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Deep Learning · Large Language Models

Ru Zhang, Renda Li, Ziyu Ma, Weijie Qiu, Chongyang Tao, Yong Wang, Xiangxiang Chu

Reinforcement learning (RL) has demonstrated potential for enhancing reasoning in large language models (LLMs). However, effective RL training, which requires medium-difficulty training samples, faces two fundamental challenges: Effective Data Scarcity and Dynamic Difficulty Shifts, where medium-difficulty samples are scarce and become trivial as models improve. Existing methods mitigate this scarcity to some extent by generating training samples. However, these approaches suffer from anchor-free generation, ignoring co-evolution, and difficulty mismatch. To address these issues, we propose D²Evo, a Dual Difficulty-aware self-Evolution RL framework. In each iteration, our method mines medium-difficulty anchors based on the current Solver's capability, trains the Questioner to generate diverse questions at appropriate difficulty levels, and jointly optimizes both components to enable progressive reasoning gains. Extensive experiments demonstrate that D²Evo outperforms existing methods on mathematical reasoning benchmarks with fewer than 2K real mathematical samples, and exhibits strong generalization on general reasoning benchmarks.

Deep Learning · Large Language Models

Haoyu Wang, Guozheng Ma, Shugang Cui, Yilun Kong, Haotian Luo, Li Shen, Mengya Gao, Yichao Wu, Xiaogang Wang, Dacheng Tao

While Large Language Models (LLMs) excel in language-based agentic tasks, their applicability to unseen, nonlinguistic environments (e.g., symbolic or spatial tasks) remains limited. Previous work attributes this performance gap to the mismatch between the pretraining distribution and the testing distribution. In this work, we demonstrate the primary bottleneck is the prohibitive cost of exploration: mastering these tasks requires extensive trial-and-error, which is computationally unsustainable for parameter-heavy LLMs operating in a high dimensional semantic space. To address this, we propose SCOUT (Sub-Scale Collaboration On Unseen Tasks), a novel framework that decouples exploration from exploitation. We employ lightweight "scouts" (e.g., small MLPs) to probe environmental dynamics at a speed and scale far exceeding LLMs. The collected trajectories are utilized to bootstrap the LLM via Supervised Fine-Tuning (SFT), followed by multi-turn Reinforcement Learning (RL) to activate its latent world knowledge. Empirically, SCOUT enables a Qwen2.5-3B-Instruct model to achieve an average score of 0.86, significantly outperforming proprietary models, including Gemini-2.5-Pro (0.60), while saving about 60% GPU hours consumption.

Deep Learning · Large Language Models

Howard Chen, Noam Razin, Karthik Narasimhan, Danqi Chen

Adapting language models (LMs) to new tasks via post-training carries the risk of degrading existing capabilities -- a phenomenon classically known as catastrophic forgetting. In this paper, toward identifying guidelines for mitigating this phenomenon, we systematically compare the forgetting patterns of two widely adopted post-training methods: supervised fine-tuning (SFT) and reinforcement learning (RL). Our experiments reveal a consistent trend across LM families (Llama, Qwen) and tasks (instruction following, general knowledge, and arithmetic reasoning): RL leads to less forgetting than SFT while achieving comparable or higher target task performance. To investigate the cause for this difference, we consider a simplified setting in which the LM is modeled as a mixture of two distributions, one corresponding to prior knowledge and the other to the target task. We identify that the mode-seeking nature of RL, which stems from its use of on-policy data, enables keeping prior knowledge intact when learning the target task. We then verify this insight by demonstrating that the use on-policy data underlies the robustness of RL to forgetting in practical settings, as opposed to other algorithmic choices such as the KL regularization or advantage estimation. Lastly, as a practical implication, our results highlight the potential of mitigating forgetting using approximately on-policy data, which can be substantially more efficient to obtain than fully on-policy data.

