Reinforcement Learning with Verifiable Rewards

Self-evolving methods reduce the need for human-annotated trajectories by allowing tool-using agents to generate their own training data. Yet existing methods typically separate trajectory generation from evaluation, relying on static verifiers that cannot adapt to emerging failure modes or self-consistency signals that may reinforce errors shared across trajectories. Jointly adapting planning, execution, and evaluation offers a promising alternative, but introduces a fundamental coordination challenge: each component continuously changes the data or feedback used to train the others. We address this challenge with \textbf{UnifiedPlayers}, a cooperative framework comprising a Planning Player that generates tasks, an Execution Player that produces multi-turn trajectories with Python tool calls, and an Evaluation Player that constructs executable verifiers. We design role-specific rewards that coordinate the three players toward a shared learning objective under GRPO. Across two model backbones and twelve reasoning benchmarks, UnifiedPlayers outperforms the strongest prior baseline by at least 3.5% on mathematical reasoning and 3.9% on general reasoning tasks. Moreover, the learned verifier achieves 84.2% adversarial detection accuracy, while its reward signal exhibits 2.03$\times$ higher per-question variance than a self-consistency baseline, providing more discriminative verifications. These results highlight cooperation among specialized players as a promising path toward self-enhanced tool-integrated agents.

Reinforcement learning with verifiable rewards (RLVR) has significantly improved the reasoning capabilities of large vision-language models (LVLMs). However, standard on-policy RLVR algorithms face a critical optimization bottleneck in preserving and reinforcing visually grounded reasoning behaviors: valuable visually-grounded reasoning trajectories are discarded after a single update, while uniform token advantage allocation prevents the model from reinforcing critical perception or reasoning steps. To bridge this gap, we propose PIVOT, a dual-level learning framework that anchors policy optimization around informative visual reasoning signals. Specifically, PIVOT introduces a self-calibrated experience replay mechanism, which selectively collects and replays visually-grounded historical experiences as stable reference anchors for policy optimization. Building upon this, we further design a vision-guided advantage allocation mechanism to allocate additional vision-aware advantages to tokens based on their local visual support and impact on downstream reasoning. Extensive experiments across diverse benchmarks demonstrate that PIVOT achieves highly competitive performance in enhancing the multimodal reasoning capabilities of LVLMs.

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models (LLMs). We introduce Bellman Policy Optimization (BPO), a critic-free method derived from Policy Mirror Descent (PMD). For autoregressive generation with terminal rewards, BPO uses the Bellman equations to reformulate PMD as a trajectory-level objective. The reformulation avoids estimating state values at intermediate states. We prove that it has the same unique optimal solution as the original PMD objective. We derive the practical BPO loss by approximating this objective. Its mismatch-correction weight is a smoothed ratio of complementary token probabilities. Experiments on mathematical reasoning benchmarks demonstrate the effectiveness of BPO.

Reinforcement learning with verifiable rewards (RLVR) has become a central approach for improving mathematical reasoning in language models, but long-form completions introduce a difficult credit-assignment problem: different parts of a solution trace may contribute unevenly to final correctness. Existing policyoptimization objectives for RLVR commonly apply importance-sampling correction at either the token level (GRPO, DAPO) or the sequence level (GSPO), imposing different granularities for assigning credit across a response. We introduce Hierarchical Importance-Sampling Policy Optimization (HISPO), a segment-level policy-optimization method that constructs rollout-time entropy-derived contiguous segments, assigns soft entropy-based saliency weights, and applies clipped importance-sampling correction at the segment granularity. This provides an intermediate correction unit between token-level GRPO/DAPO and sequence-level GSPO. We evaluate HISPO by fine-tuning Qwen3-1.7B-Base on mathematical reasoning tasks. Across six benchmarks, HISPO improves Pass@8 over the strongest baseline on all benchmarks and matches or exceeds the strongest baseline in Acc@8 on five of them. On AIME25, HISPO improves over GRPO by +3.75 Acc@8 and +3.78 Pass@8, and over GSPO by +2.50 Acc@8 and +1.27 Pass@8. These results suggest that segment-level correction is a promising granularity for RLVR in long-form mathematical reasoning.

