Daily Papers

Scientific discovery requires developing worthwhile hypotheses into practical investigations, yet learning from this evolving research process remains challenging. We introduce an operational definition of valuable and testable research hypotheses: evidence-grounded claims about consequential uncertainties, coupled with feasible investigations, explicit decision criteria, and alternative explanations. Our DiscoveryRSI framework develops hypothesis trees through multi-agent evolutionary search, compiles selected investigations into executable Harbor tasks, and recursively learns through three mechanisms: hypothesis credit optimization attributes scientific assessments to documented research contributions; harness replay identifies productive strategies and recurring failures to refine research workflows; and rediscovery applies accepted improvements to new investigations, generating further experience for subsequent learning. We also introduce DFM-Bench, which provides comprehensive assessment of hypothesis quality and cumulative research progress at the levels of hypotheses, revisions, development paths and research runs. Across four life-science domains, automated evaluation shows that hypothesis quality rises from 4.86 for the base model to 5.39 after two rounds of self-improvement, with the large gains in falsifiability and data resolvability. We further validate hypothesis quality through expert review, comparing our DiscoveryRSI-27B with other research agents. Preliminary human assessments show that DiscoveryRSI-27B scores higher than GPT-6 Luna on hypothesis importance and whether claims are plausible and evidence-bounded. DiscoveryRSI-27B achieved a 6.3% rate of hypothesis correspondence with research published after the model cutoff, largely outperform GPT-6 with 2.5% and Claude Opus 5 with 2.3%, while delivering greater human-rated improvement along research paths.

Collaborative multi-agent large language models (LLMs) can solve complex reasoning tasks by decomposing roles, but reinforcement learning for such systems is limited by credit assignment: shared terminal rewards obscure individual contributions and can encourage free-riding. We introduce Collaborative Credit Policy Optimization (CCPO), an optimizer-agnostic credit assignment layer that converts team-level outcomes into agent-specific learning signals. CCPO provides two complementary allocators. Counterfactual credit estimates an agent's marginal contribution by comparing the realized team outcome with a counterfactual outcome where that agent is removed. Verifier-anchored LLM self-evaluation is an exploratory allocator that uses constrained self- and peer-evaluations to redistribute credit while keeping the external verifier outcome dominant. The resulting role-specific rewards can be consumed by GRPO-style updates or other policy-gradient optimizers such as GSPO and REINFORCE++. We instantiate CCPO in a sequential Think--Solve setting and evaluate it on mathematical reasoning benchmarks. Results show that explicit credit assignment often improves dual-agent reasoning, especially on MATH500 and several out-of-distribution settings, while gains vary across models and datasets.

Credit risk modeling relies extensively on Weight of Evidence (WoE) and Information Value (IV) for feature engineering, and Population Stability Index (PSI) for drift monitoring, yet their theoretical foundations remain disconnected. We establish a unified information-theoretic framework revealing these industry-standard metrics as instances of classical information divergences. Specifically, we prove that IV exactly equals PSI (Jeffreys divergence) computed between good and bad credit outcomes over identical bins. Through the delta method applied to WoE transformations, we derive standard errors for IV and PSI, enabling formal hypothesis testing and probabilistic fairness constraints for the first time. We formalize credit modeling's inherent performance-fairness trade-off as maximizing IV for predictive power while minimizing IV for protected attributes. Using automated binning with depth-1 XGBoost stumps, we compare three encoding strategies: logistic regression with one-hot encoding, WoE transformation, and constrained XGBoost. All methods achieve comparable predictive performance (AUC 0.82-0.84), demonstrating that principled, information-theoretic binning outweighs encoding choice. Mixed-integer programming traces Pareto-efficient solutions along the performance-fairness frontier with uncertainty quantification. This framework bridges theory and practice, providing the first rigorous statistical foundation for widely-used credit risk metrics while offering principled tools for balancing accuracy and fairness in regulated environments.

Reinforcement learning with verifiable rewards scales multimodal reasoning, but an outcome reward says how much a trajectory is worth, not how that value should be spread over the decisions that produced it. We introduce Residual Visual Credit Optimization (RVCO), which treats token credit as a conserved routing problem. A controlled visual intervention yields a per-token evidence response; robust within-trajectory coordinates remove incidental scale; and a budgeted entropic router distributes a fixed amount of sequence utility according to perceptual dependence. A residual support path guarantees positive credit at every valid position, and an analytic correction restores the prescribed credit mass exactly. The resulting field is selective, bounded, full-support, and invariant to response-local score shifts, and recovers hard token selection as a limiting case. Across four model families and seven reasoning benchmarks, RVCO improves accuracy over strong RLVR baselines while maintaining late-stage optimization stability, corruption robustness, and competitive training cost. Rewards, rollouts, and the group-relative advantage estimator are unchanged; only the geometry of token-level credit differs.

Current critic-free RL methods for large reasoning models suffer from severe inefficiency when training on positive homogeneous prompts (where all rollouts are correct), resulting in waste of rollouts due to zero advantage estimates. We introduce a radically simple yet powerful solution to Mine intrinsic mastery (Miner), that repurposes the policy's intrinsic uncertainty as a self-supervised reward signal, with no external supervision, auxiliary models, or additional inference cost. Our method pioneers two key innovations: (1) a token-level focal credit assignment mechanism that dynamically amplifies gradients on critical uncertain tokens while suppressing overconfident ones, and (2) adaptive advantage calibration to seamlessly integrate intrinsic and verifiable rewards. Evaluated across six reasoning benchmarks on Qwen3-4B and Qwen3-8B base models, Miner achieves state-of-the-art performance among the other four algorithms, yielding up to 4.58 absolute gains in Pass@1 and 6.66 gains in Pass@K compared to GRPO. Comparison with other methods targeted at exploration enhancement further discloses the superiority of the two newly proposed innovations. This demonstrates that latent uncertainty exploitation is both necessary and sufficient for efficient and scalable RL training of reasoning models.

Reinforcement Learning with Verifiable Rewards (RLVR) has improved the reasoning abilities of Large Language Models (LLMs) by using rule-based binary feedback, helping to mitigate reward hacking. However, current RLVR methods typically treat whole responses as single actions, assigning the same reward to every token. This coarse-grained feedback hampers precise credit assignment, making it hard for models to identify which reasoning steps lead to success or failure, and often results in suboptimal policies and inefficient learning. Methods like PPO provide credit assignment through value estimation, but often yield inaccurate and unverifiable signals due to limited sampling. On the other hand, methods using Process Reward Models can provide step-by-step judgments for each reasoning step, but they require high-quality process supervision labels and are time-consuming when applied in online reinforcement learning (RL). To overcome these limitations, we introduce a simple but efficient method Credit Assignment Policy Optimization (CAPO). Given a reasoning response rollout from the policy model, CAPO directly leverages an off-the-shelf, general-purpose LLM as a Generative Process Reward Model (LLM-as-GenPRM) to generate all step-wise critique by one pass, thereby providing verifiable token-level rewards to refine the tokens that were originally assigned identical rule-based rewards. This enables more fine-grained credit assignment in an effective way. Furthermore, to enhance the accuracy and robustness of CAPO, we employ voting mechanisms that scale with the number of generated critiques. Extensive experiments using different backbones like Llama and Qwen models and in different sizes show that CAPO consistently outperforms supervised learning-based and RL-based fine-tuning methods across six challenging mathematical benchmarks and three out-of-domain benchmarks.

Scaling test-time compute is crucial for enhancing the reasoning capabilities of large language models (LLMs). Existing approaches typically employ reinforcement learning (RL) to maximize a verifiable reward obtained at the end of reasoning traces. However, such methods optimize only the final performance under a large and fixed token budget, which hinders efficiency in both training and deployment. In this work, we present a novel framework, AnytimeReasoner, to optimize anytime reasoning performance, which aims to improve token efficiency and the flexibility of reasoning under varying token budget constraints. To achieve this, we truncate the complete thinking process to fit within sampled token budgets from a prior distribution, compelling the model to summarize the optimal answer for each truncated thinking for verification. This introduces verifiable dense rewards into the reasoning process, facilitating more effective credit assignment in RL optimization. We then optimize the thinking and summary policies in a decoupled manner to maximize the cumulative reward. Additionally, we introduce a novel variance reduction technique, Budget Relative Policy Optimization (BRPO), to enhance the robustness and efficiency of the learning process when reinforcing the thinking policy. Empirical results in mathematical reasoning tasks demonstrate that our method consistently outperforms GRPO across all thinking budgets under various prior distributions, enhancing both training and token efficiency.

RLVR provides reliable trajectory-level credit, while OPSD offers dense supervision for token-level credit. This exposes a fundamental coupling when updating step-level credit direction and magnitude with teacher supervision, preventing steps from receiving reliable credit directions and contribution magnitudes, while making both vulnerable to teacher judgment errors and preference variance, as supported by our theoretical analysis. To separate credit direction from its contribution magnitude, we introduce Decoupled Credit Self-Distillation (DCSD), which theoretically decouples credit direction and magnitude into two reliable signals and uses them to calibrate privileged teacher supervision. Specifically, we design belief-margin probing to determine credit direction and marginal information gain to quantify credit magnitude, enabling step-to-token credit assignment for policy optimization. Across 11 benchmarks, DCSD achieves the best overall scores against GRPO, OPSD, RLSD, and RLCSD. Compared with base models, DCSD improves the overall score by 8.45 points on mathematical reasoning and 7.01 points on multimodal reasoning, while correcting the credit direction for 6\% of tokens and yielding a 1.5times reduction in token credit magnitude.

This paper proposes a novel reinforcement learning (RL) framework for credit underwriting that tackles ungeneralizable contextual challenges. We adapt RL principles for credit scoring, incorporating action space renewal and multi-choice actions. Our work demonstrates that the traditional underwriting approach aligns with the RL greedy strategy. We introduce two new RL-based credit underwriting algorithms to enable more informed decision-making. Simulations show these new approaches outperform the traditional method in scenarios where the data aligns with the model. However, complex situations highlight model limitations, emphasizing the importance of powerful machine learning models for optimal performance. Future research directions include exploring more sophisticated models alongside efficient exploration mechanisms.

Recent advancements in reasoning language models have been driven by Reinforcement Learning (RL) fine-tuning. Most often, these rely on the Group Relative Policy Optimization (GRPO) algorithm or modifications thereof to steer the models to produce Chain-of-Thought (CoT) traces. The final answer can only be verified, and the reward assigned, after the CoT trace is complete, making it a delayed reward problem. GRPO and its modifications correspond to Monte Carlo methods in standard RL, which are known to suffer from high variance. A possible solution to this problem is the redistribution of rewards through credit assignment, where segments of the CoT trace that are important for arriving at the desirable solution are emphasized by assigning a higher reward. While Monte Carlo sampling can be used to provide an unbiased estimate of intermediate state values, its computational overhead makes it unsuitable for train-time credit assignment in long contexts at high granularity. We introduce RREDCoT (Reward REDistribution for Chain of Thoughts), which utilizes the model itself to approximate the optimal reward redistribution without additional generation. We investigate the advantages of our method compared to MC sampling and several attribution methods. We further analyze several aspects relevant to the construction of the redistribution such as segmentation of CoT traces and state value estimation.

Reinforcement Learning (RL) serves as a potent paradigm for enhancing reasoning capabilities in Large Language Models (LLMs), yet standard outcome-based approaches often suffer from reward sparsity and inefficient credit assignment. In this paper, we propose a novel framework designed to provide continuous reward signals, which introduces a Step-wise Marginal Information Gain (MIG) mechanism that quantifies the intrinsic value of reasoning steps against a Monotonic Historical Watermark, effectively filtering out training noise. To ensure disentangled credit distribution, we implement a Decoupled Masking Strategy, applying process-oriented rewards specifically to the chain-of-thought (CoT) and outcome-oriented rewards to the full completion. Additionally, we incorporate a Dual-Gated SFT objective to stabilize training with high-quality structural and factual signals. Extensive experiments across textual and multi-modal benchmarks (e.g., MATH, Super-CLEVR) demonstrate that our approach consistently outperforms baselines such as GRPO in both sample efficiency and final accuracy. Furthermore, our model exhibits superior out-of-distribution robustness, demonstrating promising zero-shot transfer capabilities to unseen and challenging reasoning tasks.

State-of-the-art reasoning models utilize long chain-of-thought (CoT) to solve increasingly complex problems using more test-time computation. In this work, we explore a long CoT setting where the model makes up to K successive attempts at solving a problem, in which each attempt is allowed to build on earlier ones after the model receives a hard verifier feedback. This motivates RL methods that can harness per-attempt rewards by carefully weighting individual attempts. We study optimizing the Verification@K reward (the model succeeds by the K-th attempt) and show that naively weighing the attempts by their pass/fail results in biased gradients. We introduce Calibrated Attempt-Level (CAL) GRPO by devising a weighing strategy to obtain unbiased gradients while maintaining small variance. Our theory reveals how incorporating per-attempt rewards influence the training and the eventual Verification@K performance. Experiments, baselines, and ablations on synthetic and real data corroborate our theory and the benefits of CAL-GRPO over vanilla GRPO as well as naive weighting.

Reinforcement learning with verifiable rewards improves reasoning, while the allocation of learning signal shapes which solutions remain accessible under repeated sampling. Group-relative objectives assign equal advantages to equally rewarded responses, making aggregate credit proportional to sampled mode frequency. We introduce Exploration-Preserving Policy Optimization (ExPPO), a lightweight advantage-shaping rule that redistributes credit using prompt-relative, length-normalized response surprisal and prompt pass rate. ExPPO combines bounded shaping with shared normalization to preserve verifier polarity and approximately maintain each prompt group's total absolute sequence-advantage mass. Our analysis characterizes response-level credit allocation alongside sampled mode updates, deriving local conditions for gains in entropy and correct-mode discovery. Experiments show improved in-domain and out-of-domain reasoning coverage, higher aggregate response accuracy, and strong coverage at large sampling budgets. A controlled multi-answer evaluation further demonstrates increased correct-mode yield and gains in diversity among verified-correct responses. Code is available at https://github.com/jinhangzhan/ExPPO

Reinforcement learning has become a cornerstone technique for developing reasoning models in complex tasks, ranging from mathematical problem-solving to imaginary reasoning. The optimization of these models typically relies on policy gradient methods, whose efficacy hinges on the accurate estimation of an advantage function. However, prevailing methods typically employ static advantage estimation, a practice that leads to inefficient credit assignment by neglecting the dynamic utility of training samples over time. This limitation results in suboptimal policy updates, which in turn manifest as slower convergence rates and increased learning instability, as models fail to adapt to evolving sample utilities effectively. To address this problem, we introduce ADORA (Advantage Dynamics via Online Rollout Adaptation), a novel framework for policy optimization. ADORA dynamically adjusts the advantage function's weighting by adaptively categorizing training data into temporarily advantageous and disadvantageous samples, based on their evolving utility during online model rollouts. This tailored data differentiation strategy allows ADORA to be seamlessly integrated into existing policy optimization algorithms without significant architectural modifications, enabling the policy to prioritize learning from more informative experiences and thereby achieve more efficient policy updates. Extensive evaluations across diverse model families and varying data scales demonstrate that ADORA is a robust and efficient framework. It significantly enhances long reasoning in both geometric and mathematical tasks, consistently achieving notable performance gains without requiring sensitive hyperparameter tuning.

Agentic multimodal models perform diverse operations on an image via code and reason over the returned view, an effective paradigm for fine-grained visual question answering. However, code operations can be useful, redundant, or misleading. Outcome-only rewards cannot precisely distinguish these cases, and existing process rewards either fail to attribute final correctness to individual tool calls, or require an external judge model. To address this, we introduce Tool-Augmented Credit Optimization (TACO), a GRPO variant for code-tool agents built on two coupled advantage channels. The first, Differential Answer-Probe Reward (DAPR), is a self-supervised, judge-free tool-contribution advantage that credits each tool call by its own effect on answering correctly. Probe tokens inserted into the model's reasoning elicit its predictions with and without the tool, and the difference in outcome reward is taken as the call's value: positive for a useful call, negative for a misleading one, and zero for one that changes nothing. This reuses the existing answer checker with no auxiliary judge, and, being a difference rather than an absolute probe score, is naturally robust to probe-hacking. The second is the outcome advantage from the final answer, distributed by Outcome-Gated Advantage Routing (OGAR): a parameter-free rule that, conditioned on the call's outcome, delivers this credit only to the responsible segments, suppressing wasted tool calls without any cost term. We train TACO through a two-stage SFT+RL pipeline. Extensive experiments across perception, reasoning, and general multimodal benchmarks show that it yields consistent accuracy gains and learns to invoke its tools only when they help.