Deep Learning · Large Language Models

Yulin Chen, He He, Chen Zhao

Reinforcement Learning with Verifiable Reward (RLVR) has proven effective in improving Large Language Model's (LLM) reasoning ability. However, the learning dynamics of RLVR remain underexplored. In this paper, we reveal a curious phenomenon: among hard examples that the model initially struggles with, a substantial subset remains unlearnable even when correct rollouts present. To understand the phenomenon, we first demonstrate that existing optimization and sampling techniques fail to resolve unlearnability. With cross-example gradient analysis, we show that unlearnable examples have fundamental representation issue, characterized by low gradient similarity with the rest of the examples and ungeneralizable reasoning patterns. We further show that representation flaws are difficult to mitigate in RL, as data augmentation does not improve gradient similarity. Our study provides the first systematic characterization of unlearnable data in RLVR training and reveals fundamental limitations in current RL approaches for reasoning tasks.

Reinforcement Learning · Deep RL

Shiping Gao, Hongzhan Chen, Xiaojun Quan, Qifan Wang, Lifu Huang

Process reward models (PRMs) provide fine-grained reward signals along the reasoning process, improving credit assignment beyond outcome-only rewards. Training reliable PRMs often relies on step annotations or heavy verification pipelines, making them expensive to scale and refresh during online RL. Implicit PRMs mitigate this cost by learning decomposable token/step rewards from trajectory-level outcome labels, but they suffer a train-inference mismatch: training only constrains a sequence-level aggregate, while deployment queries token-level scores as local step quality. As a result, token credits are weakly identified and can become predictive of final success without faithfully reflecting which step is correct. This unreliability can even undermine a key promise of implicit PRMs—scoring many candidate tokens—because noisy per-token advantages may systematically reinforce incorrect continuations. We address this with a novel Implicit Prefix-Value Reward Model (IPVRM), which directly learns a prefix-conditioned value function estimating the probability of eventual correctness, and derives step signals via temporal-difference (TD) differences. IPVRM substantially improves step-verification F1 on ProcessBench. Building on these calibrated signals, we further propose Distribution-Level RL (DistRL), which computes TD advantages not only for sampled tokens but also for high-probability candidate tokens across the vocabulary, enabling dense counterfactual updates without additional rollouts. DistRL brings limited benefits with mis-calibrated implicit rewards, but consistently improves downstream reasoning once powered by IPVRM’s reliable prefix values.

Deep Learning · Large Language Models

Zexi Liu, Jingyi Chai, Xinyu Zhu, shuo tang, Rui Ye, Weiyu Ma, Bo Zhang, LEI BAI, Siheng Chen

The emergence of large language model (LLM)-based agents has significantly advanced the development of autonomous machine learning (ML) engineering. However, the dominant prompt-based paradigm exhibits limitations: smaller models lack the capacity to learn from execution trajectories for generalization, while large proprietary models incur high computational overhead, restricting accessibility and scalability. Focusing on this, for the first time, we explore the paradigm of learning-based agentic ML, where an LLM agent learns through interactive experimentation on ML tasks using online reinforcement learning (RL). To realize this, we propose a novel agentic ML training framework with three key components: (1) exploration-enriched fine-tuning, which enables LLM agents to generate diverse actions for enhanced RL exploration; (2) step-wise RL, which enables training on a single action step, accelerating experience collection and improving training efficiency; (3) an agentic ML-specific reward module, which unifies varied ML feedback signals into consistent rewards for RL optimization. Leveraging this framework, we train ML-Agent, driven by a 7B-sized Qwen-2.5 LLM for autonomous ML. Despite training on only 9 ML tasks, our 7B-sized ML-Agent achieves comparable performance to agents using much larger proprietary LLMs (e.g., GPT-5) but at significantly lower computational cost, demonstrating strong performance and cross-task generalization.