Reinforcement learning with verifiable rewards is typically performed on-policy, keeping training data close to the current policy but limiting learning to trajectories that the policy can discover itself. Off-policy methods such as supervised fine-tuning, on the other hand, can leverage external knowledge beyond the base model's capabilities, but may suffer from large distribution shift. The key challenge is thus to expand exploration without sacrificing learnability. In this work, we introduce Minimal Intervention Reinforcement Learning (MInTRL), which expands the exploration frontier through sparse, local interventions in otherwise on-policy rollouts. During generation, a judge-intervention policy periodically reviews the current policy's output, replaces erroneous suffixes with short corrections, and immediately returns control to the policy. During training, MInTRL adopts a sequence-level advantage-regression objective that eliminates the need for importance sampling. We show that sparse, local interventions can substantially improve coverage beyond finite-budget on-policy sampling while preserving the overall on-policy nature of the resulting trajectories. Across math and code benchmarks, MInTRL consistently outperforms standard on-policy and off-policy baselines. Ablations show that MInTRL remains effective with self-intervention and across different judge policies, while performance peaks at moderate intervention intensity, highlighting the importance of intervening minimally. These results establish minimal intervention as an effective paradigm for enhancing on-policy RL.

Agent usage is shifting toward long-horizon tasks such as coding and scientific discovery, among which terminal tasks are especially important. We introduce T1, a Mixture-of-Experts model of 122B total trained with reinforcement learning, operating a real shell in a cloud sandbox for up to 300+ tool-call turns per task, rewarded by executing each task's own verifier. We provide a comprehensive recipe: First, an aggressively warm-started to stabilize actor-critic training, with a dense process reward scoring trajectories by the absolute number of passing verifiers. Second, stable optimization through TITO construction, training on the exact sampled token identifiers with drift repair at turn boundaries, and rollout routing replay, recording the sampler's per-token expert choices at every MoE layer and replaying them during training. Third, fully out-of-distribution training corpus: isolated seeds and synthesized tasks disjoint from Terminal-Bench 2.1 ensures gains reflect genuine capability transfer over benchmark overfitting. Together, TITO and R3 cut the training-to-inference log-probability difference from 0.021 to 0.013, with exactly aligned zero token drift in the loss region. On Terminal-Bench 2.1, our post-train pipeline raises initial base model from 43.8% to T1 with 64.0% resolved. On Long-Horizon Terminal Bench, T1 reaches 27.9% and surpasses GPT-5.4 and GLM-5.1.

Tree-structured rollouts give critic-free reinforcement learning with verifiable rewards (RLVR) step-level credit: fork a chain at an intermediate point, and sibling outcome differences estimate step value. Each fork adds sampling cost, so realistic budgets typically allow only a few forks per chain. A fork placed where the outcome is already largely settled yields siblings that mostly agree and provide almost no credit signal; hence, for a given tree size, where forks are placed largely determines how much step-level RL can gain. Most existing mainstream methods place forks by structure, such as fixed lengths, midpoints, and delimiters, or by next-token entropy. We formalize fork placement as locating the \emph{pivots} of the chain's value curve, where the expected outcome turns. We propose \emph{belief-shift branching}: read the model's answer belief at candidate boundaries and fork just before the step where consecutive beliefs diverge most. Three instantiations, none needing step-level supervision, span access levels: a black-box probe, a logit-lens depth profile, and a learned activation direction, which is fit offline and therefore used only in the validation before RL training. The signal only \emph{places} forks, and the probe costs about $1\%$ of step compute on mathematics and under $5\%$ on code when it runs inside the rollout engine. In that validation, against Monte-Carlo value curves, a belief-shift signal ranks first in each of the eight model$\times$benchmark panels, ahead of entropy, structural, and LLM-judge baselines. In RL across three model families and two domains, belief-shift forking leads every mathematics aggregate, on OLMo-3-7B by $+2.6$ aggregate and $+2.9$ on AIME 2026 over the strongest baseline, and sweeps every OLMo code column, by $+6.5$ on LiveCodeBench-medium.