We propose a criterion for discrimination against a specified sensitive attribute in supervised learning, where the goal is to predict some target based on available features. Assuming data about the predictor, target, and membership in the protected group are available, we show how to optimally adjust any learned predictor so as to remove discrimination according to our definition. Our framework also improves incentives by shifting the cost of poor classification from disadvantaged groups to the decision maker, who can respond by improving the classification accuracy. In line with other studies, our notion is oblivious: it depends only on the joint statistics of the predictor, the target and the protected attribute, but not on interpretation of individualfeatures. We study the inherent limits of defining and identifying biases based on such oblivious measures, outlining what can and cannot be inferred from different oblivious tests. We illustrate our notion using a case study of FICO credit scores.

Large Language Models (LLMs) in multi-agent systems (MAS) have shown promise for complex tasks, yet current training methods lack principled ways to connect system-level evaluation with agent- and message-level learning. We propose a theoretical framework that unifies cooperative game-theoretic attribution with process reward modeling to transform system evaluation to agent credit to response-level signals. Unlike prior approaches that rely only on attribution (Shapley) or step-level labels (PRM), our method produces local, signed, and credit-conserving signals. In success cases, Shapley-based credit assignment fairly allocates outcomes across agents and is refined into per-message rewards that promote cooperation while discouraging redundancy or sabotage; in failure cases, first-error localization yields repair-aware preferences that penalize harmful steps while rewarding corrective attempts. The resulting signals are bounded, cooperative, and directly compatible with reinforcement- or preference-based post-training, providing a unified and auditable pathway from global evaluation to local supervision in LLM multi-agent training. Our contribution is conceptual: we present a theoretical foundation and training signals, leaving empirical validation for future work.

Machine learning models are increasingly used to automate decisions that affect humans - deciding who should receive a loan, a job interview, or a social service. In such applications, a person should have the ability to change the decision of a model. When a person is denied a loan by a credit score, for example, they should be able to alter its input variables in a way that guarantees approval. Otherwise, they will be denied the loan as long as the model is deployed. More importantly, they will lack the ability to influence a decision that affects their livelihood. In this paper, we frame these issues in terms of recourse, which we define as the ability of a person to change the decision of a model by altering actionable input variables (e.g., income vs. age or marital status). We present integer programming tools to ensure recourse in linear classification problems without interfering in model development. We demonstrate how our tools can inform stakeholders through experiments on credit scoring problems. Our results show that recourse can be significantly affected by standard practices in model development, and motivate the need to evaluate recourse in practice.

Credit assignment, the process of attributing credit or blame to individual agents for their contributions to a team's success or failure, remains a fundamental challenge in multi-agent reinforcement learning (MARL), particularly in environments with sparse rewards. Commonly-used approaches such as value decomposition often lead to suboptimal policies in these settings, and designing dense reward functions that align with human intuition can be complex and labor-intensive. In this work, we propose a novel framework where a large language model (LLM) generates dense, agent-specific rewards based on a natural language description of the task and the overall team goal. By learning a potential-based reward function over multiple queries, our method reduces the impact of ranking errors while allowing the LLM to evaluate each agent's contribution to the overall task. Through extensive experiments, we demonstrate that our approach achieves faster convergence and higher policy returns compared to state-of-the-art MARL baselines.

Group-advantage-based reinforcement learning methods, such as GRPO and DAPO, have demonstrated strong performance across diverse domains, including mathematical reasoning and text-to-image generation. However, their reliance on sample-level rewards introduces a key limitation as uniform credit assignment across all tokens fails to capture fine-grained, token-level contributions. To address this issue, we propose Guidance Contrastive Policy Optimization (GCPO), a novel algorithm that enables per-token credit assignment by contrasting model predictions under positive and negative prompts. Rather than uniformly broadcasting sample-level advantages, GCPO assigns token-level advantages proportional to the difference between these contrastive predictions, allowing more precise and informative learning signals. Empirically, we find that GCPO emphasizes semantically relevant regions such as visual areas aligned with textual prompts in text-to-image generation, and critical keywords within reasoning traces for chain-of-thought tasks. Through extensive experiments, GCPO consistently outperforms GRPO and DAPO baselines on both text-to-image generation and chain-of-thought reasoning benchmarks, demonstrating its effectiveness as a general and scalable optimization strategy for discrete policy learning.

Credit and risk assessments are cornerstones of the financial landscape, impacting both individual futures and broader societal constructs. Existing credit scoring models often exhibit limitations stemming from knowledge myopia and task isolation. In response, we formulate three hypotheses and undertake an extensive case study to investigate LLMs' viability in credit assessment. Our empirical investigations unveil LLMs' ability to overcome the limitations inherent in conventional models. We introduce a novel benchmark curated for credit assessment purposes, fine-tune a specialized Credit and Risk Assessment Large Language Model (CALM), and rigorously examine the biases that LLMs may harbor. Our findings underscore LLMs' potential in revolutionizing credit assessment, showcasing their adaptability across diverse financial evaluations, and emphasizing the critical importance of impartial decision-making in the financial sector. Our datasets, models, and benchmarks are open-sourced for other researchers.

Reinforcement learning (RL) for large language models (LLMs) increasingly relies on sparse, outcome-level rewards -- yet determining which actions within a long trajectory caused the outcome remains difficult. This credit assignment (CA) problem manifests in two regimes: reasoning RL, where credit must be distributed across tokens and steps within a single chain-of-thought generation (500--30K+ tokens); and agentic RL, where multi-turn environment interaction introduces stochastic transitions, partial observability, and horizons of 100+ turns (100K--1M tokens), making episode-level credit increasingly uninformative. We survey 47 CA methods (41 core, 6 adjacent enablers) published between 2024 and early 2026, organizing them in a two-dimensional taxonomy by assignment granularity (token, segment, step, turn, multi-agent) and methodology (Monte Carlo, temporal difference, model-based, game-theoretic, information-theoretic). Beyond the survey itself, we contribute three reusable resources: (1) a structured, machine-readable paper inventory with taxonomy labels, baseline families, and evidence levels; (2) a reporting checklist for future CA papers, validated against the reviewed literature to identify systematic methodological gaps; and (3) a benchmark protocol specification with task families, metadata requirements, and controlled bifurcation tasks, accompanied by a method selection decision tree. Our synthesis suggests that the shift from reasoning to agentic RL complicates and reshapes the credit assignment landscape: reasoning CA is maturing around process reward models and critic-free group comparison, while agentic CA is driving genuinely new approaches -- hindsight counterfactual analysis, privileged asymmetric critics, and turn-level MDP reformulations -- that have no direct precedent in reasoning RL.

Rubric-based reinforcement learning extends reward-driven optimization to open-ended tasks by assigning partial credit to individual response requirements. However, rubric judges can assign a high criterion score even when the information or action it requires is absent from the response, a failure mode we term Vacuous Credit. Such awards persist after the required information is removed and can reverse the sign of a response's GRPO advantage. To address this problem, we introduce MetaRubric, which alternates evidence-aware policy optimization with response-guided rubric adaptation. We construct counterfactual counterparts by changing one task-relevant fact in each prompt. During policy optimization, credit is assigned only when the response contains sufficient evidence to satisfy the required rubric criterion. After each policy-optimization stage, current policy responses guide revisions to original and counterfactual criteria while preserving the meaning of the original prompt's initial rubric as interpreted under each prompt's facts. We also adapt criterion weights at stage boundaries to better address observed policy errors. Across multiple backbones, MetaRubric improves PubMedQA accuracy by 6.00--20.40 percentage points over static-judge GRPO, with further gains on HealthBench-Hard and two multimodal medical benchmarks.

In this work we build a stack of machine learning models aimed at composing a state-of-the-art credit rating and default prediction system, obtaining excellent out-of-sample performances. Our approach is an excursion through the most recent ML / AI concepts, starting from natural language processes (NLP) applied to economic sectors' (textual) descriptions using embedding and autoencoders (AE), going through the classification of defaultable firms on the base of a wide range of economic features using gradient boosting machines (GBM) and calibrating their probabilities paying due attention to the treatment of unbalanced samples. Finally we assign credit ratings through genetic algorithms (differential evolution, DE). Model interpretability is achieved by implementing recent techniques such as SHAP and LIME, which explain predictions locally in features' space.

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative objectives, such as GRPO, summarize each sampled group with scalar statistics and therefore discard fine-grained relational information among candidate responses. This weakens credit assignment under sparse outcome rewards, especially when multiple generated solutions differ only subtly in reasoning quality. We propose LamPO, a Lambda-Style Policy Optimization method that replaces scalar group advantages with a Pairwise Decomposed Advantage. LamPO aggregates pairwise reward gaps within each response group and modulates each comparison by a confidence-aware weight computed from sequence log-probability differences, while retaining the critic-free and clipped-update structure of PPO-style optimization. When reference solutions are available, we further add a lightweight ROUGE-L-based dense auxiliary reward to reduce reward sparsity. Experiments on AIME24, AIME25, MATH-500, and GPQA-Diamond with Qwen3-1.7B, Qwen3-4B, and Phi-4-mini show that LamPO consistently improves over GRPO and recent RLVR variants, with more stable training dynamics and better sample efficiency.

Combinatorial optimization (CO) problems are often NP-hard and thus out of reach for exact algorithms, making them a tempting domain to apply machine learning methods. The highly structured constraints in these problems can hinder either optimization or sampling directly in the solution space. On the other hand, GFlowNets have recently emerged as a powerful machinery to efficiently sample from composite unnormalized densities sequentially and have the potential to amortize such solution-searching processes in CO, as well as generate diverse solution candidates. In this paper, we design Markov decision processes (MDPs) for different combinatorial problems and propose to train conditional GFlowNets to sample from the solution space. Efficient training techniques are also developed to benefit long-range credit assignment. Through extensive experiments on a variety of different CO tasks with synthetic and realistic data, we demonstrate that GFlowNet policies can efficiently find high-quality solutions.

Reinforcement learning with verifiable rewards (RLVR) enhances reasoning in large language models (LLMs) through outcome-level feedback, yet recent approaches to finer-grained credit assignment often require auxiliary models, additional sampling, or privileged information. Although policy entropy provides a readily available signal, prioritizing uncertain positions under both reinforcement and penalization concentrates penalties where failed responses still retain alternatives for recovery, which can suppress opportunities for exploration. To address this, we introduce Entropic Advantage Policy Optimization (EAPO), an entropy-guided credit assignment method that treats success and failure asymmetrically. Specifically, motivated by the observation that success under uncertainty is less repeatable while confident failures tend to recur, EAPO couples normalized policy entropy with the sign of the response advantage to reinforce surprising success and correct repeated failure. It assigns stronger reinforcement to high-entropy decisions in successful responses and stronger penalties to low-entropy decisions in failed responses, while attenuating penalties at uncertain positions to preserve opportunities for recovery. By redistributing the response advantage across tokens, EAPO derives token-level credit directly from existing rollout signals without additional supervision. We validate EAPO on a range of reasoning tasks across both base and reasoning backbones, demonstrating that it achieves the best overall performance. We further show that EAPO promotes more effective exploration, broadening problem coverage and generating more diverse candidate answers.

Agentic reinforcement learning requires assigning credit to environment-facing actions such as searches, clicks, edits, navigation commands, and object interactions. Standard GRPO uses the final verifier outcome as a uniform advantage over all action tokens. This outcome signal is useful but structurally incomplete: it punishes useful exploration in failed rollouts and reinforces redundant or regressive actions in successful rollouts. We propose TRIAGE, a role-typed credit assignment framework that adds a semantic role axis to outcome credit. A structured judge classifies each segment as decisive progress, useful exploration, no-progress infrastructure, or regression, and a fixed role-conditioned rule maps these labels to bounded segment-level process rewards. This keeps verifier outcomes as the source of optimization direction while correcting the two main blind spots of outcome-only credit. We further show that role-conditioned credit is the optimal segment-level correction expressible from role labels alone -- a projection of the per-segment advantage residual onto the role variable -- so that the fixed role constants reduce advantage estimation error whenever the judge is reliable, and we connect this to lower-variance policy gradients. Across ALFWorld, Search-QA, and WebShop, TRIAGE improves success rates over GRPO for two policy models and outperforms both a scalar judge-derived process reward and an outcome-supervised shared-backbone value baseline. Ablations show that the gain comes from role typing rather than merely adding dense rewards: reliable detection of regression inside successful trajectories is the dominant contributor, while exploration credit provides a consistent secondary gain; on completed ALFWorld and WebShop rollouts, TRIAGE also reduces environment-facing turns by an additional 10.4% and 14.8% relative to GRPO.

Large Language Model (LLM)-based search agents trained with reinforcement learning (RL) have significantly improved the performance of knowledge-intensive tasks. However, existing methods encounter critical challenges in long-horizon credit assignment: (i) Reward Sparsity, where models receive only outcome feedback without step-level guidance to differentiate action quality; (ii) Isolated Credit, where credit is assigned to steps independently, failing to capture sequential dependencies; and (iii) Distributional Shift, where rewards are estimated on templates that deviate from the model's natural generative distribution. To address these issues, we propose Pivot-Based Credit Assignment (PiCA), a novel step reward mechanism that reformulates the search trajectory as a sequential process of cumulative search progress. Unlike prior isolated step rewards, PiCA defines process rewards as success probabilities dependent on the historical context based on Potential-Based Reward Shaping (PBRS). This approach identifies pivot steps, which comprise target golden sub-queries and sub-answers derived from historical trajectories, as information peaks that significantly boost the likelihood of a correct final answer. By anchoring these step rewards to the final task objective, PiCA provides dense, pivot-aware and trajectory-dependent guidance while maintaining distributional consistency. Extensive experiments show that PiCA outperforms existing strong baselines across seven knowledge-intensive QA benchmarks, achieving 15.2% and 2.2% improvements for 3B and 7B models. The consistent performance gains across various models show PiCA's robust generalization. The code is available at https://github.com/novdream/PiCA.

Contemporary reinforcement learning with verifiable reward methods post-train language models on multi-step reasoning by assigning a single outcome reward uniformly across all tokens in a trajectory. Such uniform assignment ignores which steps contributed to success or failure. Improving credit assignment can address this limitation by enabling targeted refinement of faulty reasoning steps, rather than updating entire trajectories uniformly. Resets are one such simple mechanism, enabling more precise credit assignment by returning to an intermediate state and resampling counterfactual continuations, so that outcome differences can be attributed to decisions made at that point. We propose two such methods: Random-Reset Policy Optimization (RRPO), where reset states are drawn randomly from reasoning steps, and Self-Reset Policy Optimization (SRPO), where the model self-localizes the erroneous step in an incorrect trajectory and resets there. We analyze these methods within the Conservative Policy Iteration (CPI) framework. Extending CPI with a credit-assignment oracle that targets improvable states yields provable improvements over random resets. Across models and reasoning benchmarks, SRPO consistently outperforms standard GRPO and RRPO by sampling multiple suffix continuations at a self-localized reset and learning from their rewards, using only the model itself with no external supervision.

Current reinforcement learning from human feedback (RLHF) pipelines for large language model (LLM) alignment typically assign scalar rewards to sequences, using the final token as a surrogate indicator for the quality of the entire sequence. However, this leads to sparse feedback and suboptimal token-level credit assignment. In this work, we frame reward shaping as an optimization problem focused on token-level credit assignment. We propose a reward-shaping function leveraging explainability methods such as SHAP and LIME to estimate per-token rewards from the reward model. To learn parameters of this shaping function, we employ a bilevel optimization framework that integrates Bayesian Optimization and policy training to handle noise from the token reward estimates. Our experiments show that achieving a better balance of token-level reward attribution leads to performance improvements over baselines on downstream tasks and finds an optimal policy faster during training. Furthermore, we show theoretically that explainability methods that are feature additive attribution functions maintain the optimal policy as the original reward.