Deep Learning · Large Language Models

Zhichen Dong, Yang Li, Yuhan Sun, Weixun Wang, Yijia Luo, Zinian Peng, Wenbo Su, YuCheng, Bo Zheng, Junchi Yan

Token-level credit assignment remains a key obstacle for reinforcement learning (RL) in large language models (LLMs), where RL recipes typically treat all tokens equally, failing to distinguish decisive reasoning steps from routine formatting or fluent filler. Recent attempts leverage model-internal signals to assign finer-grained credit, but these are often point-wise heuristics that ignore the global structure of information propagation. We propose FlowTracer, an RL framework that traces \emph{answer-targeted reasoning flow} on an attention-induced directed acyclic graph in which nodes correspond to tokens and edge capacities come from aggregated attention weights and derives token credit from this global structure. The edge capacities are reweighted to retain only the influence that can reach the answer region, while enforcing local flow conservation so intermediate tokens neither lose nor gain effective mass due to path length or irrelevant branches. On this graph, FlowTracer extracts an information-flow backbone connecting the question to the answer and scores tokens by flow throughput, revealing high-impact hubs and aggregation checkpoints that mediate long-range dependencies. These derived importances are used to shape token-level rewards, enabling learning signals to focus precisely on the tokens that route information toward (or away from) correct answers and delivering consistent performance gains across a range of reasoning tasks.

Reinforcement Learning · Deep RL

Giorgi Butbaia, Paul Orland, Coco Huang, Davide Passaro, Lucas Fagan, Michele Tarquini, Hailong Dao, David Eisenbud, Ali Shehper, Sergei Gukov

Applying machine learning techniques to solving long-standing mathematical conjectures can be particularly challenging due to their extreme reward sparsity. As an illustrative example, we consider Kalai's algebraic Hirsch conjecture and recast the construction of its counterexamples as a sparse-reward reinforcement learning problem on graphs. We propose a constrained options-based HRL framework with an equivariant graph neural network policy, which allows us to learn useful temporal abstractions for this task. We evaluate our approach over a wide range of degrees and demonstrate that it consistently outperforms classical RL algorithms as well as greedy search. By exploiting the hierarchical structure of the problem, we effectively provide a first-of-its-kind application of HRL to a problem in commutative algebra.

Reinforcement Learning · Deep RL

Lucas Fagan, Michele Tarquini, Ali Shehper, Maksymilian Manko, Angus Gruen, Coco Huang, Giorgi Butbaia, Davide Passaro, Sergei Gukov

Mathematical search problems present a unique challenge for Reinforcement Learning (RL) due to vast search spaces and sparse rewards. In previous works, the Andrews-Curtis (AC) conjecture was established as an illustrative example of such problems. In this work, we identify a critical structural barrier in the AC landscape: a "Two Hump" distribution, where problem instances are either trivially solvable or effectively impossible, with a scarcity of intermediate "hard-but-solvable" instances required for effective learning. We tackle this challenge through two primary avenues: novel data generation techniques to populate the difficulty gap, and significant algorithmic enhancements including the introduction of supermoves and Transformer-based architectures. We demonstrate substantial performance improvements over previous baselines, and release new comprehensive benchmark datasets including **AC-19** (125,192 AC-trivial presentations of varying difficulty with length at most 19) and **AC-1M** (1,136,154 hard AC-trivial presentations of length at most 30), the first large-scale, publicly available datasets of this kind.

Deep Learning · Large Language Models

Shyam Sundhar Ramesh, Xiaotong Ji, Matthieu Zimmer, Sangwoong Yoon, Zhiyong Wang, Haitham Bou Ammar, Aurelien Lucchi, Ilija Bogunovic

RL-based post-training with GRPO is widely used to improve large language models on individual reasoning tasks. However, real-world deployment requires reliable performance across diverse tasks. A straightforward multi-task adaptation of GRPO often leads to imbalanced outcomes, with some tasks dominating optimization while others stagnate. Moreover, tasks can vary widely in how frequently prompts yield zero advantages (and thus zero gradients), which further distorts their effective contribution to the optimization signal. To address these issues, we propose a novel Multi-Task GRPO (MT-GRPO) algorithm that (i) dynamically adapts task weights to explicitly optimize worst-task performance and promote balanced progress across tasks, and (ii) introduces a ratio-preserving sampler to ensure task-wise policy gradients reflect the adapted weights. Experiments on both 3-task and 9-task settings show that MT-GRPO consistently outperforms baselines in worst-task accuracy. In particular, MT-GRPO achieves 16–28\% and 6\% absolute improvement on worst-task performance over standard GRPO and DAPO, respectively, while maintaining competitive average accuracy. Moreover, MT-GRPO requires 50\% fewer training steps to reach 50\% worst-task accuracy in the 3-task setting, demonstrating substantially improved efficiency in achieving reliable performance across tasks.

