Enhancing Rubric-based RL via Self-Distillation

Rubric-based RL has recently shown promise in improving LLMs on open-ended tasks. A widely recognized limitation of rubric-based RL is limited exploration: criteria that no rollout manages to satisfy (Unexplored Criteria, UC) receive no optimization signal. Recent methods address this by incorporating rubric information as external guidance during rollout, yet they introduce a train-inference mismatch: the policy is optimized on rollouts produced under external guidance while this guidance is absent at inference time, causing error accumulation through autoregressive decoding. Moreover, these exploration-focused approaches overlook a fundamentally different failure mode that we term Suppressed Criteria (SC) -- criteria that are satisfied by some rollouts yet whose learning signals are lost during optimization because scalar reward aggregation assigns them non-positive aggregate advantages. Our analysis reveals that SC are remarkably prevalent: over 57% of samples exhibit this failure mode throughout training, with an average of 1.8 SC per sample. To simultaneously address both UC and SC without introducing training-inference mismatch, we propose Criterion-Distilled Policy Optimization (CriPO), which enhances rubric-based RL via on-policy self-distillation. For UC, CriPO constructs a criterion-injection self-teacher and computes a localized forward-KL loss to inject missing behaviors into the policy. For SC, CriPO employs a counterfactual self-teacher to locate criterion-relevant tokens in negative-advantage rollouts and flips their token-level advantages to positive values, preserving useful patterns that would otherwise be suppressed. Experiments on medicine and science benchmarks demonstrate that CriPO consistently outperforms rubric-based RL, achieving stronger final performance with approximately $2\times$ fewer optimization steps.

OPRD: On-Policy Representation Distillation

On-policy distillation (OPD) supervises the student only in output space by matching next-token probabilities. This output-only paradigm has two limits: (1) sampling variance from Monte Carlo KL estimates over large vocabularies (e.g., Qwen's ~150k tokens) persists throughout training, and (2) it treats the teacher as a black-box, discarding all intermediate hidden states after the LM head. We propose On-Policy Representation Distillation (OPRD), which lifts distillation into hidden-state space by aligning student and teacher representations across selected layers on the same rollouts, bypassing the LM head entirely. Theoretically, OPRD eliminates sampling variance and provides richer per-layer structural information. Empirically, OPRD closes the student-teacher gap on AIME 2024/2025 and AIMO, while output-space OPD baselines plateau below the teacher. OPRD also trains 1.44x faster and uses 54% less memory than top-k OPD. Code: https://github.com/ShenzhiYang2000/OPRD.

GeoMin: Data-Efficient Semi-Supervised RLVR via Geometric Distribution Modeling

Reinforcement learning with verifiable rewards (RLVR) significantly advances LLM reasoning, yet it faces a dilemma: standard supervised scaling is throttled by high annotation costs, while unsupervised alternatives suffer from severe model collapse. Recent semi-supervised RLVR methods address this by using a small labeled set to guide unlabeled data, achieving a promising trade-off between training efficacy and annotation cost. However, they suffer from a severe data-efficiency bottleneck due to the reliance on coarse performance heuristics, leaving a vast majority of valuable instances underutilized. To this end, we propose GeoMin, which models global feature distributions on labeled data to decode the structural discrepancy between correct and incorrect rollouts, thereby establishing a robust prior to assess the reliability of self-reward signals and fully unleash the potential of unlabeled data. Empirically, GeoMin outperforms the strongest baselines by +4.1% and even surpasses fully supervised models with only 10% of the annotations, demonstrating remarkable data efficiency.

Smart Picks in the Dark: Towards Efficient RLVR for Reasoning via Tracing Metacognitive Pivots

Reinforcement learning with verifiable rewards (RLVR) has greatly advanced large reasoning models (LRMs), but it requires timely training on a huge fully-annotated dataset. To this end, data-efficient RLVR methods have been widely studied from two perspectives: (i) data selection methods identify a small subset of "golden" samples that yield near-full-data performance, but they rely on a pre-existing pool of labeled data. (ii) unsupervised RLVR methods train the model using its own internal supervision signals on large-scale unlabeled data, yet they exhibit suboptimal performance. Accordingly, we investigate the "pick in the dark" setup for RLVR, which aims to select, without prior supervision, unlabeled samples that are most beneficial for training and worthy of annotation. Through systematic analysis, we demonstrate that smart picks hinge on a well-calibrated uncertainty estimator to enable strategic partitioning of data for adaptive training regimes. Building on this insight, we propose PivotTrace, a three-way data triage framework that leverages attention dynamics to trace metacognitive pivots during reasoning. By precisely quantifying uncertainty through pivot density, PivotTrace achieves automated data routing to synergistically maximize both annotation and training efficiency. Empirically, PivotTrace surpasses the fully supervised LRM with only 29.3% annotated samples and 2.75 faster convergence.