Large reasoning models (LRMs) have recently shown promise in solving complex math problems when optimized with Reinforcement Learning (RL). But conventional approaches rely on outcome-only rewards that provide sparse feedback, resulting in inefficient optimization process. In this work, we investigate the function of process reward models (PRMs) to accelerate the RL training for LRMs. We propose a novel intrinsic signal-driven generative process evaluation mechanism operating at the thought level to address major bottlenecks in RL-based training. Specifically, instead of requiring PRMs to know how to solve problems, our method uses intrinsic signals in solutions to judge stepwise correctness and aggregate contiguous correct/incorrect steps into coherent 'thought' units. This structured, thought-level rewards enable more reliable credit assignment by reducing ambiguity in step segmentation and alleviating reward hacking. We further introduce a capability-adaptive reward mechanism that dynamically balances exploration and exploitation based on the LRM's current proficiency, guiding learning without stifling creative trial-and-error. These innovations are integrated into a new off-policy RL algorithm, TP-GRPO, which extends grouped proximal optimization with process-based rewards and improves training efficiency. Experiments on 1.5B and 7B parameter LRMs demonstrate that our method achieves higher problem-solving accuracy with significantly fewer training samples than outcome-only reward baselines. The results validate that well-structured process rewards can substantially accelerate LRM optimization in math reasoning tasks. Code is available at https://github.com/cs-holder/tp_grpo.

Credit assignment is a central challenge in reinforcement learning (RL). Classical actor-critic methods address this challenge through fine-grained advantage estimation based on a learned value function. However, learned value models are often avoided in modern large language model (LLM) RL because conventional discriminative critics are difficult to train reliably. We revisit value modeling and argue that this difficulty is partly due to limited expressiveness. In particular, representation complexity theory suggests that value functions can be hard to approximate under the one-shot prediction paradigm used by existing value models, and our scaling experiments show that such critics do not improve reliably with scale. Motivated by this observation, we propose Generative Actor-Critic (GenAC), which replaces one-shot scalar value prediction with a generative critic that performs chain-of-thought reasoning before producing a value estimate. We further introduce In-Context Conditioning, which helps the critic remain calibrated to the current actor throughout training. GenAC improves value approximation, ranking reliability, and out-of-distribution generalization, and these gains translate into stronger downstream RL performance than both value-based and value-free baselines. Overall, our results suggest that stronger value modeling is a promising direction for improving credit assignment in LLM reinforcement learning.

Outcome-reward reinforcement learning (RL) has proven effective at improving the reasoning capabilities of large language models (LLMs). However, standard RL assigns credit only at the level of the final answer, penalizing entire reasoning traces when the outcome is incorrect and uniformly reinforcing all steps when it is correct. As a result, correct intermediate steps may be discouraged in failed traces, while spurious steps may be reinforced in successful ones. We refer to this failure mode as the problem of credit assignment. While a natural remedy is to train a process reward model, accurately optimizing such models to identify corrective reasoning steps remains challenging. We introduce Intervention Training (InT), a training paradigm in which the model performs fine-grained credit assignment on its own reasoning traces by proposing short, targeted corrections that steer trajectories toward higher reward. Using reference solutions commonly available in mathematical reasoning datasets and exploiting the fact that verifying a model-generated solution is easier than generating a correct one from scratch, the model identifies the first error in its reasoning and proposes a single-step intervention to redirect the trajectory toward the correct solution. We then apply supervised fine-tuning (SFT) to the on-policy rollout up to the point of error concatenated with the intervention, localizing error to the specific step that caused failure. We show that the resulting model serves as a far better initialization for RL training. After running InT and subsequent fine-tuning with RL, we improve accuracy by nearly 14% over a 4B-parameter base model on IMO-AnswerBench, outperforming larger open-source models such as gpt-oss-20b.

Reinforcement Learning with Verifiable Rewards (RLVR) elicits long chain-of-thought reasoning in large language models (LLMs), but outcome-based rewards lead to coarse-grained advantage estimation. While existing approaches improve RLVR via token-level entropy or sequence-level length control, they lack a semantically grounded, step-level measure of reasoning progress. As a result, LLMs fail to distinguish necessary deduction from redundant verification: they may continue checking after reaching a correct solution and, in extreme cases, overturn a correct trajectory into an incorrect final answer. To remedy the lack of process supervision, we introduce a training-free probing mechanism that extracts intermediate confidence and correctness and combines them into a Step Potential signal that explicitly estimates the reasoning state at each step. Building on this signal, we propose Step Potential Advantage Estimation (SPAE), a fine-grained credit assignment method that amplifies potential gains, penalizes potential drops, and applies penalty after potential saturates to encourage timely termination. Experiments across multiple benchmarks show SPAE consistently improves accuracy while substantially reducing response length, outperforming strong RL baselines and recent efficient reasoning and token-level advantage estimation methods. The code is available at https://github.com/cii030/SPAE-RL.

Large language models (LLMs) are increasingly applied to complex reasoning tasks that require executing several complex steps before receiving any reward. Properly assigning credit to these steps is essential for enhancing model performance. Proximal Policy Optimization (PPO), a state-of-the-art reinforcement learning (RL) algorithm used for LLM finetuning, employs value networks to tackle credit assignment. However, value networks face challenges in predicting the expected cumulative rewards accurately in complex reasoning tasks, often leading to high-variance updates and suboptimal performance. In this work, we systematically evaluate the efficacy of value networks and reveal their significant shortcomings in reasoning-heavy LLM tasks, showing that they barely outperform a random baseline when comparing alternative steps. To address this, we propose VinePPO, a straightforward approach that leverages the flexibility of language environments to compute unbiased Monte Carlo-based estimates, bypassing the need for large value networks. Our method consistently outperforms PPO and other RL-free baselines across MATH and GSM8K datasets with fewer gradient updates (up to 9x), less wall-clock time (up to 3.0x). These results emphasize the importance of accurate credit assignment in RL finetuning of LLM and demonstrate VinePPO's potential as a superior alternative.

Reinforcement learning (RL) is a pivotal task for enhancing Large Language Model (LLM) reasoning. Conventional algorithms, however, typically adhere to a coarse-grained credit assignment paradigm, applying a uniform reward to all tokens in a sequence, a critical flaw in long-chain reasoning tasks. In this paper, we address this challenge and propose Dynamic Entropy Weighting, a novel mechanism that facilitates fine-grained rewards through two new algorithms: Group Token Policy Optimization (GTPO), which assigns an entropy-weighted reward to each token, and the analogous algorithm Sequence-Level GRPO (GRPO-S). Our approach is founded on the hypothesis that high policy entropy within a reasoning path is a powerful heuristic for cognitive effort at pivotal junctures, which can be repurposed into a learning signal. By repurposing policy entropy for reward shaping, we achieve true per-token credit assignment. Experimental results across challenging reasoning benchmarks validate the superiority of our approach, showing our methods significantly outperform a strong DAPO baseline and confirming our entropy-weighting mechanism as the key driver of this performance boost.

On-policy self-distillation has emerged as a promising paradigm for post-training language models, in which the model conditions on environment feedback to serve as its own teacher, providing dense token-level rewards without external teacher models or step-level annotations. Despite its empirical success, what this reward actually measures and what kind of credit it assigns remain unclear. Under a posterior-compatibility interpretation of feedback conditioning, standard in the implicit-reward literature, we show that the self-distillation token reward is a Bayesian filtering increment whose trajectory sum is exactly the pointwise mutual information between the response and the feedback given the input. This pMI can be raised by input-specific reasoning or by input-generic shortcuts, so we further decompose the teacher log-probability along the input axis. Based on this analysis, we propose CREDIT (Contrastive REward from DIsTillation), which isolates the input-specific component with a batch-contrastive baseline. At the sequence level, CREDIT is a teacher-side surrogate for a contrastive pMI objective that also penalizes responses remaining likely under unrelated inputs. Across coding, scientific reasoning, and tool-use benchmarks on two model families, CREDIT delivers the strongest aggregate performance at negligible additional compute.

Despite the strong performance achieved by reinforcement learning-trained information-seeking agents, learning in open-ended web environments remains severely constrained by low signal-to-noise feedback. Text-based parsers often discard layout semantics and introduce unstructured noise, while long-horizon training typically relies on sparse outcome rewards that obscure which retrieval actions actually matter. We propose a visual-native search framework that represents webpages as visual snapshots, allowing agents to leverage layout cues to quickly localize salient evidence and suppress distractors. To learn effectively from these high-dimensional observations, we introduce Information-Aware Credit Assignment (ICA), a post-hoc method that estimates each retrieved snapshot's contribution to the final outcome via posterior analysis and propagates dense learning signals back to key search turns. Integrated with a GRPO-based training pipeline, our approach consistently outperforms text-based baselines on diverse information-seeking benchmarks, providing evidence that visual snapshot grounding with information-level credit assignment alleviates the credit-assignment bottleneck in open-ended web environments. The code and datasets will be released in https://github.com/pc-inno/ICA_MM_deepsearch.git.

Recent advancements in the Generative Reward Model (GRM) have demonstrated its potential to enhance the reasoning abilities of LLMs through Chain-of-Thought (CoT) prompting. Despite these gains, existing implementations of GRM suffer from two critical limitations. First, CoT prompting is applied indiscriminately to all inputs regardless of their inherent complexity. This introduces unnecessary computational costs for tasks amenable to fast, direct inference. Second, existing approaches primarily rely on voting-based mechanisms to evaluate CoT outputs, which often lack granularity and precision in assessing reasoning quality. In this paper, we propose E-GRM, an efficient generative reward modeling framework grounded in model-internal uncertainty. E-GRM leverages the convergence behavior of parallel model generations to estimate uncertainty and selectively trigger CoT reasoning only when needed, without relying on handcrafted features or task-dependent signals. To improve reward fidelity, we introduce a lightweight discriminative scorer trained with a hybrid regression--ranking objective to provide fine-grained evaluation of reasoning paths. Experiments on multiple reasoning benchmarks show that E-GRM substantially reduces inference cost while consistently improving answer accuracy, demonstrating that model-internal uncertainty is an effective and general signal for efficient reasoning-aware reward modeling.

Evolving borrower behaviors, shifting economic conditions, and changing regulatory landscapes continuously reshape the data distributions underlying modern credit-scoring systems. Conventional explainability techniques, such as SHAP, assume static data and fixed background distributions, making their explanations unstable and potentially unfair when concept drift occurs. This study addresses that challenge by developing adaptive explanation frameworks that recalibrate interpretability and fairness in dynamically evolving credit models. Using a multi-year credit dataset, we integrate predictive modeling via XGBoost with three adaptive SHAP variants: (A) per-slice explanation reweighting that adjusts for feature distribution shifts, (B) drift-aware SHAP rebaselining with sliding-window background samples, and (C) online surrogate calibration using incremental Ridge regression. Each method is benchmarked against static SHAP explanations using metrics of predictive performance (AUC, F1), directional and rank stability (cosine, Kendall tau), and fairness (demographic parity and recalibration). Results show that adaptive methods, particularly rebaselined and surrogate-based explanations, substantially improve temporal stability and reduce disparate impact across demographic groups without degrading predictive accuracy. Robustness tests, including counterfactual perturbations, background sensitivity analysis, and proxy-variable detection, confirm the resilience of adaptive explanations under real-world drift conditions. These findings establish adaptive explainability as a practical mechanism for sustaining transparency, accountability, and ethical reliability in data-driven credit systems, and more broadly, in any domain where decision models evolve with population change.

Traditional retrieval pipelines optimize utility through stages of candidate retrieval and reranking, where ranking operates over a predefined candidate set. Large Language Models (LLMs) broaden this into a generative process: given a candidate pool, an LLM can generate a subset and order it within a single autoregressive pass. However, this flexibility introduces a new optimization challenge: the model must search a combinatorial output space while receiving utility feedback only after the full ranked list is generated. Because this feedback is defined over the completed sequence, it cannot distinguish whether a poor result arises from failing to generate a relevant subset or from failing to rank that subset correctly. This credit assignment gap makes end-to-end optimization unstable and sample-inefficient. Existing systems often address this by separating candidate generation from ranking. However, such decoupling remains misaligned with downstream utility because ranking is limited by the candidate set it receives. To bridge this gap, we propose a unified framework that performs both within a single autoregressive rollout and optimizes them end-to-end via factorized group-relative policy optimization (F-GRPO). Our framework factorizes the policy into candidate generation and ranking while sharing a single LLM backbone, and jointly trains them with an order-invariant coverage reward and a position-aware utility reward. To address the resulting phase-specific credit assignment problem, we use separate group-relative advantages for generation and ranking within a two-phase sequence-level objective. Across sequential recommendation and multi-hop question answering benchmarks, F-GRPO improves top-ranked performance over GRPO and decoupled baselines, outperforms supervised alternatives, and remains competitive with strong zero-shot rerankers, with no architectural changes at inference time.

In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true one, with precision growing only with the square root of the batch size. A theoretical justification is with the help of stochastic approximation theory. However, the conditions for the validity of this theory are not satisfied in the usual learning rate schedules. Batch processing is also difficult to combine with efficient second-order optimization methods. This proposal is based on another hypothesis: the loss minimum of the training set can be expected to be well-approximated by the minima of its subsets. Such subset minima can be computed in a fraction of the time necessary for optimizing over the whole training set. This hypothesis has been tested with the help of the MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks, optionally extended by training data augmentation. The experiments have confirmed that results equivalent to conventional training can be reached. In summary, even small subsets are representative if the overdetermination ratio for the given model parameter set sufficiently exceeds unity. The computing expense can be reduced to a tenth or less.

Reinforcement learning with verifiable rewards (RLVR) has improved the reasoning capabilities of large language models (LLMs), yet their predictions remain sensitive to task-irrelevant prompt features. We investigate this sensitivity through semifactual prompt interventions that preserve the underlying problem and its answer. Our analysis reveals substantial variation in token-level sensitivity and shows that suppressing high-drift token candidates during decoding improves reasoning accuracy without updating model weights. These findings highlight a limitation of Group Relative Policy Optimization (GRPO), which assigns the same outcome-derived advantage to every response token and may reinforce potential spurious dependence alongside useful reasoning. Motivated by this observation, we introduce Semifactual Credit-Augmented Policy Optimization (SCAPO), a causally inspired variant of GRPO that incorporates semifactual stability into token-level credit assignment. SCAPO measures token probability drift for fixed responses under semifactual interventions and uses normalized stability scores to reduce advantages for relatively unstable tokens during early training, while granting no additional credit for stability alone. On Qwen3-4B-Base and Qwen3-1.7B-Base, SCAPO improves AIME 2024-2026 accuracy over GRPO by 5.63 and 4.17 percentage points, respectively. At both model scales, SCAPO achieves the best results on most evaluated mathematics benchmarks and all evaluated out-of-distribution benchmarks among the compared methods. These results suggest that semifactual stability provides an effective training signal for improving reasoning and generalization through finer-grained credit assignment in RLVR. The code is available at https://github.com/DtYXs/SCAPO.

Rubric-based reinforcement learning enriches language model training by evaluating model outputs against explicit criteria. Yet in GRPO-style pipelines, these structured judgments are reduced to a scalar response-level reward and converted into a response-level advantage, which is broadcast uniformly to all generated tokens. This leaves no explicit mechanism for allocating credit within a response, even when different criteria are grounded in different spans, formatting decisions, or semantic choices. We propose CoRT, a token-level credit weighting method for rubric-conditioned GRPO. Instead of training an auxiliary token scoring model, CoRT uses counterfactual replay to rescore the same sampled response under the original rubric-conditioned prompt and a matched criteria-free prompt. The resulting tokenwise log-likelihood contrasts serve as a proxy for dependence on the rubric context. CoRT maps these contrasts to bounded, response-normalized weights and uses them to redistribute the signed GRPO advantage across tokens, without introducing an auxiliary scorer or changing the response-level reward. Experiments across instruction-tuned models and reward granularities show that CoRT improves over matched response-level GRPO in the vast majority of comparisons, with an average gain of 4.4 percentage points. The method remains competitive with learned token-level credit baselines while avoiding a separate relevance-learning stage. These results suggest that policy-internal counterfactual likelihood contrasts provide an effective training signal for within-response credit allocation while retaining the simplicity and stability of GRPO.