Reinforcement learning with verifiable rewards (RLVR) has advanced language-model reasoning in domains such as mathematics and code, where objective answers are inexpensive to check. Diagnostic reasoning over complex data lacks this advantage: establishing the true cause of an anomaly often requires costly expert investigation and may remain ambiguous after the fact. We ask whether this asymmetry of verification can instead be engineered. We sample an intervention, inject it into a controlled simulator, and generate the observations it would produce. The hidden intervention provides an oracle label and objective reward, while the agent must still investigate noisy, confounded, and distributed evidence. We instantiate this approach in TRACE, a digital-advertising diagnostic environment with 12 root causes and fine-grained segment attribution. Agents investigate each episode using Python and SQL and must identify both the root cause and, when applicable, the affected segment assignment. On a held-out 235-episode test set, the strongest prompted baseline, Claude Opus 5, reaches 0.686 FullAttr@1. Supervised fine-tuning raises Qwen3.5-35B-A3B from 0.159 to 0.637, and subsequent RL with synthesized rewards reaches 0.757, outperforming all evaluated prompted baselines, including frontier closed-source models and a prompted Qwen3.5-122B-A10B model. The resulting policy also uses substantially fewer tool calls than the prompted 35B base. These results provide evidence that access to a scalable, objective training signal can be a more important constraint than model scale alone. More broadly, simulation-based verification can make otherwise ambiguous diagnostic reasoning tasks amenable to scalable reinforcement learning.

Frontier gains in language-model reasoning come from reinforcement learning on reasoning traces and are concentrated in domains with a cheap, sound verifier. We argue the field's binding constraint is the verification gap: no scalable, incorruptible reward for reasoning outside formal domains. We make four contributions. (1) Theory: in a joint-Gaussian model of best-of-N selection, verifier-gold correlation rho is the exact exchange rate between test-time compute and capability, and an unsound verifier pays a polynomial penalty N^(1/rho^2); a margin-free copula form predicts realized soundness of real LLM judges to 4% median error. (2) Demonstration: in program-synthesis testbeds with executable ground truth, including a pre-registered scaled replication, unsound verifiers lose Soundness-under-Pressure as optimization grows (0.94 to 0.32 at N=4096) while a sound verifier improves monotonically; reality-anchored settlement beats a frozen verifier under i.i.d. and adversarial pressure, driving the hacking gap from ~0.27 to ~0; soundness scales log-linearly with settled labels, with on-policy settlement ~10x more label-efficient than random labeling. With real LLM judges and unit-test execution as gold, a weak judge loses soundness under best-of-N (p<0.001), a stronger judge is more robust, and selection alone manufactures +0.53 hacking gaps from honest samples. Under real GRPO training, a frozen reward model traces the full overoptimization curve (executed reward collapses 90%) while the same model refit on a 10% settlement stream preserves 6x the executed reward. (3) Paradigm: proof-carrying cognition, where reasoning steps are typed probabilistic claims priced by a self-built world model trained only on held-out reality and settled by proper scoring rules. (4) Benchmark: we specify Soundness-under-Pressure as the headline metric for a reality-settled reasoning benchmark.

In reinforcement learning with verifiable rewards (RLVR) trained with group relative policy optimization (GRPO), the KL-free reward-advantage term studied here depends on within-group reward variation. If all rollouts in a group are correct or all are wrong, their group-relative advantages are identically zero; these zero-advantage silent groups provide no reward-advantage gradient, yet uniform sampling spends 39% of a run's rollouts on them. History-based prompt selection must first spend target-policy rollouts to estimate difficulty, creating a cold start with rollout waste; ThinkPrior instead uses an external anchor in one offline pass to construct a zero-rollout difficulty prior before the first target-policy rollout. The verifier-scored anchor pass rate supplies an external-anchor initialization for a Beta posterior; ThinkPrior selects by expected learnability and then updates from training outcomes, changing neither the loss nor the optimizer. On Qwen2.5-Math-7B across sixteen seeds, ThinkPrior more than halves early silent groups and cuts wasted rollouts through step 30 by nearly a fifth, while we detect no difference in final accuracy. On this 250-prompt pool the fixed-budget result is a reallocation rather than a net saving. The measured ThinkPrior+DAPO composition reduces generated rollouts by 10.6% while both arms retain the same 3840-rollout update budget. The prior requires no target-policy rollout before the first selection, but the posterior thereafter uses target-policy outcomes.

Reinforcement Learning with Verifiable Rewards (RLVR) has been central to the recent success of Large Reasoning Models. However, while RLVR significantly improves single-sample accuracy, it often fails to expand the model's intrinsic reasoning coverage (pass@k) due to limited exploration during training. To address this, we optimize the structural design of train-time rollouts to enhance pass@k. Our analysis identifies three key design principles: (1) difficulty-adaptive rollout can play an important role in expanding pass@k, beyond serving as an efficiency heuristic; (2) tree-based rollout outperforms parallel sampling in discovering correct answers; and (3) sentence-entropy-guided forking overcomes the localization phenomenon of token-level branching to maximize semantic diversity. Building on these insights, we propose DATPO (Difficulty-Adaptive Sentence-entropy-guided Tree-structured Policy Optimization). DATPO integrates difficulty-adaptive tree search with a sibling-diversity advantage term, explicitly promoting semantic diversity to expand reasoning coverage during training. Experiments on mathematical reasoning benchmarks demonstrate that DATPO outperforms baselines especially in pass@k, which directly translates to superior test-time scaling performance.