Can LLMs Learn to Reason Robustly under Noisy Supervision?

Reinforcement Learning with Verifiable Rewards (RLVR) effectively trains reasoning models that rely on abundant perfect labels, but its vulnerability to unavoidable noisy labels due to expert scarcity remains critically underexplored. In this work, we take the first step toward a systematic analysis of noisy label mechanisms in RLVR. In contrast to supervised classification, most RLVR algorithms incorporate a rollout-based condition: a label's influence on training is contingent on whether the current policy can generate rollouts that realize it, a property that naturally extends to noisy labels. Based on this observation, we distinguish two types of noise: inactive noisy labels, which reduce data efficiency, and active noisy labels, which are reinforced and risk skewing the model toward incorrect distributions. From experiments on training with noisy samples, we identify an Early Correctness Coherence phenomenon: although noisy samples begin to lag behind in later stages, accuracy on both clean and noisy samples increases similarly in early training. Motivated by this dynamic, we propose Online Label Refinement (OLR), which progressively corrects potentially noisy labels with majority-voted answers when two conditions hold: a positive slope in the majority answer's rollout pass rate and stable historical consistency across updates, enabling gradual self-correction as the policy improves. We evaluate OLR on six in-distribution mathematical reasoning benchmarks (AIME24/25, AMC, MATH-500, Minerva, and Olympiad) and three out-of-distribution tasks (ARC-c, GPQA-diamond, and MMLU-pro). Across noise ratios from 0.1 to 0.9, OLR consistently improves robustness under both inactive and active noisy-label settings, achieving average gains of 3.6% to 3.9% on in-distribution benchmarks and 3.3% to 4.6% on out-of-distribution evaluations.

AgentProcessBench: Diagnosing Step-Level Process Quality in Tool-Using Agents

While Large Language Models (LLMs) have evolved into tool-using agents, they remain brittle in long-horizon interactions. Unlike mathematical reasoning where errors are often rectifiable via backtracking, tool-use failures frequently induce irreversible side effects, making accurate step-level verification critical. However, existing process-level benchmarks are predominantly confined to closed-world mathematical domains, failing to capture the dynamic and open-ended nature of tool execution. To bridge this gap, we introduce AgentProcessBench, the first benchmark dedicated to evaluating step-level effectiveness in realistic, tool-augmented trajectories. The benchmark comprises 1,000 diverse trajectories and 8,509 human-labeled step annotations with 89.1% inter-annotator agreement. It features a ternary labeling scheme to capture exploration and an error propagation rule to reduce labeling ambiguity. Extensive experiments reveal key insights: (1) weaker policy models exhibit inflated ratios of correct steps due to early termination; (2) distinguishing neutral and erroneous actions remains a significant challenge for current models; and (3) process-derived signals provide complementary value to outcome supervision, significantly enhancing test-time scaling. We hope AgentProcessBench can foster future research in reward models and pave the way toward general agents. The code and data are available at https://github.com/RUCBM/AgentProcessBench.

TraPO: A Semi-Supervised Reinforcement Learning Framework for Boosting LLM Reasoning