Reinforcement learning drives recent advances in LLM reasoning and agentic capabilities, yet current approaches struggle with both exploration and exploitation. Exploration suffers from low success rates on difficult tasks and high costs of repeated rollouts from scratch. Exploitation suffers from coarse credit assignment and training instability: Trajectory-level rewards penalize valid prefixes for later errors, and failure-dominated groups overwhelm the few positive signals, leaving optimization without constructive direction. To this end, we propose R^3L, Reflect-then-Retry Reinforcement Learning with Language-Guided Exploration, Pivotal Credit, and Positive Amplification. To synthesize high-quality trajectories, R^3L shifts from stochastic sampling to active synthesis via reflect-then-retry, leveraging language feedback to diagnose errors, transform failed attempts into successful ones, and reduce rollout costs by restarting from identified failure points. With errors diagnosed and localized, Pivotal Credit Assignment updates only the diverging suffix where contrastive signals exist, excluding the shared prefix from gradient update. Since failures dominate on difficult tasks and reflect-then-retry produces off-policy data, risking training instability, Positive Amplification upweights successful trajectories to ensure positive signals guide the optimization process. Experiments on agentic and reasoning tasks demonstrate 5\% to 52\% relative improvements over baselines while maintaining training stability. Our code is released at https://github.com/shiweijiezero/R3L.

Reinforcement learning with verifiable rewards (RLVR) enables language models to learn multi-turn interaction with external tools, yet its sparse outcome rewards provide no signal for identifying which intermediate decisions are responsible for success. Branch sampling induces local comparisons among alternative continuations, but existing methods tend to conflate two distinct problems: allocating a fixed rollout budget and translating branch outcomes into token-level credit. We introduce Contrastive Branch Policy Optimization (CBPO), which disentangles these two problems and assigns a dedicated mechanism to each. Generation entropy screens candidate branch positions across the entire response, while path-level and node-level decay distribute a fixed budget across trajectories and positions to prevent exploration from collapsing onto a few paths or adjacent tokens. A parent trajectory together with the branches that share an identical token prefix forms an exact-prefix group, and the reward variation within this controlled group defines the Contrastive Branch Value (CBV), an outcome-based estimate of local decision sensitivity that rescales continuation advantages without altering their sign. When multiple nodes are selected along the same trajectory, CBPO partitions it into non-overlapping credit segments, thereby avoiding duplicated gradients on shared tokens. Requiring only outcome rewards and no process-level annotation, CBPO provides a practical solution for fine-grained credit assignment in tool-integrated agent training. Extensive experiments on ten benchmarks, including five for mathematical reasoning and five for knowledge-intensive search, show that CBPO consistently outperforms state-of-the-art policy-optimization and branch-based methods, attaining the highest macro-average accuracy in both domains and across two model scales.

Being prompted to engage in reasoning has emerged as a core technique for using large language models (LLMs), deploying additional inference-time compute to improve task performance. However, as LLMs increase in both size and adoption, inference costs are correspondingly becoming increasingly burdensome. How, then, might we optimize reasoning's cost-performance tradeoff? This work introduces a novel approach based on computational models of metareasoning used in cognitive science, training LLMs to selectively use intermediate reasoning steps only when necessary. We first develop a reward function that incorporates the Value of Computation by penalizing unnecessary reasoning, then use this reward function with Expert Iteration to train the LLM. Compared to few-shot chain-of-thought prompting and STaR, our method significantly reduces inference costs (20-37\% fewer tokens generated across three models) while maintaining task performance across diverse datasets.

Agent frameworks increasingly package procedural knowledge as skills: instruction files an agent reads on demand, while public libraries now hold thousands of them. Which skill to read has thus become a decision the policy itself makes in the middle of an episode, yet no existing signal trains it. We show that the default remedy, outcome-rewarded RL over the candidate slate, cannot teach it, for a structural reason we identify and name selector credit starvation: under a broadcast, sequence-level advantage, the few tokens that name the chosen skill carry a vanishing share of the loss, and the credit they inherit is increasingly wrong-signed as trajectories lengthen. A correct choice is punished whenever the execution after it fails, even though the choice itself is among the most valuable decisions in the trajectory. Auditing a completed run's own training artifacts confirms all three properties, each worsening monotonically with horizon. SkillGate removes the failure by construction: it partitions the token support into two disjoint credit channels, outcome credit reaching only execution tokens, and a separate action-local advantage reaching exactly the skill-naming tokens, positive only when a trajectory's single read is the correct one. On five agentic benchmarks under a 16-candidate slate, SkillGate lifts a 9B policy from 40.8% to 53.2% trial success, well ahead of the identical budget spent on outcome reward alone, while cutting exposure to misleading candidates by two thirds and reading fewer skills.

Large language models (LLMs) have shown promise in automating scientific hypothesis generation, yet existing approaches primarily yield coarse-grained hypotheses lacking critical methodological and experimental details. We introduce and formally define the novel task of fine-grained scientific hypothesis discovery, which entails generating detailed, experimentally actionable hypotheses from coarse initial research directions. We frame this as a combinatorial optimization problem and investigate the upper limits of LLMs' capacity to solve it when maximally leveraged. Specifically, we explore four foundational questions: (1) how to best harness an LLM's internal heuristics to formulate the fine-grained hypothesis it itself would judge as the most promising among all the possible hypotheses it might generate, based on its own internal scoring-thus defining a latent reward landscape over the hypothesis space; (2) whether such LLM-judged better hypotheses exhibit stronger alignment with ground-truth hypotheses; (3) whether shaping the reward landscape using an ensemble of diverse LLMs of similar capacity yields better outcomes than defining it with repeated instances of the strongest LLM among them; and (4) whether an ensemble of identical LLMs provides a more reliable reward landscape than a single LLM. To address these questions, we propose a hierarchical search method that incrementally proposes and integrates details into the hypothesis, progressing from general concepts to specific experimental configurations. We show that this hierarchical process smooths the reward landscape and enables more effective optimization. Empirical evaluations on a new benchmark of expert-annotated fine-grained hypotheses from recent chemistry literature show that our method consistently outperforms strong baselines.

Chain-of-Thought (CoT) prompting improves LLM accuracy on complex tasks but often increases token usage and inference cost. Existing "Budget Forcing" methods reducing cost via fine-tuning with heuristic length penalties, suppress both essential reasoning and redundant filler. We recast efficient reasoning as a lossy compression problem under the Information Bottleneck (IB) principle, and identify a key theoretical gap when applying naive IB to transformers: attention violates the Markov property between prompt, reasoning trace, and response. To resolve this issue, we model CoT generation under the Conditional Information Bottleneck (CIB) principle, where the reasoning trace Z acts as a computational bridge that contains only the information about the response Y that is not directly accessible from the prompt X. This yields a general Reinforcement Learning objective: maximize task reward while compressing completions under a prior over reasoning traces, subsuming common heuristics (e.g., length penalties) as special cases (e.g., uniform priors). In contrast to naive token-counting-based approaches, we introduce a semantic prior that measures token cost by surprisal under a language model prior. Empirically, our CIB objective prunes cognitive bloat while preserving fluency and logic, improving accuracy at moderate compression and enabling aggressive compression with minimal accuracy drop.

Training large language models to reason with search engines via reinforcement learning is hindered by a fundamental credit assignment problem: existing methods such as Search-R1 provide only a sparse outcome reward after an entire multi-step trajectory, making it infeasible to attribute success or failure to individual reasoning and retrieval decisions. Process-reward methods like StepSearch alleviate this by introducing step-level supervision, but rely on heuristic rewards such as TF-IDF overlap with gold documents, and still sample k complete trajectories per example, retaining high gradient variance. We propose SLATE, a framework built on two complementary ideas: (1) truncated step-level sampling, which generates k trajectories that share a common prefix and differ only at the next step, and (2) dense LLM-as-judge rewards, which replace heuristic scoring with a capable LLM evaluator that assesses the quality of each reasoning step, search query, and answer, providing richer and more reliable supervision. We theoretically prove that under the same dense reward structure, truncated sampling reduces the variance of advantage estimates by up to a factor of T compared to full-trajectory sampling for T-step trajectories, yielding lower-variance, better-targeted policy gradients. Experiments on seven QA benchmarks confirm that SLATE consistently outperforms both sparse-reward and process-reward baselines, with the largest gains on harder multi-hop tasks and smaller models.

Reinforcement learning with verifiable rewards (RLVR) is central to improving long-CoT reasoning in large language models. Critic-free methods such as GRPO convert response-level rewards into advantages and uniformly broadcast them across tokens, overlooking their unequal contributions to the final outcome. On-policy self-distillation (OPSD) instead provides dense distributional supervision by minimizing the forward KL divergence between an unprivileged policy and a privileged self-teacher, implicitly assuming that the resulting likelihood shifts encode reliable answer-aligned information. We test this premise by fixing each sampled trajectory and re-scoring it under two opposing outcome conditions, one asserting correctness and the other incorrectness. Most affected tokens shift in the same direction under both conditions, with few sign reversals and substantial overlap in the induced optimization signals. Large shifts also concentrate on highly substitutable surface-form tokens, whereas tokens carrying problem-specific reasoning content are less sensitive. These findings show that privileged shifts fail to provide reliable answer-aligned directions, while their magnitudes primarily reflect counterfactual sensitivity rather than token-level learning value. Based on these observations, we propose Counterfactual Sensitivity Credit Reallocation (CSCR), a simple extension of GRPO that reduces credit for highly sensitive tokens and renormalizes token-level advantages to preserve both the original credit budget and verifier-determined direction. On long-CoT mathematical reasoning benchmarks, CSCR consistently outperforms GRPO baseline with the same number of policy updates. Targeted ablations further corroborate our diagnosis: privilege-induced directions are unreliable, moderate downweighting is most effective, and stronger modulation destabilizes optimization.

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 and data are available at https://github.com/Simplified-Reasoning/TRM.

Reinforcement Learning with Verifiable Rewards (RLVR) has catalyzed significant breakthroughs in complex LLM reasoning within verifiable domains, such as mathematics and programming. Recent efforts have sought to extend this paradigm to open-ended tasks by employing LLMs-as-a-Judge to provide sequence-level rewards for policy optimization. However, these rewards are inherently sparse, failing to provide the fine-grained supervision necessary for generating complex, long-form trajectories. Furthermore, current work treats the Judge as a black-box oracle, discarding the rich intermediate feedback signals encoded in it. To address these limitations, we introduce Grad2Reward, a novel framework that extracts dense process rewards directly from the Judge's model inference process via a single backward pass. By leveraging gradient-based attribution, Grad2Reward enables precise token-level credit assignment, substantially enhancing training efficiency and reasoning quality. Additionally, Grad2Reward introduces a self-judging mechanism, allowing the policy to improve through its own evaluative signals without training specialized reward models or reliance on superior external Judges. The experiments demonstrate that policies optimized with Grad2Reward achieve outstanding performance across diverse open-ended tasks, affirming its effectiveness and broad generalizability.

Long-horizon agentic tasks pose a fundamental credit assignment challenge for outcome-base reinforcement learning: trajectory-level rewards verify final correctness but provide limited guidance on which intermediate reasoning steps or tool interactions contribute to the outcome. The difficulty is especially pronounced in multi-turn search agents, where successful trajectories may contain misleading actions and failed trajectories may contain valuable evidence-gathering steps. We propose PBSD (Privileged Bayesian Self-Distillation), a Bayes-calibrated self-distillation method for fine-grained credit assignment under sparse final rewards. PBSD measures trajectory quality through the posterior-to-prior probability ratio of the verified answer and applies Bayes' rule to convert this hard-to-estimate answer-side ratio into a tractable likelihood ratio between a standard student model and a privileged answer-conditioned teacher model. Autoregressive decomposition of this Bayesian evidence score yields turn-level signals that identify whether each intermediate turn supports or undermines the verified outcome. Consequently, PBSD provides a principled and elegant reweighting scheme that transforms sparse outcome supervision into Bayes-calibrated turn-level credit signals, while remaining fully compatible with standard policy optimization. Experiments demonstrate that PBSD consistently enhances performance across both in-domain and out-of-domain settings, and effectively transfers knowledge from short-context training to long-context inference, suggesting that its fine-grained credit assignment mechanism facilitates more effective policy learning and yields improved generalization.

Reinforcement learning has become a central component of large language model (LLM) post-training, yet token-level credit lacks a generally accepted mathematical definition, leaving its relationship to commonly used training signals unclear. We formulate three regularity conditions, namely Completeness, Prefix Consistency, and Neutrality, and prove that they uniquely determine token-level credit. This characterization provides a unified basis for explaining phenomena across existing algorithms and guides the development of an improved actor-critic training procedure. Through this lens, an ideal teacher in On-Policy Distillation (OPD) acts as an implicit critic, yielding an expected policy gradient proportional to that induced by token-level credit. Response-level REINFORCE Leave-One-Out (RLOO) signals match the expected policy-gradient contribution of token-level credit despite their coarser granularity. We further establish approximate credit sparsity under bounded outcome rewards and show how intermediate critic errors in Generalized Advantage Estimation (GAE) can become comparable to the underlying credit. These motivate Policy Aligned Critic Training (PACT), which adopts an Actor-then-Critic update order to apply importance sampling correction to critic training and better align the critic with the updated policy. In agentic mathematical reasoning, PACT achieves 72.87% average accuracy across four benchmarks, outperforming GRPO and PPO by 8.80 and 13.16 percentage points, respectively. On SWE-bench Verified, PACT achieves a pass rate of 67.4%, outperforming PPO, GRPO, and SAO by 2.4, 2.0, and 3.8 percentage points, respectively.

The temporal credit assignment problem is a central challenge in Reinforcement Learning (RL), concerned with attributing the appropriate influence to each actions in a trajectory for their ability to achieve a goal. However, when feedback is delayed and sparse, the learning signal is poor, and action evaluation becomes harder. Canonical solutions, such as reward shaping and options, require extensive domain knowledge and manual intervention, limiting their scalability and applicability. In this work, we lay the foundations for Credit Assignment with Language Models (CALM), a novel approach that leverages Large Language Models (LLMs) to automate credit assignment via reward shaping and options discovery. CALM uses LLMs to decompose a task into elementary subgoals and assess the achievement of these subgoals in state-action transitions. Every time an option terminates, a subgoal is achieved, and CALM provides an auxiliary reward. This additional reward signal can enhance the learning process when the task reward is sparse and delayed without the need for human-designed rewards. We provide a preliminary evaluation of CALM using a dataset of human-annotated demonstrations from MiniHack, suggesting that LLMs can be effective in assigning credit in zero-shot settings, without examples or LLM fine-tuning. Our preliminary results indicate that the knowledge of LLMs is a promising prior for credit assignment in RL, facilitating the transfer of human knowledge into value functions.

This paper introduces a novel Hamiltonian-inspired neural network approach to credit scoring, designed to address the challenges of class imbalance and out-of-time (OOT) prediction in financial risk management. Drawing from concepts in Hamiltonian mechanics, we develop a symplectic optimizer and a new loss function to capture the complex dynamics of credit risk evolution. Using the Freddie Mac Single-Family Loan-Level Dataset, we evaluate our model's performance against other machine learning approaches. Our method shows superior discriminative power in OOT scenarios, as measured by the Area Under the Curve (AUC), indicating better ranking ability and robustness to class imbalance. The Hamiltonian-inspired approach shows particular strength in maintaining consistent performance between in-sample and OOT test sets, suggesting improved generalization to future, unseen data. These findings suggest that physics-inspired techniques offer a promising direction for developing more robust and reliable credit scoring models, particularly in uncertain economic situations.

Counterfactual explanations is one of the post-hoc methods used to provide explainability to machine learning models that have been attracting attention in recent years. Most examples in the literature, address the problem of generating post-hoc explanations for black-box machine learning models after the rejection of a loan application. In contrast, in this work, we investigate mathematical programming formulations for scorecard models, a type of interpretable model predominant within the banking industry for lending. The proposed mixed-integer programming formulations combine objective functions to ensure close, realistic and sparse counterfactuals using multi-objective optimization techniques for a binary, probability or continuous outcome. Moreover, we extend these formulations to generate multiple optimal counterfactuals simultaneously while guaranteeing diversity. Experiments on two real-world datasets confirm that the presented approach can generate optimal diverse counterfactuals addressing desired properties with assumable CPU times for practice use.

