distill-Llama-8B, on six widely used challenging mathematical benchmarks show consistent gains: our method achieves +19.3% improvement over LoRA-based fine-tuning and +29.9% over LRMs without fine-tuning on average, with up to +23.4 accuracy improvement on AIME2024/2025 under the same tight cache budgets. These results demonstrate that Progressive Thought Encoding not only improves reasoning accuracy but also makes RL training of LRMs substantially more efficient and scalable under real-world memory constraints.

Exploration remains a key bottleneck for reinforcement learning (RL) post-training of large language models (LLMs), where sparse feedback and large action spaces can lead to premature collapse into repetitive behaviors. We propose Verbalized Action Masking (VAM), which verbalizes an action mask in the prompt and enforces that the model outputs an action from the masked set. Building on this interface, we introduce iterative action-space pruning: if the target action is not sampled, we remove valid sampled actions from the mask and resample under the reduced candidate set, repeating until the target is sampled or a fixed budget is exhausted. We study VAM in chess and evaluate it under two training regimes: an engine-play regime that generates states via play against an engine opponent and a fixed-dataset regime that trains from a fixed dataset of positions with verifier scores. Across held-out chess puzzles and full-game play measured by average centipawn loss (ACPL), VAM improves learning efficiency and final performance over strong baselines, highlighting verbalized masking as a practical mechanism for controllable exploration in LLM RL post-training.

Fast weight architectures offer a promising alternative to standard transformers for long-context modeling by replacing the KV-cache with a recurrently updated fixed-size memory. Despite this architectural shift, they are typically trained with the same next-token prediction (NTP) objective as standard transformers. This creates a mismatch: fast weight models rely on an evolving memory state to support future predictions, while NTP provides only token-level supervision for the immediate next token. We address this mismatch with next-sequence prediction (NSP), a sequence-level extension of NTP that trains models to produce coherent multi-token continuations from their recurrent memory state. To optimize this sequence-level objective, we propose ReFINE (Reinforced Fast weIghts via Next sEquence prediction). ReFINE selects informative token positions based on prediction entropy, generates multi-token rollouts, assigns sequence-level rewards, and optimizes the model with Group Relative Policy Optimization (GRPO). ReFINE is applicable throughout the training lifecycle of pre-trained language models: mid-training, post-training, and test-time training. Experiments on LaCT-760M and DeltaNet-1.3B show that ReFINE consistently outperforms NTP-based supervised fine-tuning in needle-in-a-haystack retrieval, long-context question answering, and diverse tasks in LongBench. ReFINE provides an effective and versatile framework for improving long-context modeling in fast weight architectures.

Building agentic systems that can autonomously self-improve from experience is a longstanding goal of AI. Large language models (LLMs) today primarily self-improve via two mechanisms: self-reflection for context updates, and reinforcement learning (RL) for weight updates. In this work, we propose Evolutionary System Prompt Learning (E-SPL), a method for jointly improving model contexts and model weights. In each RL iteration, E-SPL samples trajectories under multiple system prompts in parallel, then jointly applies RL updates to LLM weights and evolutionary updates to system prompts. System prompts evolve via mutation and crossover, two genetic operators driven by LLM self-reflection; selection is based on relative performance ratings updated across RL iterations. E-SPL encourages a natural division between declarative knowledge encoded in prompts and procedural knowledge encoded in weights, resulting in improved performance across reasoning and agentic tasks. For instance, in an easy-to-hard (AIME $\rightarrow$ BeyondAIME) generalization setting, E-SPL improves RL success rate from 38.8% $\rightarrow$ 45.1% while also outperforming reflective prompt evolution (40.0%). Overall, our results demonstrate that RL and system prompt evolution are deeply synergistic, and combining the two yields consistent gains in sample efficiency and generalization. Code: https://github.com/LunjunZhang/E-SPL

Reinforcement learning (RL) has enhanced the capabilities of large language models (LLMs) through reward-driven training. Nevertheless, this process can introduce excessively long responses, inflating inference latency and computational overhead. Prior length-control approaches typically rely on fixed heuristic reward shaping, which can misalign with the task objective and require brittle tuning. In this work, we propose LACONIC, a reinforcement learning method that enforces a target token budget during training. Specifically, we update policy models using an augmented objective that combines the task reward with a length-based cost. To balance brevity and task performance, the cost scale is adaptively adjusted throughout training. This yields robust length control while preserving task reward. We provide a theoretical guarantee that support the method. Across mathematical reasoning models and datasets, LACONIC preserves or improves pass@1 while reducing output length by over 50%. It maintains out-of-domain performance on general knowledge and multilingual benchmarks with 44% fewer tokens. Moreover, LACONIC integrates into standard RL-tuning with no inference changes and minimal deployment overhead.

While Group Relative Policy Optimization (GRPO) offers a powerful framework for LLM post-training, its effectiveness in open-ended domains like Machine Translation hinges on accurate intra-group ranking. We identify that standard Pointwise Quality Metrics (PQM) fall short in this context: candidates are evaluated in isolation, so the comparative context is missing for distinguishing fine-grained linguistic nuances. To address this, we introduce the Group Quality Metric (GQM) paradigm and its instantiation, the Group Relative Reward Model (GRRM). Unlike traditional independent scorers, GRRM jointly processes the entire candidate group, leveraging comparative analysis to rigorously resolve relative quality and adaptive granularity. Empirical evaluations confirm that GRRM achieves competitive ranking accuracy among all baselines; integrating GRRM into the GRPO training not only improves general translation quality but also unlocks reasoning capabilities comparable to state-of-the-art reasoning models. We release codes, datasets, and model checkpoints at https://github.com/NJUNLP/GRRM.

Recent agentic time series forecasting (TSF) approaches use large language models (LLMs) to autonomously orchestrate analytical and forecasting tools and reason about temporal patterns using the resulting evidence. However, many such approaches rely on powerful LLMs in training-free, prompt-driven workflows, leaving open whether smaller models can learn these interaction and reasoning capabilities. In this paper, we introduce Cast-R1, an 8Bparameter agentic forecasting model trained through trajectory distillation and multi-turn reinforcement learning with structured memory. First, we develop a forecasting agent harness with specialized analysis and prediction tools to generate multi-turn interaction trajectories using a teacher LLM, which are subsequently evaluated and selected for supervised fine-tuning. Second, we apply group relative policy optimization (GRPO) across multi-turn forecasting episodes, with structured memory preserving diagnostic evidence and intermediate forecasts for state construction. Rewards based on prediction accuracy and temporal structure guide tool selection, model routing, and forecast refinement. A difficulty-aware curriculum combines sample filtering and progressive sample ordering during training. Extensive experiments on multiple datasets demonstrate the effectiveness of Cast-R1. These findings highlight the potential of forecasting-specific post-training to equip smaller LLMs with multi-turn, tool-augmented forecasting capabilities within structured workflows.