Deep Learning · Foundation Models

Ting Huang, Zeyu Zhang, Hao Tang

This position paper argues that reinforcement learning (RL) should be used to *adjust* foundation models after pretraining and cold-start supervision, not *abused* as a default recipe for capability creation or early-stage training. We view RL as a high-cost, high-leverage post-training operator that reallocates probability mass toward behaviors a model can already express, but rarely creates new reasoning capacities from scratch in a compute-efficient, stable, and controllable way. This distinction matters now because “RL-zero” narratives risk normalizing expensive and brittle RL-first pipelines as the primary path to reasoning, even though practice increasingly shows that cold-start supervision is a prerequisite for reliable RL and that RL is most effective as targeted refinement. Across modalities and domains, we emphasize a recurring regularity: supervision establishes usable reasoning structure, while RL mainly sharpens correctness, consistency, and constraint satisfaction, especially under hard constraints or distribution shift. We further argue for reward minimalism: simple, verifiable rewards often suffice and reduce proxy-driven failure modes relative to over-engineered reward models. Finally, we discuss how self-supervised RL can support self-evolution when grounded in verifiable signals and structured interaction environments. Together, these arguments motivate treating RL as a disciplined adjustment stage with explicit entry criteria and compute-accountable evaluation.

Raj Ghugare, Michał Bortkiewicz, Alicja Ziarko, Benjamin Eysenbach

How does the amount of compute available to a reinforcement learning (RL) policy affect its learning? Can policies using a fixed amount of parameters, still benefit from additional compute? The standard RL framework does not provide a language to answer these questions formally. Empirically, deep RL policies are often parameterized as neural networks with static architectures, conflating the amount of compute and the number of parameters. In this paper, we formalize compute bounded policies and prove that policies which use more compute can solve problems and generalize to longer-horizon tasks that are outside the scope of policies with less compute. Building on prior work in algorithmic learning and model-free planning, we propose a minimal architecture that can use a variable amount of compute. Our experiments complement our theory. On a set 31 different tasks spanning online and offline RL, we show that $(1)$ this architecture achieves stronger performance simply by using more compute, and $(2)$ stronger generalization on longer-horizon test tasks compared to standard feedforward networks or deep residual network using upto 5 times more parameters.

Reinforcement Learning · Deep RL

Dohyung Kim, Minbeom Kim, Jeonghye Kim, Lee Sangmook, Sojeong Rhee, Kyomin Jung

Reward-maximizing RL methods enhance the reasoning performance of LLMs, but often reduce the diversity among outputs. Recent works address this issue by adopting GFlowNets, training LLMs to match a target distribution while jointly learning its partition function. In contrast to prior works that treat this partition function solely as a normalizer, we reinterpret it as a per-prompt expected-reward (i.e., online accuracy) signal, leveraging this unused information to improve sample efficiency. Specifically, we first establish a theoretical relationship between the partition function and per-prompt accuracy estimates. Building on this key insight, we propose \textbf{Pa}rtition Fun\textbf{c}tion-Guid\textbf{ed} \textbf{RL} (PACED-RL), a post-training framework that leverages accuracy estimates to prioritize informative question prompts during training, and further improves sample efficiency through an accuracy estimate error–prioritized replay. Crucially, both components reuse information already produced during GFlowNet training, effectively amortizing the compute overhead into the existing optimization process. Extensive experiments across diverse benchmarks demonstrate strong performance improvements over GRPO and prior GFlowNet approaches, highlighting PACED-RL as a promising direction for a more sample efficient distribution-matching training for LLMs.