We present Future-KL Influenced Policy Optimization (FIPO), a reinforcement learning algorithm designed to overcome reasoning bottlenecks in large language models. While GRPO style training scales effectively, it typically relies on outcome-based rewards (ORM) that distribute a global advantage uniformly across every token in a trajectory. We argue that this coarse-grained credit assignment imposes a performance ceiling by failing to distinguish critical logical pivots from trivial tokens. FIPO addresses this by incorporating discounted future-KL divergence into the policy update, creating a dense advantage formulation that re-weights tokens based on their influence on subsequent trajectory behavior. Empirically, FIPO enables models to break through the length stagnation seen in standard baselines. Evaluated on Qwen2.5-32B, FIPO extends the average chain-of-thought length from roughly 4,000 to over 10,000 tokens and increases AIME 2024 Pass@1 accuracy from 50.0% to a peak of 58.0% (converging at approximately 56.0\%). This outperforms both DeepSeek-R1-Zero-Math-32B (around 47.0%) and o1-mini (approximately 56.0%). Our results suggest that establishing dense advantage formulations is a vital path for evolving ORM-based algorithms to unlock the full reasoning potential of base models. We open-source our training system, built on the verl framework.

Reinforcement learning improves LLM reasoning, yet sparse delayed reward over long sequences makes token-level credit assignment the key bottleneck. We study the verifiable-reward setting, where the final answer is checkable and multiple responses can be drawn per prompt. Reasoning tasks in math and medical QA align with this setup, where only a few decision tokens significantly impact the outcome. PPO offers token-level advantages with a learned value model, but it is complex to train both the actor and critic models simultaneously, and it is not easily generalizable, as the token-level values from the critic model can make training prone to overfitting. GRPO is critic-free and supports verifiable rewards, but spreads a single sequence-level return across tokens and ignores branching. We introduce Prefix-to-Tree (P2T), a simple procedure that converts a group of responses into a prefix tree and computes nonparametric prefix values \(V(s)\) by aggregating descendant outcomes. Built on P2T, we propose TEMPO (\textbf{Tree-Estimated Mean Prefix Value for Policy Optimization}), a critic-free algorithm that augments the group-relative outcome signal of GRPO with branch-gated temporal-difference corrections derived from the tree. At non-branch tokens, the temporal-difference (TD) term is zero, so TEMPO reduces to GRPO; at branching tokens, it supplies precise token-level credit without a learned value network or extra judges/teachers. On Qwen3-1.7B/4B, TEMPO outperforms PPO and GRPO on in-distribution (MATH, MedQA) and out-of-distribution (GSM-HARD, AMC23, MedMCQA, MMLU-Medical) benchmarks, and reaches higher validation accuracy with roughly the same wall-clock time.

Long-horizon agents rely on memory mechanisms to compress interaction history, but optimizing memory writing faces a distinct credit assignment challenge: a memory update may be rewarded or penalized due to downstream tool failures, noisy observations, or reasoning errors rather than its own contribution. This causally entangled credit can lead agents to discard useful evidence or preserve irrelevant information. We propose HiMPO, a Hindsight-Informed Memory Policy Optimization framework for assigning less-entangled credit to memory-writing actions in long-horizon agents. HiMPO first estimates the local utility of a memory update by comparing the task-relevant information recoverable from the previous and updated memories under the same pre-write state. It then uses hindsight relevance as a bounded retrospective filter that attenuates memory credit when local utility is not supported by the target outcome. The resulting memory-specific advantage is applied only to memory tokens, while trajectory-level rewards optimize the rest of the agent behavior. Across judge-based open-domain tasks and objective compressive-memory QA, HiMPO improves over strong memory-based and RL-based baselines while preserving compressed-context efficiency. Controlled interventions further show that HiMPO reduces blame leakage from tool-induced errors and improves attribution fidelity of memory updates.

Reinforcement learning has significantly enhanced the reasoning capabilities of Large Language Models (LLMs) in complex problem-solving tasks. Recently, the introduction of DeepSeek R1 has inspired a surge of interest in leveraging rule-based rewards as a low-cost alternative for computing advantage functions and guiding policy optimization. However, a common challenge observed across many replication and extension efforts is that when multiple sampled responses under a single prompt converge to identical outcomes, whether correct or incorrect, the group-based advantage degenerates to zero. This leads to vanishing gradients and renders the corresponding samples ineffective for learning, ultimately limiting training efficiency and downstream performance. To address this issue, we propose a consistency-aware policy optimization framework that introduces a structured global reward based on outcome consistency, the global loss based on it ensures that, even when model outputs show high intra-group consistency, the training process still receives meaningful learning signals, which encourages the generation of correct and self-consistent reasoning paths from a global perspective. Furthermore, we incorporate an entropy-based soft blending mechanism that adaptively balances local advantage estimation with global optimization, enabling dynamic transitions between exploration and convergence throughout training. Our method introduces several key innovations in both reward design and optimization strategy. We validate its effectiveness through substantial performance gains on multiple mathematical reasoning benchmarks, highlighting the proposed framework's robustness and general applicability. Code of this work has been released at https://github.com/hijih/copo-code.git.

Reinforcement learning has become a powerful paradigm for post-training large language model agents, yet credit assignment in multi-turn environments remains a challenge. Agents often receive sparse, trajectory-level rewards only at the end of an episode, making it difficult to determine which intermediate actions contributed to success or failure. As a result, propagating delayed outcomes back to individual decision steps without relying on costly auxiliary value models remains an open problem. We propose Generalized Advantage Grouped Policy Optimization (GAGPO), a critic-free reinforcement learning method for precise, step-aligned temporal credit assignment. GAGPO constructs a non-parametric grouped value proxy from sampled rollouts and uses it to compute TD/GAE-style temporal advantages, recursively propagating outcome supervision backward through time. Combined with group-wise advantage normalization and an action-level importance ratio, GAGPO extracts stable, localized optimization signals directly from multi-turn trajectories. Experiments on ALFWorld and WebShop show that GAGPO outperforms strong reinforcement learning baselines. Further analyses demonstrate faster early-stage learning, improved interaction efficiency, and smoother optimization dynamics, suggesting that GAGPO offers a simple yet effective framework for multi-turn agentic reinforcement learning.

In this paper, we introduce a novel predict-and-optimize method for profit-driven churn prevention. We frame the task of targeting customers for a retention campaign as a regret minimization problem. The main objective is to leverage individual customer lifetime values (CLVs) to ensure that only the most valuable customers are targeted. In contrast, many profit-driven strategies focus on churn probabilities while considering average CLVs. This often results in significant information loss due to data aggregation. Our proposed model aligns with the guidelines of Predict-and-Optimize (PnO) frameworks and can be efficiently solved using stochastic gradient descent methods. Results from 12 churn prediction datasets underscore the effectiveness of our approach, which achieves the best average performance compared to other well-established strategies in terms of average profit.

Recent advancements in federated learning (FL) seek to increase client-level performance by fine-tuning client parameters on local data or personalizing architectures for the local task. Existing methods for such personalization either prune a global model or fine-tune a global model on a local client distribution. However, these existing methods either personalize at the expense of retaining important global knowledge, or predetermine network layers for fine-tuning, resulting in suboptimal storage of global knowledge within client models. Enlightened by the lottery ticket hypothesis, we first introduce a hypothesis for finding optimal client subnetworks to locally fine-tune while leaving the rest of the parameters frozen. We then propose a novel FL framework, FedSelect, using this procedure that directly personalizes both client subnetwork structure and parameters, via the simultaneous discovery of optimal parameters for personalization and the rest of parameters for global aggregation during training. We show that this method achieves promising results on CIFAR-10.

Reinforcement learning (RL) post-training has enabled newer capabilities in models, such as agentic tool-use for search. However, these models struggle primarily due to limitations with sparse outcome-based rewards and a lack of training data that encapsulates questions of differing hardness, which results in models not performing deeper searches with tools to collect evidence for question-answering. To address these limitations, we introduce S^3-R1 (Synthetic data and stabilized Search R1), a framework that couples a data-centric approach with denser learning signals. We first develop a synthetic generation and curation pipeline that programmatically derives diverse, multi-hop questions from existing documents. This pipeline incorporates a retrieval-based verification step to specifically isolate questions of intermediate difficulty. We then pair this expanded training set with a reward structure that evaluates both intermediate search quality and the correctness of the final answer. This setup directly mitigates the credit assignment problems inherent to sparse rewards. Our evaluations show that S^3-R1 outperforms existing baselines by learning more effective search and synthesis strategies, yielding up to a 10% improvement in robust generalization on out-of-domain datasets.

Integrating Large Language Models (LLMs) with external tools via multi-agent systems offers a promising new paradigm for decomposing and solving complex problems. However, training these systems remains notoriously difficult due to the credit assignment challenge, as it is often unclear which specific functional agent is responsible for the success or failure of decision trajectories. Existing methods typically rely on sparse or globally broadcast rewards, failing to capture individual contributions and leading to inefficient reinforcement learning. To address these limitations, we introduce the Shapley-based Hierarchical Attribution for Reinforcement Policy (SHARP), a novel framework for optimizing multi-agent reinforcement learning via precise credit attribution. SHARP effectively stabilizes training by normalizing agent-specific advantages across trajectory groups, primarily through a decomposed reward mechanism comprising a global broadcast-accuracy reward, a Shapley-based marginal-credit reward for each agent, and a tool-process reward to improve execution efficiency. Extensive experiments across various real-world benchmarks demonstrate that SHARP significantly outperforms recent state-of-the-art baselines, achieving average match improvements of 23.66% and 14.05% over single-agent and multi-agent approaches, respectively.

Reinforcement learning (RL) has achieved remarkable success in enhancing the reasoning capabilities of large language models (LLMs). However, widely used critic-free RL methods rely on uniform credit assignment, broadcasting the same advantage to all tokens regardless of their differences. We identify a critical failure mode of this design, which we refer to as Positive-Credit Contamination: low-probability tail tokens that are contextually erroneous receive identical positive credit to plausible ones within the same trajectory, resulting in the indiscriminate reinforcement of flawed reasoning behavior. To mitigate this issue, we propose Tail-Aware Credit calibratiOn (TACO), a method that calibrates uniform credit assignment to suppress undesirable positive updates. TACO first computes a tail-risk score that incorporates the local generation context to assess each token's risk of falling into the unreliable tail, distinguishing unexpected rarity from uncertainty-driven exploration. TACO then uses this score to tune positive credit for risky tokens without removing their gradients entirely, so that recurring useful rare patterns can accumulate reinforcement while incidental noise is progressively dampened. Experimental results across three LLMs and eight benchmarks show that TACO consistently outperforms GRPO-style baselines. Notably, TACO improves training stability, supporting sustained performance gains in long-horizon RL. The source code is available at: https://github.com/xiuyilou/TACO.

The optimization of expensive-to-evaluate black-box functions is prevalent in various scientific disciplines. Bayesian optimization is an automatic, general and sample-efficient method to solve these problems with minimal knowledge of the underlying function dynamics. However, the ability of Bayesian optimization to incorporate prior knowledge or beliefs about the function at hand in order to accelerate the optimization is limited, which reduces its appeal for knowledgeable practitioners with tight budgets. To allow domain experts to customize the optimization routine, we propose ColaBO, the first Bayesian-principled framework for incorporating prior beliefs beyond the typical kernel structure, such as the likely location of the optimizer or the optimal value. The generality of ColaBO makes it applicable across different Monte Carlo acquisition functions and types of user beliefs. We empirically demonstrate ColaBO's ability to substantially accelerate optimization when the prior information is accurate, and to retain approximately default performance when it is misleading.

Fine-grained credit assignment is a central challenge in reinforcement learning for long horizon LLM agents. Standard objectives often train from programmatically verifiable terminal rewards by broadcasting each sparse outcome to every action in a trajectory. Existing methods typically seek finer credit from the rollout side, constructing auxiliary trajectory signals or additional comparisons to estimate action importance. Although useful, these approaches still treat the verifier that judged success as a scalar reward, discarding its internal task structure. Our key insight is that many verifiable tasks already encode the relevant checks inside their terminal verifier. We propose VICT (VerifierInstrumented Credit Tracing), a training-time interface that exposes executable or evidence backed atoms and traces them back to actions through dependency-valid proof edges. VICT redistributes group-relative advantage only along those edges, shifting credit assignment from rollout-side inference to verifierside tracing. It preserves the original terminal reward, abstains when evidence is incomplete or ambiguous, and changes only the training-time advantage tensor, requiring no learned critic, process labels, branch rollouts, or inference-time verifier access. On ALFWorld and WebShop, VICT improves substantially over outcome-only training and achieves strong performance alongside recent fine-grained credit methods; ablations rule out dense atom rewards, final-commit credit, temporal proximity, and sparsity as sufficient explanations.

Process reward models (PRMs) have proven effective for test-time scaling of Large Language Models (LLMs) on challenging reasoning tasks. However, reward hacking issues with PRMs limit their successful application in reinforcement fine-tuning. In this paper, we identify the main cause of PRM-induced reward hacking: the canonical summation-form credit assignment in reinforcement learning (RL), which defines the value as cumulative gamma-decayed future rewards, easily induces LLMs to hack steps with high rewards. To address this, we propose PURE: Process sUpervised Reinforcement lEarning. The key innovation of PURE is a min-form credit assignment that formulates the value function as the minimum of future rewards. This method significantly alleviates reward hacking by limiting the value function range and distributing advantages more reasonably. Through extensive experiments on 3 base models, we show that PRM-based approaches enabling min-form credit assignment achieve comparable reasoning performance to verifiable reward-based methods within only 30% steps. In contrast, the canonical sum-form credit assignment collapses training even at the beginning! Additionally, when we supplement PRM-based fine-tuning with just 10% verifiable rewards, we further alleviate reward hacking and produce the best fine-tuned model based on Qwen2.5-Math-7B in our experiments, achieving 82.5% accuracy on AMC23 and 53.3% average accuracy across 5 benchmarks. Moreover, we summarize the observed reward hacking cases and analyze the causes of training collapse. Code and models are available at https://github.com/CJReinforce/PURE.

Large Language Models (LLMs) are increasingly relied upon for solving complex reasoning tasks in domains such as mathematics, logic, and multi-step question answering. A growing line of work seeks to improve reasoning quality by scaling inference time compute particularly through Process Reward Models (PRMs), used to reward the reasoning at intermediate steps. While effective, these methods introduce substantial computational overhead, especially when generating large numbers of solutions in parallel. In this paper, we investigate whether PRMs can be used mid-generation to provide early signals that enable the rejection of suboptimal candidates before full generation of step is complete. We introduce the hypothesis that PRMs are also Partial Reward Models, meaning that the scores they assign to partially completed reasoning step are predictive of final output quality. This allows for principled early rejection based on intermediate token-level signals. We support this hypothesis both theoretically, by proving that the risk of discarding optimal beams decreases exponentially with generation length and empirically, by demonstrating a strong correlation between partial and final rewards across multiple reward models. On math reasoning benchmarks, our method achieves up to 1.4times-9times reduction in inference FLOPs without degrading final performance. These results suggest that early rejection is a powerful mechanism for improving the compute-efficiency of reasoning in LLMs.

In financial Retrieval-Augmented Generation (RAG) systems, models frequently rely on retrieved documents to generate accurate responses due to the time-sensitive nature of the financial domain. While retrieved documents help address knowledge gaps, model-generated responses still suffer from hallucinations that contradict the retrieved information. To mitigate this inconsistency, we propose a Reinforcement Learning framework enhanced with Fine-grained Knowledge Verification (RLFKV). Our method decomposes financial responses into atomic knowledge units and assesses the correctness of each unit to compute the fine-grained faithful reward. This reward offers more precise optimization signals, thereby improving alignment with the retrieved documents. Additionally, to prevent reward hacking (e.g., overly concise replies), we incorporate an informativeness reward that encourages the policy model to retain at least as many knowledge units as the base model. Experiments conducted on the public Financial Data Description (FDD) task and our newly proposed FDD-ANT dataset demonstrate consistent improvements, confirming the effectiveness of our approach.