Reinforcement learning with verifiable rewards (RLVR) is sensitive to which problems a model trains on, yet existing selection criteria--difficulty filtering, hand-curation, reward-trajectory scoring--assess data value as an intrinsic property of problems, independent of the model that will learn from them. We introduce Circuit Reasoning Score (CRS), a selection signal derived from 46 reasoning-sensitive attention heads identified via contrastive ablation, computed in a single forward pass on the frozen base model without reward labels or rollouts. CRS runs against the intuitive hypothesis that stronger reasoning-circuit engagement produces better training data: on Qwen2.5-Math-7B, the lowest-engagement decile improves over random selection on three medium-difficulty benchmarks (GSM8K +2.0 pp, OlympiadBench +1.6 pp, Minerva +2.9 pp), while the highest-engagement decile gains less and is indistinguishable from the middle decile. The advantage has boundary conditions: on a domain-curated pool no selection method separates from the others; at 1.5B scale the useful direction differs; and the lowest-reward training condition produces the strongest downstream generalization. Within the Qwen2.5-Math settings tested, RLVR data selection appears regime-dependent rather than reducible to a static ranking of problem quality.

Verifiable rewards improve language models through reliable task-level feedback, but methods based on Group Relative Policy Optimization (GRPO) apply a sequence-level advantage uniformly across all tokens. This coarse credit assignment reinforces or penalizes entire responses without identifying which local decisions to preserve, reinforce, or revise. Conversely, evidence-conditioned self-distillation provides denser token-level supervision, yet teacher imitation can transfer stylistic artifacts and miscalibrated confidence that destabilize training when misaligned with task success. We introduce VERPO, which converts evidence-conditioned guidance into reward-aligned token-level credit assignment while retaining the outcome objective. VERPO decomposes teacher guidance into an evidence-free reference term and signed, evidence-induced corrections at each token. A stopped controller combines selective acceptance, token-wise localization, and cost-aware scaling by balancing alignment with the local GRPO update direction against Fisher movement cost. Furthermore, we introduce Fisher Evidence Contrast (FEC), which attenuates nuisance shifts along an estimated evidence-presence direction through a regularized projection. Across five scientific reasoning and tool-use tasks, VERPO prevents optimization collapse and consistently achieves the highest multi-task average across model backbones, yielding marked improvements particularly on smaller models over strong baselines. Qualitative diagnostics confirm that token acceptance selectively targets reasoning bottlenecks consistent with local reward alignment and Fisher movement cost.

Reinforcement learning with verifiable rewards (RLVR) and on-policy distillation (OPD) have emerged as two dominant methods for post-training reasoning LLMs. Prior work uses OPD's dense token-level supervision to complement the sparse RL reward, fusing the two signals within a single step: either as a \emph{weighted-additive combination} or a \emph{teacher-modulated rescaling} of the RL advantage. In this paper, we show that a simple two-stage scheme, OPD-then-RL, consistently outperforms pure OPD, pure RLVR, and all such joint baselines across logic and math reasoning benchmarks. Beyond the empirical results, we further provide a systematic understanding of this through pass@$k$ behavior, learning dynamics, and parameter updates, yielding a consistent explanation: OPD expands the student's coverage of teacher-supported solutions and RL sharpens within that support, while jointly optimizing the two signals causes them to interfere.To provide a practical recipe, we find that the OPD validation score is the key signal for when to switch to RL, and that OPD is a better cold start for RL than SFT. Together, our results establish OPD-then-RL as a simple yet strong way to combine the two methods, turning two entangled signals into complementary stages.

Group Relative Policy Optimization (GRPO) is widely studied for reinforcement learning with verifiable rewards, where its advantage estimator assigns each rollout a magnitude from within-group reward statistics. In the common case, this magnitude rewards rollouts that reach the correct answer through reasoning. Yet, an overlooked case shares the same surface: a rollout may land on it by guessing, and the formula still assigns a high magnitude, which we identify as the spurious advantage. This arises in three cases: bounded-answer tasks with a small candidate set; open-answer sets hosting bounded sub-cases; and search agents whose budget opens many paths to the same answer. In all three, this misleads the policy toward guess-like behaviors. We propose SIGNBALANCE, whose magnitude is composition-free: it keeps the verifier sign, uses a global scale, and restores zero-mean balance via a stop-gradient per-class rescaling. Across math and search agent benchmarks at different scales, SIGNBALANCE matches GRPO on open-answer math and improves on bounded-answer math and search agents. Code will be released.