Reinforcement Learning · Deep RL

Haoxi Li, Qinglin Hou, Jianfei Ma, Jinxiang Lai, Tao Han, Sikai Bai, Jingcai Guo, Jie ZHANG, Song Guo

To navigate partially observable visual environments, recent VLM agents increasingly internalize world modeling capabilities directly into their policies via explicit CoT reasoning with reinforcement learning (RL). However, mere passive exploitation of reasoning on visited states is insufficient for sparse-reward agentic tasks, as it lacks the epistemic drive to actively uncover the *known unknown* required for robust generalization. We ask: *Can VLM agents actively find signals that challenge and update their internal world model through curiosity-driven exploration?* In this work, we propose **GLANCE**, a unified framework that bridges reasoning and exploration by grounding the agent's linguistic world model into the stable visual representations of an evolving target network. Crucially, **GLANCE** leverages the discrepancy between linguistic prediction and visual reality as an intrinsic curiosity signal within reinforcement learning, steering the agent to actively explore areas where its internal model is uncertain. Extensive experiments across a series of agentic tasks show the effectiveness of **GLANCE**, and demonstrate that aligning *what the agent thinks* with *what the agent sees* is key to solving complex or sparse agentic tasks.

Deep Learning · Large Language Models

Ilze Amanda Auzina, Joschka Strüber, Sergio Hernández-Gutiérrez, Shashwat Goel, Ameya Pandurang Prabhu, Matthias Bethge

How can we train agents to navigate uncertainty over long horizons? In this work, we propose ∆Belief-RL, which leverages a language model's own intrinsic beliefs to reward intermediate progress. Our method utilizes the change in the probability an agent assigns to the target solution for credit assignment. By training on synthetic interaction data, ∆Belief-RL teaches information-seeking capabilities that consistently outperform purely outcome-based rewards for RL, with improvements generalizing to out-of-distribution applications ranging from customer service to personalization. Notably, the performance continues to improve as we scale test-time interactions beyond the training horizon, with interaction-efficiency increasing even on Pass@k metrics. Overall, our work introduces a scalable training strategy for navigating uncertainty over a long-horizon, by enabling credit assignment to intermediate actions via intrinsic ∆Belief rewards.

Deep Learning · Large Language Models

Xingrun Xing, Zhiyuan Fan, Jie Lou, Guoqi Li, Jiajun Zhang, Debing Zhang

Recent reinforcement learning (RL) based large-thinking models demonstrate impressive expert-level abilities, i.e., software and math, but still rely heavily on verifiable rewards in specific domains, which places a significant bottleneck to extend the performance boundary of general reasoning capabilities. In this work, we propose PretrainZero, a reinforcement active learning framework built on the pretraining corpus to extend RL from domain-specific post-training to general pretraining. PretrainZero features the following characteristics: 1) Active pretraining: inspired by the active learning ability of humans, PretrainZero learns a unified reasoning policy to actively identify reasonable and informative contents from pretraining corpus, and reason to predict these contents by RL. 2) Self-supervised learning: without any verifiable labels, pretrained reward models, or supervised fine-tuning, we directly pretrain reasoners from $3\sim30$B base models on the general Wikipedia corpus using RL, significantly breaking the verification data-wall for general reasoning. 3) Verification scaling: by tackling increasingly challenging masked spans, PretrainZero substantially enhances the general reasoning abilities of pretrained base models. In reinforcement pretraining, PretrainZero improves Qwen3-4B-Base for 8.43, 5.96 and 10.60 on MMLU-Pro, SuperGPQA and math average benchmarks. In post-training, the pretrained models can also serve as reasoning foundation models for downstream RLVR tasks.

Reinforcement Learning · Deep RL

Zhishuai Liu, Pan Xu

We study a simple yet principled modification of classical Q-learning that clips the value estimate in the Bellman backup by a threshold $\lambda$. The resulting algorithm, clipped Q-learning, is motivated by a key theoretical insight: the clipped Bellman backup is an unbiased one-sample estimation of a robust Bellman operator arising naturally from a transition-regularized MDP framework. This formulation corresponds to optimizing performance against a specific class of adversarial dynamics perturbations at the test time that reallocate transition probability mass away from high-value states, thereby inducing conservative but stable decision making. Under this interpretation, clipped Q-learning can be viewed as tracking the fixed point of the robust Bellman equation and learning policies that hedge against adversarial dynamics shifts at test time. We analyze two clipped Q-learning variants with an optimistic exploration bonus and establish polynomial regret guarantees, demonstrating statistical efficiency. Beyond the tabular setting, our framework suggests that value clipping is a modular mechanism that can be incorporated into general value-based RL algorithms with function approximation. As a proof of concept, we evaluate a clipped Double DQN algorithm on a control task and observe robustness improvements consistent with our theoretical predictions.