We study the incentivized information acquisition problem, where a principal hires an agent to gather information on her behalf. Such a problem is modeled as a Stackelberg game between the principal and the agent, where the principal announces a scoring rule that specifies the payment, and then the agent then chooses an effort level that maximizes her own profit and reports the information. We study the online setting of such a problem from the principal's perspective, i.e., designing the optimal scoring rule by repeatedly interacting with the strategic agent. We design a provably sample efficient algorithm that tailors the UCB algorithm (Auer et al., 2002) to our model, which achieves a sublinear T^{2/3}-regret after T iterations. Our algorithm features a delicate estimation procedure for the optimal profit of the principal, and a conservative correction scheme that ensures the desired agent's actions are incentivized. Furthermore, a key feature of our regret bound is that it is independent of the number of states of the environment.

Learning from changing tasks and sequential experience without forgetting the obtained knowledge is a challenging problem for artificial neural networks. In this work, we focus on two challenging problems in the paradigm of Continual Learning (CL) without involving any old data: (i) the accumulation of catastrophic forgetting caused by the gradually fading knowledge space from which the model learns the previous knowledge; (ii) the uncontrolled tug-of-war dynamics to balance the stability and plasticity during the learning of new tasks. In order to tackle these problems, we present Progressive Learning without Forgetting (PLwF) and a credit assignment regime in the optimizer. PLwF densely introduces model functions from previous tasks to construct a knowledge space such that it contains the most reliable knowledge on each task and the distribution information of different tasks, while credit assignment controls the tug-of-war dynamics by removing gradient conflict through projection. Extensive ablative experiments demonstrate the effectiveness of PLwF and credit assignment. In comparison with other CL methods, we report notably better results even without relying on any raw data.

Hypothesis ranking is a crucial component of automated scientific discovery, particularly in natural sciences where wet-lab experiments are costly and throughput-limited. Existing approaches focus on pre-experiment ranking, relying solely on large language model's internal reasoning without incorporating empirical outcomes from experiments. We introduce the task of experiment-guided ranking, which aims to prioritize candidate hypotheses based on the results of previously tested ones. However, developing such strategies is challenging due to the impracticality of repeatedly conducting real experiments in natural science domains. To address this, we propose a simulator grounded in three domain-informed assumptions, modeling hypothesis performance as a function of similarity to a known ground truth hypothesis, perturbed by noise. We curate a dataset of 124 chemistry hypotheses with experimentally reported outcomes to validate the simulator. Building on this simulator, we develop a pseudo experiment-guided ranking method that clusters hypotheses by shared functional characteristics and prioritizes candidates based on insights derived from simulated experimental feedback. Experiments show that our method outperforms pre-experiment baselines and strong ablations.

Reinforcement learning has emerged as an effective paradigm for enhancing the mathematical reasoning capabilities of large language models. Among existing policy optimization methods, Proximal Policy Optimization (PPO) remains particularly appealing because its learned critic can, in principle, provide token-level credit assignment. However, in mathematical reasoning tasks characterized by long reasoning horizons and sparse outcome rewards, reliable token-level credit assignment remains challenging. The standard critic often fails to accurately evaluate intermediate reasoning states, resulting in noisy advantage estimates and suboptimal policy updates. In this paper, we propose ReDiPPO, a Reference-guided and Discrepancy-aware PPO framework for mathematical reasoning. ReDiPPO introduces a reference-guided critic that uses reference answers as training-time privileged signals to provide more accurate value estimation. Meanwhile, it retains a standard critic and quantifies the token-level reference-standard discrepancy between the standard value estimate and the reference-guided value estimate. This discrepancy serves as an indicator of difficult reasoning states and is used to reweight the corresponding token-level advantages during PPO optimization. Extensive experiments on diverse mathematical reasoning benchmarks demonstrate that ReDiPPO improves value-estimation accuracy and consistently outperforms strong policy optimization baselines, including PPO, DAPO, and GSPO, in final reasoning performance. Our code is available on https://github.com/cii030/ReDiPPO.

Text-to-image models produce images that align well with natural language prompts, but compositional generation has long been a central challenge. Models often struggle to satisfy multiple concepts within a single prompt, frequently omitting some concepts and resulting in partial success. Such failures highlight the difficulty of jointly optimizing multiple concepts during reward optimization, where competing concepts can interfere with one another. To address this limitation, we propose Correlation-Weighted Multi-Reward Optimization (\ours), a framework that leverages the correlation structure among concept rewards to adaptively weight each attribute concept in optimization. By accounting for interactions among concepts, \ours balances competing reward signals and emphasizes concepts that are partially satisfied yet inconsistently generated across samples, improving compositional generation. Specifically, we decompose multi-concept prompts into pre-defined concept groups (\eg, objects, attributes, and relations) and obtain reward signals from dedicated reward models for each concept. We then adaptively reweight these rewards, assigning higher weights to conflicting or hard-to-satisfy concepts using correlation-based difficulty estimation. By focusing optimization on the most challenging concepts within each group, \ours encourages the model to consistently satisfy all requested attributes simultaneously. We apply our approach to train state-of-the-art diffusion models, SD3.5 and FLUX.1-dev, and demonstrate consistent improvements on challenging multi-concept benchmarks, including ConceptMix, GenEval 2, and T2I-CompBench.

Memory systems are widely adopted to enhance LLMs for long-horizon tasks, and are commonly organized as multi-agent pipelines with memory building, summarizing, and retrieval agents. To empower this system, existing RL-based methods either apply final downstream task rewards (e.g., QA accuracy) for all agents uniformly, which are coarse and ambiguous, or design task-specific rewards for agents on different subtasks, which require costly annotations (e.g., key evidence) and are difficult to define reliably. To address these limitations, we propose Tree-based Credit Assignment for Multi-Agent Memory Systems (TreeMem), which derives agent-specific credit from the final reward without task-specific annotations. Specifically, TreeMem extends the multi-agent pipeline (builder--summarizer--retrieval) into a tree structure, where each agent's outputs are expanded into multiple subsequent branches. The contribution of each agent is estimated via Monte Carlo averaging over its subsequent branches, capturing how intermediate agent actions may influence the final reward. This converts the coarse final reward into agent-specific optimization signals. These signals are then used to update all agent policies simultaneously, helping heterogeneous agents specialize effectively. Experiments on long-horizon benchmarks show that TreeMem improves memory system performance over strong baselines, validating the effectiveness of tree-structured credit assignment for the multi-agent memory system.

While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using reinforcement learning, they may also drastically increase the output length due to overthinking, characterized by unnecessarily complex reasoning paths that waste computation and potentially degrade the performance. We hypothesize that such inefficiencies stem from LRMs' limited capability to dynamically select the proper modular reasoning strategies, termed thinking patterns at the right position. To investigate this hypothesis, we propose a dynamic optimization framework that segments model-generated reasoning paths into distinct thinking patterns, systematically identifying and promoting beneficial patterns that improve the answer while removing detrimental ones. Empirical analysis confirms that our optimized thinking paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintaining accuracy for originally correct responses. Moreover, a non-trivial portion of originally incorrect responses are transformed into correct ones, achieving a 15.6% accuracy improvement with reduced length. Motivated by the improvement brought by the optimized thinking paths, we apply a preference optimization technique supported by a pairwise dataset contrasting suboptimal and optimal reasoning paths. Experimental evaluations across multiple mathematical reasoning benchmarks reveal that our method notably reduces computational overhead while simultaneously improving reasoning accuracy, achieving up to a 12% accuracy improvement and reducing token usage from approximately 5,000 to 3,000 tokens.

Training diffusion models with multiple rewards requires distinguishing user preference from reward informativeness. User preference determines how much each reward should contribute to the overall objective; reward informativeness determines when its feedback is useful during denoising. Some rewards can meaningfully evaluate a sample as soon as global structure emerges, but others become informative only when the sample is nearly clean. To address both questions jointly, we propose ReCAST (Reward Credit ASsignment across T}imesteps), the first method, to our knowledge, for per-reward, timestep-dependent credit assignment in diffusion reward fine-tuning. ReCAST separates user preferences from temporal allocation through a reward-by-timestep weight matrix W, whose row sums match the user-specified reward budgets λ, while its column sums are equal, assigning the same total weight to each denoising step. Under these marginal constraints, ReCAST allocates weight according to each reward's informativeness, quantified by its Rényi discriminability gain at each step. These gains telescope to the total discriminability between the reward-induced positive policy and the current policy, providing a basis for temporal credit assignment. We evaluate ReCAST by training SD3.5-Medium under two distinct four-reward settings, each across five reward budgets λ. ReCAST improves the training rewards in one setting and matches them in the other, improves every held-out judge in both, and is preferred by an independent LLM-as-a-Judge. Together, these results show that ReCAST yields improvements that generalize beyond the training rewards and support its core principle: assigning each reward greater weight at the denoising timesteps where its feedback is most informative.

Despite its simplicity and efficacy, the high token expenditure of self-consistency can limit its practical utility. Here we investigate if self-consistency can be made more token-efficient for long chain-of-thought reasoning tasks, while preserving its parallelism, through early hypothesis pruning. Concretely, we generate all solutions in parallel, but periodically prune intermediate hypotheses that are deemed unnecessary based on two lightweight indicators: (a) the model's own confidence in individual hypotheses, and (b) lexical coverage of all current hypotheses by candidate subsets that are under consideration for continued retention. We design a fast weighted set cover algorithm that utilizes the two indicators; our evaluation of five LLMs on three math benchmarks shows that this method can improve token efficiency for all models, by 10-35% in many cases.

Recent advancements in large language models (LLMs) have been driven by their emergent reasoning capabilities, particularly through long chain-of-thought (CoT) prompting, which enables thorough exploration and deliberation. Despite these advances, long-CoT LLMs often exhibit suboptimal reasoning behaviors, such as overthinking and excessively protracted reasoning chains, which can impair performance. In this paper, we analyze reasoning processes through an optimization lens, framing CoT as a gradient descent procedure where each reasoning step constitutes an update toward problem resolution. Building on this perspective, we introduce RePro (Rectifying Process-level Reward), a novel approach to refine LLM reasoning during post-training. RePro defines a surrogate objective function to assess the optimization process underlying CoT, utilizing a dual scoring mechanism to quantify its intensity and stability. These scores are aggregated into a composite process-level reward, seamlessly integrated into reinforcement learning with verifiable rewards (RLVR) pipelines to optimize LLMs. Extensive experiments across multiple reinforcement learning algorithms and diverse LLMs, evaluated on benchmarks spanning mathematics, science, and coding, demonstrate that RePro consistently enhances reasoning performance and mitigates suboptimal reasoning behaviors.

Large reasoning models (LRMs) boosted by Reinforcement Learning from Verifier Reward (RLVR) have shown great power in problem solving, yet they often cause overthinking: excessive, meandering reasoning that inflates computational cost. Prior designs of penalization in RLVR manage to reduce token consumption while often harming model performance, which arises from the oversimplicity of token-level supervision. In this paper, we argue that the granularity of supervision plays a crucial role in balancing efficiency and accuracy, and propose Group Relative Segment Penalization (GRSP), a step-level method to regularize reasoning. Since preliminary analyses show that reasoning segments are strongly correlated with token consumption and model performance, we design a length-aware weighting mechanism across segment clusters. Extensive experiments demonstrate that GRSP achieves superior token efficiency without heavily compromising accuracy, especially the advantages with harder problems. Moreover, GRSP stabilizes RL training and scales effectively across model sizes.

Improving the multi-step reasoning ability of large language models (LLMs) with offline reinforcement learning (RL) is essential for quickly adapting them to complex tasks. While Direct Preference Optimization (DPO) has shown promise in aligning LLMs with human preferences, it is less suitable for multi-step reasoning tasks because (1) DPO relies on paired preference data, which is not readily available for multi-step reasoning tasks, and (2) it treats all tokens uniformly, making it ineffective for credit assignment in multi-step reasoning tasks, which often come with sparse reward. In this work, we propose OREO (Offline Reasoning Optimization), an offline RL method for enhancing LLM multi-step reasoning. Building on insights from previous works of maximum entropy reinforcement learning, it jointly learns a policy model and value function by optimizing the soft Bellman Equation. We show in principle that it reduces the need to collect pairwise data and enables better credit assignment. Empirically, OREO surpasses existing offline learning methods on multi-step reasoning benchmarks, including mathematical reasoning tasks (GSM8K, MATH) and embodied agent control (ALFWorld). The approach can be extended to a multi-iteration framework when additional resources are available. Furthermore, the learned value function can be leveraged to guide the tree search for free, which can further boost performance during test time.

While large reasoning models trained with critic-free reinforcement learning and verifiable rewards (RLVR) represent the state-of-the-art, their practical utility is hampered by ``overthinking'', a critical issue where models generate excessively long reasoning paths without any performance benefit. Existing solutions that penalize length often fail, inducing performance degradation due to a fundamental misalignment between trajectory-level rewards and token-level optimization. In this work, we introduce a novel framework, DECS, built on our theoretical discovery of two previously unaddressed flaws in current length rewards: (1) the erroneous penalization of essential exploratory tokens and (2) the inadvertent rewarding of partial redundancy. Our framework's innovations include (i) a first-of-its-kind decoupled token-level reward mechanism that surgically distinguishes and penalizes redundant tokens, and (ii) a novel curriculum batch scheduling strategy to master the efficiency-efficacy equilibrium. Experimental results show DECS can achieve a dramatic reduction in reasoning tokens by over 50\% across seven benchmarks while simultaneously maintaining or even improving performance. It demonstrates conclusively that substantial gains in reasoning efficiency can be achieved without compromising a model's underlying reasoning power. Code is available at https://github.com/pixas/DECS.

Large reasoning models, such as OpenAI o1 and DeepSeek-R1, tend to become increasingly verbose as their reasoning capabilities improve. These inflated Chain-of-Thought (CoT) trajectories often exceed what the underlying problems require, wasting compute, latency, and context budgets. While introducing length-based efficiency rewards during reinforcement learning offers a natural remedy, existing methods struggle with two fundamental challenges: the optimal balance between correctness and efficiency is non-stationary throughout training, and intrinsic reasoning budgets vary drastically across problems. Relying on static reward weights and global length constraints inevitably forces a compromise between degraded accuracy and unrealized compression. To overcome these limitations, we propose LEAD (Length-Efficient Adaptive and Dynamic reasoning), a method that replaces static heuristics with online, self-adaptive mechanisms. LEAD dynamically calibrates the correctness-efficiency trade-off at each step using a Potential-Scaled Instability, directing optimization capacity to the most informative learning signal. Furthermore, it estimates an adaptive per-problem target length online based on the model's own correct rollouts, applying a symmetric efficiency reward that penalizes both overthinking and over-compression. Evaluated on five mathematical reasoning benchmarks, LEAD achieves the highest accuracy and Accuracy-Efficiency Score among RL-trained efficient-reasoning methods while producing substantially shorter outputs than the base model.

Test-Time Scaling (TTS) has significantly enhanced the capabilities of Large Reasoning Models (LRMs) but introduces a critical side-effect known as Overthinking. We conduct a preliminary study to rethink this phenomenon from a fine-grained perspective. We observe that LRMs frequently conduct repetitive self-verification without revision even after obtaining the final answer during the reasoning process. We formally define this specific position where the answer first stabilizes as the Reasoning Anchor. By analyzing pre- and post-anchor reasoning behaviors, we uncover the structural redundancy fixed in LRMs: the meaningless repetitive verification after deriving the first complete answer, which we term the Answer-Stable Tail (AST). Motivated by this observation, we propose Anchor-based Process Reward (APR), a structure-aware reward shaping method that localizes the reasoning anchor and penalizes exclusively the post-anchor AST. Leveraging the policy optimization algorithm suitable for length penalties, our APR models achieved the performance-efficiency Pareto frontier at 1.5B and 7B scales averaged across five mathematical reasoning datasets while requiring substantially fewer computational resources for RL training.