Reinforcement learning with verifiable rewards (RLVR) has proven effective in training large reasoning models (LRMs) by leveraging answer-verifiable signals to guide policy optimization, which, however, suffers from high annotation costs. To alleviate this problem, recent work has explored unsupervised RLVR methods that derive rewards solely from the model's internal consistency, such as through entropy and majority voting. While seemingly promising, these methods often suffer from model collapse in the later stages of training, which may arise from the reinforcement of incorrect reasoning patterns in the absence of external supervision. In this work, we investigate a novel semi-supervised RLVR paradigm that utilizes a small labeled set to guide RLVR training on unlabeled samples. Our key insight is that supervised rewards are essential for stabilizing consistency-based training on unlabeled samples, ensuring that only reasoning patterns verified on labeled instances are incorporated into RL training. Technically, we propose an effective policy optimization algorithm, TraPO, that identifies reliable unlabeled samples by matching their learning trajectory similarity to labeled ones. Building on this, TraPO achieves remarkable data efficiency and strong generalization on six widely used mathematical reasoning benchmarks (AIME24/25, AMC, MATH-500, Minerva, and Olympiad) and three out-of-distribution tasks (ARC-c, GPQA-diamond, and MMLU-pro). With only 1K labeled and 3K unlabeled samples, TraPO reaches 42.6% average accuracy, surpassing the best unsupervised method trained on 45K unlabeled samples (38.3%). Notably, when using 4K labeled and 12K unlabeled samples, TraPO even outperforms the fully supervised model trained on the full 45K labeled samples on all benchmarks, while using only 10% of the labeled data. The code is available via https://github.com/ShenzhiYang2000/TRAPO.

Bounded and Uniform Energy-based Out-of-distribution Detection for Graphs

Given the critical role of graphs in real-world applications and their high-security requirements, improving the ability of graph neural networks (GNNs) to detect out-of-distribution (OOD) data is an urgent research problem. The recent work GNNSAFE proposes a framework based on the aggregation of negative energy scores that significantly improves the performance of GNNs to detect node-level OOD data. However, our study finds that score aggregation among nodes is susceptible to extreme values due to the unboundedness of the negative energy scores and logit shifts, which severely limits the accuracy of GNNs in detecting node-level OOD data. In this paper, we propose NODESAFE: reducing the generation of extreme scores of nodes by adding two optimization terms that make the negative energy scores bounded and mitigate the logit shift. Experimental results show that our approach dramatically improves the ability of GNNs to detect OOD data at the node level, e.g., in detecting OOD data induced by Structure Manipulation, the metric of FPR95 (lower is better) in scenarios without (with) OOD data exposure are reduced from the current SOTA by 28.4% (22.7%).

NodeReg: Mitigating the Imbalance and Distribution Shift Effects in Semi-Supervised Node Classification via Norm Consistency

Aggregating information from neighboring nodes benefits graph neural networks (GNNs) in semi-supervised node classification tasks. Nevertheless, this mechanism also renders nodes susceptible to the influence of their neighbors. For instance, this will occur when the neighboring nodes are imbalanced or the neighboring nodes contain noise, which can even affect the GNN's ability to generalize out of distribution. We find that ensuring the consistency of the norm for node representations can significantly reduce the impact of these two issues on GNNs. To this end, we propose a regularized optimization method called NodeReg that enforces the consistency of node representation norms. This method is simple but effective and satisfies Lipschitz continuity, thus facilitating stable optimization and significantly improving semi-supervised node classification performance under the above two scenarios. To illustrate, in the imbalance scenario, when training a GCN with an imbalance ratio of 0.1, NodeReg outperforms the most competitive baselines by 1.4%-25.9% in F1 score across five public datasets. Similarly, in the distribution shift scenario, NodeReg outperforms the most competitive baseline by 1.4%-3.1% in accuracy.

Category-free Out-of-Distribution Node Detection with Feature Resonance

Detecting out-of-distribution (OOD) nodes in the graph-based machine-learning field is challenging, particularly when in-distribution (ID) node multi-category labels are unavailable. Thus, we focus on feature space rather than label space and find that, ideally, during the optimization of known ID samples, unknown ID samples undergo more significant representation changes than OOD samples, even if the model is trained to fit random targets, which we called the Feature Resonance phenomenon. The rationale behind it is that even without gold labels, the local manifold may still exhibit smooth resonance. Based on this, we further develop a novel graph OOD framework, dubbed Resonance-based Separation and Learning (RSL), which comprises two core modules: (i) a more practical micro-level proxy of feature resonance that measures the movement of feature vectors in one training step. (ii) integrate with synthetic OOD nodes strategy to train an effective OOD classifier. Theoretically, we derive an error bound showing the superior separability of OOD nodes during the resonance period. Empirically, RSL achieves state-of-the-art performance, reducing the FPR95 metric by an average of 18.51% across five real-world datasets.