Deep Learning · Large Language Models

Haoran Zhang, Yafu Li, Zhi Wang, Zhilin Wang, Shunkai Zhang, Xiaoye Qu, Yu Cheng

Large Reasoning Models (LRMs) increasingly rely on reasoning traces with complex internal structures. However, existing work lacks a unified answer to three fundamental questions: (1) what defines high-quality reasoning, (2) how to reliably evaluate long, implicitly structured reasoning traces, and (3) how to use such evaluation signals for reasoning optimization. To address these challenges, we provide a unified perspective. (1) We introduce the ME$^2$ principle to characterize reasoning quality along macro- and micro-level concerning efficiency and effectiveness. (2) Built on this principle, we model reasoning traces as directed acyclic graphs (DAGs) and develop a DAG-based pairwise evaluation method, capturing complex reasoning structures. (3) Based on this method, we construct the TRM-Preference dataset and train a Thinking Reward Model (TRM) to evaluate reasoning quality at scale. Experiments show that thinking rewards serve as an effective optimization signal. At test time, selecting better reasoning leads to better outcomes (up to 19.3\% gain), and during RL training, thinking rewards enhance reasoning and performance (up to 3.9\% gain) across diverse tasks. Code is available in the supplementary material.

Deep Learning · Generative Models and Autoencoders

Qijie Zhu, Zeqi Ye, Han Liu, Zhaoran Wang, Minshuo Chen

Adaptation methods have been a workhorse for unlocking the transformative power of pre-trained diffusion models in diverse applications. Existing approaches often abstract adaptation objectives as a reward function and steer diffusion models to generate high-reward samples. However, these approaches can incur high computational overhead due to additional training, or rely on stringent assumptions on the reward such as differentiability. Moreover, despite their empirical success, theoretical justification and guarantees are seldom established. In this paper, we propose $\texttt{DOIT}$ ($\textbf{D}$oob-$\textbf{O}$riented $\textbf{I}$nference-time $\textbf{T}$ransformation), a training-free and computationally efficient adaptation method that applies to generic, non-differentiable rewards. The key framework underlying our method is a measure transport formulation that seeks to transport the pre-trained generative distribution to a high-reward target distribution. We leverage Doob's $h$-transform to realize this transport, which induces a dynamic correction to the diffusion sampling process and enables efficient simulation-based computation without modifying the pre-trained model. Theoretically, we establish a high probability convergence guarantee to the target high-reward distribution via characterizing the approximation error in the dynamic Doob's correction. Empirically, on D4RL offline RL benchmarks, our method consistently outperforms state-of-the-art baselines while preserving sampling efficiency.

Deep Learning · Large Language Models

Haoran Zhang, Yafu Li, Zhi Wang, Zhilin Wang, Shunkai Zhang, Xiaoye Qu, Yu Cheng

Large Reasoning Models (LRMs) increasingly rely on reasoning traces with complex internal structures. However, existing work lacks a unified answer to three fundamental questions: (1) what defines high-quality reasoning, (2) how to reliably evaluate long, implicitly structured reasoning traces, and (3) how to use such evaluation signals for reasoning optimization. To address these challenges, we provide a unified perspective. (1) We introduce the ME$^2$ principle to characterize reasoning quality along macro- and micro-level concerning efficiency and effectiveness. (2) Built on this principle, we model reasoning traces as directed acyclic graphs (DAGs) and develop a DAG-based pairwise evaluation method, capturing complex reasoning structures. (3) Based on this method, we construct the TRM-Preference dataset and train a Thinking Reward Model (TRM) to evaluate reasoning quality at scale. Experiments show that thinking rewards serve as an effective optimization signal. At test time, selecting better reasoning leads to better outcomes (up to 19.3\% gain), and during RL training, thinking rewards enhance reasoning and performance (up to 3.9\% gain) across diverse tasks. Code is available in the supplementary material.