Large Language Reasoning Models have demonstrated remarkable success on static tasks, yet their application to multi-round agentic planning in interactive environments faces two fundamental challenges. First, the intractable credit assignment problem renders conventional reinforcement learning ineffective in sparse-reward settings. Second, the computational overhead of verbose, step-by-step reasoning histories is prohibitive. To address these challenges, we propose BPO, a three-stage framework (bootstrapping, extrapolation, and refinement) that establishes a self-improving data flywheel to develop robust reasoning models for long-horizon, sparse-reward environments. Our framework first bootstraps efficient reasoning using the proposed planning quaternions with long-short chain-of-thought fusion. It then extrapolates to out-of-distribution tasks through complexity-stratified curriculum learning. Finally, the model iteratively refines itself by learning exclusively on experiences selected via reward-gated rejection sampling. Experiments on ALFWorld, ScienceWorld, and WebShop demonstrate that our approach achieves state-of-the-art with significant token efficiency, providing a new recipe for reasoning models in agentic planning.

Reinforcement learning with verifiable rewards has substantially advanced multimodal reasoning, yet it remains fundamentally limited by ambiguous token-level credit assignment. While high-entropy token heuristics encourage possibility exploration, naively extending them to video reasoning tends to induce lengthy reasoning, as the model becomes overly reliant on high-entropy visual activations. Alternative approaches that rely on counterfactual-based visual token localization for credit assignment also tend to over-prioritize visual exploration at the expense of decisive reasoning cues for answer derivation, thereby exacerbating the interference from spurious visual nuances. Moreover, these methods employ static counterfactual strategies that fail to co-evolve with the policy during training. In this paper, we introduce DyCPO, a co-evolutionary framework that jointly optimizes reliable token selection and adaptive counterfactual intervention. It constructs a multi-role dependence metric to balance visual exploration and answer-relevance mining in token-wise contrastive learning, while suppressing exploration-only filler tokens and spurious visual noise. Rather than relying on static counterfactual priors, DyCPO dynamically derives counterfactual signals from the model's own successful and failed rollouts, enabling self-diagnostic analysis and co-evolution of the optimization objective with the policy. Extensive experiments on complex video reasoning and general video understanding benchmarks demonstrate consistent performance improvements, establishing DyCPO as a robust token-level credit assignment paradigm for multimodal reinforcement learning.

Group Relative Policy Optimization (GRPO) is one of the most widely adopted RLVR algorithms for post-training large language models on reasoning tasks. We first show that GRPO admits an equivalent discriminative reformulation, in which policy optimization maximizes the expected score gap between verified positive and negative rollouts. This reformulation reveals two objective-level limitations: likelihood-misaligned surrogate scores, in which clipped ratio-based scores are optimized rather than the sequence likelihoods that govern generation, and score-insensitive credit assignment, in which rollout-level credit does not reflect the current score gaps between positive and negative rollouts. To address these limitations, we propose ConSPO, a Contrastive Sequence-level Policy Optimization method that uses length-normalized sequence log-probabilities as rollout scores and contrasts verified positive rollouts against negative distractors within the same group. ConSPO optimizes a group-wise InfoNCE-style objective to adaptively strengthen updates for poorly separated positives and high-scoring negatives, together with a curriculum-scheduled margin that preserves separation pressure as training progresses. Experiments across diverse settings show that ConSPO outperforms strong baselines on challenging reasoning benchmarks. Code will be released upon paper acceptance.

We seek a hierarchical resolution of residual error under a composite learning objective as a principled mechanism for identifying and exploiting additional information, particularly under distribution shift and perturbation. Inspired by the System 1/System 2 paradigm, we formulate this principle as a two-loop mechanism serving a common inference goal. A fast, System 1-like loop resolves the residual addressable by the available evidence; the remaining epistemic residual triggers a medium speed, System 2-like loop that actively acquires additional evidence and measures its informational value through residual reduction. Over nested solution spaces, the medium-loop optimum is provably no worse than the fast-loop optimum. Experiments show that the resulting two-loop model consistently improves upon the fast loop at approximately half the computation of the medium loop, including under unseen corruptions, and, when provided a cleaner observation, outperforms staged classifiers and learning-to-defer methods at equal computational cost.

Portfolio Selection is an important real-world financial task and has attracted extensive attention in artificial intelligence communities. This task, however, has two main difficulties: (i) the non-stationary price series and complex asset correlations make the learning of feature representation very hard; (ii) the practicality principle in financial markets requires controlling both transaction and risk costs. Most existing methods adopt handcraft features and/or consider no constraints for the costs, which may make them perform unsatisfactorily and fail to control both costs in practice. In this paper, we propose a cost-sensitive portfolio selection method with deep reinforcement learning. Specifically, a novel two-stream portfolio policy network is devised to extract both price series patterns and asset correlations, while a new cost-sensitive reward function is developed to maximize the accumulated return and constrain both costs via reinforcement learning. We theoretically analyze the near-optimality of the proposed reward, which shows that the growth rate of the policy regarding this reward function can approach the theoretical optimum. We also empirically evaluate the proposed method on real-world datasets. Promising results demonstrate the effectiveness and superiority of the proposed method in terms of profitability, cost-sensitivity and representation abilities.

Effective social interaction requires more than fluent responses: agents must reach plans that fit the participants' needs and circumstances. Existing evaluations of social agents mainly rely on LLM judges that rate the conversation, without checking the resulting plan. We introduce HICO-Bench, a benchmark of 180 everyday coordination scenarios, such as resource allocation, scheduling, and authorization, in which two agents with private information converse and then independently record the plan they agreed on. A program checks Feasibility (the two records match and satisfy both participants' private conditions), and an LLM judge checks Integrity (the conversation supports the recorded plan); passing both is a Verified Success. Each scenario has two versions that share the same public context but differ in one private condition, so the correct plan differs between them. Across thirteen LLMs, 36% of conversations rated highly for goal completion fail Verified Success. To learn from outcomes that arrive only at the end of a conversation, we propose Paired-Credit Policy Optimization (PaCPO). After each turn, PaCPO asks the agent for a tentative plan, checks it in both versions of the scenario, and rewards the turns after which the tentative plans fit their respective versions. PaCPO raises Qwen3-8B's Verified Success from 20.4% to 28.3%.

A variety of recent papers discuss the application of Shapley values, a concept for explaining coalitional games, for feature attribution in machine learning. However, the correct way to connect a machine learning model to a coalitional game has been a source of controversy. The two main approaches that have been proposed differ in the way that they condition on known features, using either (1) an interventional or (2) an observational conditional expectation. While previous work has argued that one of the two approaches is preferable in general, we argue that the choice is application dependent. Furthermore, we argue that the choice comes down to whether it is desirable to be true to the model or true to the data. We use linear models to investigate this choice. After deriving an efficient method for calculating observational conditional expectation Shapley values for linear models, we investigate how correlation in simulated data impacts the convergence of observational conditional expectation Shapley values. Finally, we present two real data examples that we consider to be representative of possible use cases for feature attribution -- (1) credit risk modeling and (2) biological discovery. We show how a different choice of value function performs better in each scenario, and how possible attributions are impacted by modeling choices.

The reasoning pattern of Large language models (LLMs) remains opaque, and Reinforcement learning (RL) typically applies uniform credit across an entire generation, blurring the distinction between pivotal and routine steps. This work positions attention as a privileged substrate that renders the internal logic of LLMs legible, not merely as a byproduct of computation, but as a mechanistic blueprint of reasoning itself. We first distinguish attention heads between locally and globally focused information processing and reveal that locally focused heads produce a sawtooth pattern near the diagonal indicating phrasal chunks, while globally focused heads expose tokens that exert broad downstream influence over future tokens. We formalize these with two metrics: 1) Windowed Average Attention Distance, which measures the extent of backward attention within a clipped window; 2) Future Attention Influence, which quantifies a token's global importance as the average attention it receives from subsequent tokens. Taken together, these signals reveal a recurring preplan-and-anchor mechanism, where the model first performs a long-range contextual reference to generate an introductory token, which is immediately followed by or coincides with a semantic anchor token that organizes subsequent reasoning. Leveraging these insights, we introduce three novel RL strategies that dynamically perform targeted credit assignment to critical nodes (preplan tokens, anchor tokens, and their temporal coupling) and show consistent performance gains across various reasoning tasks. By aligning optimization with the model's intrinsic reasoning rhythm, we aim to transform opaque optimization into an actionable structure-aware process, hoping to offer a potential step toward more transparent and effective optimization of LLM reasoning.

We investigate whether the success of a zero-shot Chain-of-Thought (CoT) process can be predicted before completion. We discover that a probing classifier, based on LLM representations, performs well even before a single token is generated, suggesting that crucial information about the reasoning process is already present in the initial steps representations. In contrast, a strong BERT-based baseline, which relies solely on the generated tokens, performs worse, likely because it depends on shallow linguistic cues rather than deeper reasoning dynamics. Surprisingly, using later reasoning steps does not always improve classification. When additional context is unhelpful, earlier representations resemble later ones more, suggesting LLMs encode key information early. This implies reasoning can often stop early without loss. To test this, we conduct early stopping experiments, showing that truncating CoT reasoning still improves performance over not using CoT at all, though a gap remains compared to full reasoning. However, approaches like supervised learning or reinforcement learning designed to shorten CoT chains could leverage our classifier's guidance to identify when early stopping is effective. Our findings provide insights that may support such methods, helping to optimize CoT's efficiency while preserving its benefits.

Reinforcement Learning (RL) has proven highly effective at enhancing the complex reasoning abilities of Large Language Models (LLMs), yet underlying mechanisms driving this success remain largely opaque. Our analysis reveals that puzzling phenomena like ``aha moments", ``length-scaling'' and entropy dynamics are not disparate occurrences but hallmarks of an emergent reasoning hierarchy, akin to the separation of high-level strategic planning from low-level procedural execution in human cognition. We uncover a compelling two-phase dynamic: initially, a model is constrained by procedural correctness and must improve its low-level skills. The learning bottleneck then decisively shifts, with performance gains being driven by the exploration and mastery of high-level strategic planning. This insight exposes a core inefficiency in prevailing RL algorithms like GRPO, which apply optimization pressure agnostically and dilute the learning signal across all tokens. To address this, we propose HIerarchy-Aware Credit Assignment (HICRA), an algorithm that concentrates optimization efforts on high-impact planning tokens. HICRA significantly outperforms strong baselines, demonstrating that focusing on this strategic bottleneck is key to unlocking advanced reasoning. Furthermore, we validate semantic entropy as a superior compass for measuring strategic exploration over misleading metrics such as token-level entropy.

The ability of large language models to solve complex mathematical problems has progressed significantly, particularly for tasks requiring advanced reasoning. However, the scarcity of sufficiently challenging problems, particularly at the Olympiad level, hinders further advancements. In this work, we introduce PromptCoT, a novel approach for automatically generating high-quality Olympiad-level math problems. The proposed method synthesizes complex problems based on mathematical concepts and the rationale behind problem construction, emulating the thought processes of experienced problem designers. We provide a theoretical analysis demonstrating that an optimal rationale should maximize both the likelihood of rationale generation given the associated concepts and the likelihood of problem generation conditioned on both the rationale and the concepts. Our method is evaluated on standard benchmarks including GSM8K, MATH-500, and AIME2024, where it consistently outperforms existing problem generation methods. Furthermore, we demonstrate that PromptCoT exhibits superior data scalability, consistently maintaining high performance as the dataset size increases, outperforming the baselines. The implementation is available at https://github.com/zhaoxlpku/PromptCoT.

Reinforcement learning from verifiable rewards (RLVR) has improved the reasoning abilities of large language models (LLMs), but most existing approaches rely on sparse outcome-level feedback. This sparsity creates a credit assignment challenge in long-horizon agentic reasoning: a trajectory may fail despite containing many correct intermediate decisions, or succeed despite containing flawed ones. In this work, we study a class of densely-verifiable agentic reasoning problems, where intermediate actions can be objectively checked by symbolic or algorithmic oracles. We propose Verifiable Process Rewards (VPR), a framework that converts such oracles into dense turn-level supervision for reinforcement learning, and instantiate it in three representative settings: search-based verification for dynamic deduction, constraint-based verification for logical reasoning, and posterior-based verification for probabilistic inference. We further provide a theoretical analysis showing that dense verifier-grounded rewards can improve long-horizon credit assignment by providing more localized learning signals, with the benefit depending on the reliability of the verifier. Empirically, VPR outperforms outcome-level reward and rollout-based process reward baselines across controlled environments, and more importantly, transfers to both general and agentic reasoning benchmarks, suggesting that verifiable process supervision can foster general reasoning skills applicable beyond the training environments. Our results indicate that VPR is a promising approach for enhancing LLM agents whenever reliable intermediate verification is available, while also highlighting its dependence on oracle quality and the open challenge of extending VPR to less structured, open-ended environments.

Claim verification is essential in combating misinformation, and large language models (LLMs) have recently emerged in this area as powerful tools for assessing the veracity of claims using external knowledge. Existing LLM-based methods for claim verification typically adopt a Decompose-Then-Verify paradigm, which involves decomposing complex claims into several independent sub-claims and verifying each sub-claim separately. However, this paradigm often introduces errors during the claim decomposition process. To mitigate these errors, we propose to develop the Chain-of-Thought (CoT)-Verify paradigm, which leverages LLM reasoning methods to generate CoT-verification paths for the original complex claim without requiring decompositions into sub-claims and separate verification stages. The CoT-Verify paradigm allows us to propose a natural fine-tuning method called Reasoning-CV to enhance the verification capabilities in LLMs. Reasoning-CV includes a supervised fine-tuning (SFT) stage and a self-improvement direct preference optimization (DPO) stage. Utilizing only an 8B pre-trained LLM, Reasoning-CV demonstrates superior knowledge-assisted claim verification performances compared to existing Decompose-Then-Verify methods, as well as powerful black-box LLMs such as GPT-4o+CoT and o1-preview. Our code is available.

Machine learning models routinely automate decisions in applications like lending and hiring. In such settings, consumer protection rules require companies that deploy models to explain predictions to decision subjects. These rules are motivated, in part, by the belief that explanations can promote recourse by revealing information that individuals can use to contest or improve their outcomes. In practice, many companies comply with these rules by providing individuals with a list of the most important features for their prediction, which they identify based on feature importance scores from feature attribution methods such as SHAP or LIME. In this work, we show how these practices can undermine consumers by highlighting features that would not lead to an improved outcome and by explaining predictions that cannot be changed. We propose to address these issues by highlighting features based on their responsiveness score -- i.e., the probability that an individual can attain a target prediction by changing a specific feature. We develop efficient methods to compute responsiveness scores for any model and any dataset. We conduct an extensive empirical study on the responsiveness of explanations in lending. Our results show that standard practices in consumer finance can backfire by presenting consumers with reasons without recourse, and demonstrate how our approach improves consumer protection by highlighting responsive features and identifying fixed predictions.

Process Reward Models (PRMs) aim to improve multi-step reasoning in Large Language Models (LLMs) by supervising intermediate steps and identifying errors. However, building effective PRMs remains challenging due to the lack of scalable, high-quality annotations. Existing approaches rely on costly human labeling, LLM-based self-evaluation that is prone to hallucination, or Monte Carlo (MC) estimation, which infers step quality solely from rollout outcomes and often introduces noisy, misaligned supervision due to credit misattribution. These issues result in three core limitations: noisy rewards, low factual fidelity, and misalignment with step-level reasoning objectives. To address these challenges, we introduce GroundedPRM, a tree-guided and fidelity-aware framework for automatic process supervision. To reduce reward noise and enable fine-grained credit assignment, we construct structured reasoning paths via Monte Carlo Tree Search (MCTS). To eliminate hallucinated supervision, we validate each intermediate step using an external tool, providing execution-grounded correctness signals. To combine both step-level validation and global outcome assessment, we design a hybrid reward aggregation mechanism that fuses tool-based verification with MCTS-derived feedback. Finally, we format the reward signal into a rationale-enhanced, generative structure to promote interpretability and compatibility with instruction-tuned LLMs. GroundedPRM is trained on only 40K automatically labeled samples, amounting to just 10% of the data used by the best-performing PRM trained with auto-labeled supervision. Nevertheless, it achieves up to a 26% relative improvement in average performance on ProcessBench. When used for reward-guided greedy search, GroundedPRM outperforms even PRMs trained with human-labeled supervision, offering a scalable and verifiable path toward high-quality process-level reasoning.

Iterative preference optimization methods have recently been shown to perform well for general instruction tuning tasks, but typically make little improvement on reasoning tasks (Yuan et al., 2024, Chen et al., 2024). In this work we develop an iterative approach that optimizes the preference between competing generated Chain-of-Thought (CoT) candidates by optimizing for winning vs. losing reasoning steps that lead to the correct answer. We train using a modified DPO loss (Rafailov et al., 2023) with an additional negative log-likelihood term, which we find to be crucial. We show reasoning improves across repeated iterations of this scheme. While only relying on examples in the training set, our approach results in increasing accuracy for Llama-2-70B-Chat from 55.6% to 81.6% on GSM8K (and 88.7% with majority voting out of 32 samples), from 12.5% to 20.8% on MATH, and from 77.8% to 86.7% on ARC-Challenge, which outperforms other Llama-2-based models not relying on additionally sourced datasets.

Test-time scaling has enabled LLMs to solve increasingly complex reasoning, discovery, and optimization tasks. However, existing approaches often gather observations while seeking evidence for current hypotheses, then generate new hypotheses conditioned on those hypotheses and their associated evidence. This couples observation discovery to existing hypotheses, favoring local refinements over exploration of unknown hypotheses regions. Inspired by the hypothetico-deductive method (Hempel, 1945) and dual-space models of scientific discovery (Klahr & Dunbar, 1988), we introduce SHELDON, a scientific reasoning harness that separately represents and jointly explores hypothesis and observation spaces. By actively seeking new observations along with new hypotheses, SHELDON can discover observations that its current hypotheses do not explain. These unexplained observations expose gaps in its understanding, motivate new investigations, and guide the generation of hypotheses beyond refinements of existing ones. Across diagnosis, abstract reasoning, and optimization benchmarks, SHELDON outperforms evaluated baselines by up to 26.7 points. Additional analysis shows that SHELDON generates up to 4.5x more novel solutions.

From a first-principles perspective, it may seem odd that the strongest results in foundation model fine-tuning (FT) are achieved via a relatively complex, two-stage training procedure. Specifically, one first trains a reward model (RM) on some dataset (e.g. human preferences) before using it to provide online feedback as part of a downstream reinforcement learning (RL) procedure, rather than directly optimizing the policy parameters on the dataset via offline maximum likelihood estimation. In fact, from an information-theoretic perspective, we can only lose information via passing through a reward model and cannot create any new information via on-policy sampling. To explain this discrepancy, we scrutinize several hypotheses on the value of RL in FT through both theoretical and empirical lenses. Of the hypotheses considered, we find the most support for the explanation that on problems with a generation-verification gap, the combination of the ease of learning the relatively simple RM (verifier) from the preference data, coupled with the ability of the downstream RL procedure to then filter its search space to the subset of policies (generators) that are optimal for relatively simple verifiers is what leads to the superior performance of online FT.

Search-augmented large language models (LLMs) trained with reinforcement learning (RL) have achieved strong results on open-domain question answering (QA), but training still remains a significant challenge. The optimization is often unstable due to sparse rewards and difficult credit assignments across reasoning and tool calls. To address this, we introduce Turn-Level Information Potential Reward Shaping (TIPS), a simple framework that assigns dense, turn-level rewards to each reasoning + tool-call segment based on the increased likelihood of the correct answer under a teacher model. By leveraging the potential-based reward shaping, TIPS offers fine-grained and policy-invariant guidance that overcomes the limitations of outcome-only optimization. Evaluated on seven QA benchmarks, TIPS consistently outperforms GRPO/PPO baselines and substantially improves training stability. For instance, with a Qwen-2.5 7B Instruct model, TIPS improves the average Exact Match score by 11.8% and F1 by 13.6% relative to PPO. Our results demonstrate that turn-level information-potential reward shaping provides an effective and general solution to sparse-reward credit assignment for multi-turn LLM reasoning.

Large Language Models (LLMs) have shown promising capabilities for solving Operations Research (OR) problems. While reinforcement learning serves as a powerful paradigm for LLM training on OR problems, existing works generally face two key limitations. First, outcome reward suffers from the credit assignment problem, where correct final answers can reinforce flawed reasoning. Second, conventional discriminative process supervision is myopic, failing to evaluate the interdependent steps of OR modeling holistically. To this end, we introduce StepORLM, a novel self-evolving framework with generative process supervision. At its core, StepORLM features a co-evolutionary loop where a policy model and a generative process reward model (GenPRM) iteratively improve on each other. This loop is driven by a dual-feedback mechanism: definitive, outcome-based verification from an external solver, and nuanced, holistic process evaluation from the GenPRM. The combined signal is used to align the policy via Weighted Direct Preference Optimization (W-DPO) and simultaneously refine the GenPRM. Our resulting 8B-parameter StepORLM establishes a new state-of-the-art across six benchmarks, significantly outperforming vastly larger generalist models, agentic methods, and specialized baselines. Moreover, the co-evolved GenPRM is able to act as a powerful and universally applicable process verifier, substantially boosting the inference scaling performance of both our own model and other existing LLMs.

While foundation models have been exploited for various expert tasks through fine-tuning, any foundation model will become outdated due to its old knowledge or limited capability. Thus the underlying foundation model should be eventually replaced by new ones, which leads to repeated cost of fine-tuning these new models. Existing work addresses this problem by inference-time tuning, i.e., modifying the output probabilities from the new foundation model with the outputs from the old foundation model and its fine-tuned model, which involves an additional overhead in inference by the latter two models. In this paper, we propose a new fine-tuning principle, Portable Reward Tuning (PRT), that reduces the inference overhead by its nature, based on the reformulation of fine-tuning as the reward maximization. Specifically, instead of fine-tuning parameters of the foundation models, PRT trains the reward model explicitly through the same loss function as in fine-tuning. During inference, the reward model can be used with any foundation model (with the same set of vocabularies or labels) through the formulation of reward maximization. Experimental results, covering both vision and language models, demonstrate that the PRT-trained model can achieve comparable accuracy to the existing work of inference-time tuning, with less inference cost.

Large language models (LLMs) solve problems more accurately and interpretably when instructed to work out the answer step by step using a ``chain-of-thought'' (CoT) prompt. One can also improve LLMs' performance on a specific task by supervised fine-tuning, i.e., by using gradient ascent on some tunable parameters to maximize the average log-likelihood of correct answers from a labeled training set. Naively combining CoT with supervised tuning requires supervision not just of the correct answers, but also of detailed rationales that lead to those answers; these rationales are expensive to produce by hand. Instead, we propose a fine-tuning strategy that tries to maximize the marginal log-likelihood of generating a correct answer using CoT prompting, approximately averaging over all possible rationales. The core challenge is sampling from the posterior over rationales conditioned on the correct answer; we address it using a simple Markov-chain Monte Carlo (MCMC) expectation-maximization (EM) algorithm inspired by the self-taught reasoner (STaR), memoized wake-sleep, Markovian score climbing, and persistent contrastive divergence. This algorithm also admits a novel control-variate technique that drives the variance of our gradient estimates to zero as the model improves. Applying our technique to GSM8K and the tasks in BIG-Bench Hard, we find that this MCMC-EM fine-tuning technique typically improves the model's accuracy on held-out examples more than STaR or prompt-tuning with or without CoT.

We consider multi-draft speculative sampling, where the proposal sequences are sampled independently from different draft models. At each step, a token-level draft selection scheme takes a list of valid tokens as input and produces an output token whose distribution matches that of the target model. Previous works have demonstrated that the optimal scheme (which maximizes the probability of accepting one of the input tokens) can be cast as a solution to a linear program. In this work we show that the optimal scheme can be decomposed into a two-step solution: in the first step an importance sampling (IS) type scheme is used to select one intermediate token; in the second step (single-draft) speculative sampling is applied to generate the output token. For the case of two identical draft models we further 1) establish a necessary and sufficient condition on the distributions of the target and draft models for the acceptance probability to equal one and 2) provide an explicit expression for the optimal acceptance probability. Our theoretical analysis also motives a new class of token-level selection scheme based on weighted importance sampling. Our experimental results demonstrate consistent improvements in the achievable block efficiency and token rates over baseline schemes in a number of scenarios.

Research agents explain planned experiments. We measure predictive credit with paired forecasts sharing an intervention, forecaster, and outcome while varying description, matched explanation, and donor context. Five checks track commitment, delivery, predictive gain, alignment, and known-signal uptake. Across 336 prospective states in controlled learning, 12 Tox21 endpoints, and 24 OpenML tasks, v5's frozen credit decision was inconclusive. Tox21's preregistered ROC AUC interval-score harm test was unmet (D-M=-.0026, 95 percent interval [-.0174, .0104]); OpenML's joint formation, point-equivalence, and repeatability rule was unmet. Matched point-accuracy gains over description remained unconfirmed, and Tox21/OpenML seed-donor intervals spanned zero. Under requested DeepSeek V4 Pro, matched and donor cards reduced secondary Tox21 drift by 64.5 and 59.1 percent. A DeepSeek V4 Flash replay raised matched point MAE from .01823 to .02020 and missed matched-donor interval-score equivalence. OpenML full-card assignment widened nominal 80 percent intervals by 21 percent, with 49.3 percent coverage versus 51.4 percent for description and content in 66/144 cards. Direct-text Flash delivered all 144 notes without detectable matched point-accuracy gain. A researcher-authored mechanism positive control lowered point MAE by 2.60 percentage points versus description. The protocol measures predictive credit for research-agent benchmarks and scientific forecasting; natural-explanation credit remained unconfirmed at the tested donor resolutions.

To develop a trustworthy AI system, which aim to identify the input regions that most influence the models decisions. The primary task of existing attribution methods lies in efficiently and accurately identifying the relationships among input-prediction interactions. Particularly when the input data is discrete, such as images, analyzing the relationship between inputs and outputs poses a significant challenge due to the combinatorial explosion. In this paper, we propose a novel and efficient black-box attribution mechanism, LiMA (Less input is More faithful for Attribution), which reformulates the attribution of important regions as an optimization problem for submodular subset selection. First, to accurately assess interactions, we design a submodular function that quantifies subset importance and effectively captures their impact on decision outcomes. Then, efficiently ranking input sub-regions by their importance for attribution, we improve optimization efficiency through a novel bidirectional greedy search algorithm. LiMA identifies both the most and least important samples while ensuring an optimal attribution boundary that minimizes errors. Extensive experiments on eight foundation models demonstrate that our method provides faithful interpretations with fewer regions and exhibits strong generalization, shows an average improvement of 36.3% in Insertion and 39.6% in Deletion. Our method also outperforms the naive greedy search in attribution efficiency, being 1.6 times faster. Furthermore, when explaining the reasons behind model prediction errors, the average highest confidence achieved by our method is, on average, 86.1% higher than that of state-of-the-art attribution algorithms. The code is available at https://github.com/RuoyuChen10/LIMA.

Recent work on enhancing the reasoning abilities of large language models (LLMs) has introduced explicit length control as a means of constraining computational cost while preserving accuracy. However, existing approaches rely on fixed-length training budgets, which do not take advantage of the natural progression from exploration to compression during learning. In this work, we propose a curriculum learning strategy for length-controlled reasoning using Group Relative Policy Optimization (GRPO). Our method starts with generous token budgets and gradually tightens them over training, encouraging models to first discover effective solution strategies and then distill them into more concise reasoning traces. We augment GRPO with a reward function that balances three signals: task correctness (via verifier feedback), length efficiency, and formatting adherence (via structural tags). Experiments on GSM8K, MATH500, SVAMP, College Math, and GSM+ demonstrate that curriculum-based training consistently outperforms fixed-budget baselines at the same final budget, achieving higher accuracy and significantly improved token efficiency. We further ablate the impact of reward weighting and decay schedule design, showing that progressive constraint serves as a powerful inductive bias for training efficient reasoning models. Our code and checkpoints are released at: https://github.com/hammoudhasan/curriculum_grpo.

Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all tokens, thereby overlooking the intrinsic information heterogeneity along reasoning chains. We show that this coarse-grained credit assignment leads to premature entropy collapse and encourages the model to generate redundant, low-quality reasoning paths. Through systematic empirical analysis, we identify Critical Decision Pivots (CDPs): transient high-entropy states where the policy's trajectory is most sensitive to perturbations. These pivots represent the "forks in the road" where effective multi-path exploration is most crucial yet often suppressed by uniform advantage signals. Building on these insights, we propose Entropy-Regulated Policy Optimization (ERPO), which transitions the optimization focus from coarse sequences to fine-grained token dynamics. ERPO introduces three synergistic components: (i) Entropy-aware Gating, which adaptively amplifies exploration at CDPs to facilitate diverse path discovery; (ii) Bucket-based Implicit Normalization, which mitigates difficulty bias by aligning token progress windows; and (iii) Result-anchored Advantage Synthesis, which re-weights token-level signals via outcome-driven anchors. Extensive experiments on competitive mathematical benchmarks demonstrate that ERPO significantly outperforms GRPO. Notably, ERPO not only boosts reasoning accuracy but also yields significantly more concise and robust derivation paths, while achieving performance comparable to large models with orders of magnitude more parameters.

Verifier-guided reinforcement learning has become a powerful paradigm for improving LLM reasoning. In multi-turn settings, models receive a verifier score after each turn and iteratively refine their outputs. Although such scores provide dense feedback, they do not directly provide dense credit: a score measures the quality of the current output, while credit should measure how the current turn changes the refinement trajectory. We propose TCPO, a turn-level credit assignment method for verifier-guided multi-turn RL. TCPO casts credit assignment as score-to-credit conversion and constructs turn-level advantages through reference-based comparisons: retrospective credit captures immediate progress and regression relative to the best prior state; hindsight delayed credit identifies non-improving turns with later payoff; and selective fixed-history counterfactual estimation refines high-surprisal turns under the same history. Experiments on math reasoning, code generation, and AppWorld agent tasks show that TCPO improves or matches the strongest baselines across model scales, task domains, and verifier types. TCPO achieves the best or tied-best best-turn Pass@8 on Qwen3-4B and DeepSeek-R1-Distill-Llama-8B, reduces turns to success, and improves multi-turn agent performance. These results highlight score-to-credit conversion as a central ingredient for verifier-guided multi-turn policy optimization.

Reinforcement learning with verifiable rewards (RLVR) has become a core technique for post-training of Large Language Models (LLMs). While policy optimization is driven by all sampled tokens under a globally broadcast scalar reward, the heterogeneous policy behaviors exhibited along trajectories are largely overlooked without differentiation. Existing works address this by credit allocation, including token-level advantage reweighting, and selective token optimization, however, the allocation criterion are principally stagnant throughout training, limiting resilient policy evolution. In this work, we argue that when learning signals are scheduled can be as important as where they are allocated across tokens, and introduce the temporal dimension that scheduling the credit allocation criteria over the course of RLVR optimization. We find that prioritizing targeted tokens emphasized with specific policy behaviors, and gradually attenuating toward general optimization leads to more stable and efficient learning dynamics. Furthermore, we show that simple trajectory percentiles provide a natural perspective for distinguishing policy behaviors, and works effectively with temporal scheduling. Our analysis reveals that standard optimization substantially sacrifices policy entropy when simultaneously accommodating heterogeneous behaviors, whereas temporal scheduling yields healthier policy evolution dynamics. Experiments across mathematical and general reasoning benchmarks demonstrate consistent improvements, suggesting that temporal scheduling constitutes a promising optimization dimension.

Text-to-image (T2I) models can synthesize realistic, prompt-aligned images, yet samples generated for the same prompt often cover only a small subset of visually distinct modes. This limits the diversity of images, and for person-centric prompts, can reflect or amplify demographic skew. We formalize this problem as coverage of a predefined set of semantically specified modes, which we call target-mode coverage. We then propose multi-axis max@K, a group-based reinforcement learning objective for improving such coverage in diffusion-based T2I models. Given a group of samples and one score per target category, multi-axis max@K first takes the maximum score across samples for each category and then sums these category-wise maxima. The resulting credit assignment gives a sample positive weight on a category only when it increases that category's group-wise maximum, allowing different samples to contribute to different categories. We first validate the credit-assignment mechanism on a synthetic mixture and on SD3.5-M using deterministic pixel-based color rewards. We then evaluate the same objective on perceived-appearance fairness. Across three automatic evaluators on held-out prompts, multi-axis max@K improves the Fairness Score by 0.23-0.36 relative to the base model, while maintaining image quality and text alignment.