Banks need conversational systems that can answer product questions, assist customers with account-related requests, and operate safely within strict operational and regulatory constraints. General-purpose language models do not reliably meet these requirements. They fall short when a task requires grounded information, correct tool use, or cautious handling of bank-specific sensitive situations. We introduce FiMI Banking, a controlled Indian retail-banking setting. We build it from vetted banking documents, structured ground truth, synthetic customer backgrounds, and banking tools. We evaluate two post-training approaches: preference optimization for response-level behavior, and reinforcement learning with verifiable rewards for multi-turn tool-use tasks. Preference optimization improves safe behavior substantially: out-of-scope refusal rises from 52% to 80%. Reinforcement learning improves edge-case performance from 0.509 to 0.718 and order-sensitive task performance from 0.590 to 0.679, while using 29% fewer generated tokens. These results show that preference optimization and verifiable-reward reinforcement learning address complementary requirements for reliable banking agents.

Reinforcement learning from verifiable rewards (RLVR) drives chain-of-thought reasoning in large language models, yet its binary outcome reward cannot distinguish among correct trajectories. Existing dense reward alternatives, from surface heuristics to process reward models, either ignore the expert solutions already present in training corpora or require expensive offline annotation. We propose Gradient-Aligned Reward (GAR), which operates in the policy's own gradient space: truncated backpropagation through the output projection layer extracts a compact gradient vector for each rollout, and cosine similarity with an expert-anchor gradient yields a dense, reasoning-aware reward with less than 9% wall-clock overhead. We prove that this cosine admits a multiplicative decomposition into prediction-error and activation-pattern factors, providing a concrete characterization of what the alignment signal measures. On Qwen3-4B and Qwen3-8B, GAR consistently improves over GRPO and other baselines on competition-level math benchmarks and transfers to GPQA Diamond and MMLU-Pro without domain-specific data. Code and data are available at https://github.com/LQgdwind/GAR.

Reinforcement learning with verifiable rewards (RLVR) improves large language model reasoning, but its practical scaling is constrained by expensive on-policy rollouts and the cost of obtaining reliable targets at scale. Existing methods address sample selection, incomplete supervision, or noisy labels separately, often entangling supervision logic with distributed training and hindering controlled comparison and reuse. We present DE-Venus, a unified framework for data-efficient RLVR that treats supervision as evolving state across data preparation and policy optimization. It organizes this lifecycle into three modules: Active Data Selection allocates training and annotation budgets; Weak Supervision Construction derives learning signals from unlabeled examples; and Training-Time Supervision Refinement filters or corrects unreliable supervision. DE-Venus supports seven representative methods and a data-selection pipeline by expressing method-specific decisions as offline dataset transitions or online transformations of targets, rewards, batches, and advantages while preserving verl's distributed execution contracts. Across public benchmarks and three business scenarios, separate configurations preserve or improve model quality with only 10% of labels or as little as 13% of relevant data; selected business configurations also reduce observed convergence steps by 63%--75%. DE-Venus thus reduces annotation and training costs without sacrificing scalable RL execution.

A reasoning model can improve from its own on-policy experience, but this inner loop is fragile: terminal verifiers provide reliable yet sparse supervision, while dense same-model guidance can reinforce false confidence or overconcentrate learning on a narrow solution mode. We introduce FlowBalance, a verifier-grounded self-improvement method that learns a normalized distribution over complete responses. For each on-policy trajectory, a frozen training-time view of the same policy uses privileged context to produce token-level log-probability gains, which are aggregated into a trajectory-level self-guidance score. FlowBalance calibrates this score with the verifier-derived group advantage: guidance is retained on positive-advantage trajectories, reversed on negative-advantage trajectories, and disabled when the rollout group provides no outcome preference. The resulting energy exponentially reweights a reference policy, and profiled trajectory balance fits the normalized target with one log-partition estimate per rollout group. This realizes outcome-calibrated self-guidance via trajectory balance, without a separate token-level imitation loss. Our analysis establishes within-group contrast preservation, a minimum-change reverse-KL characterization, monotonic verifier control of target reward, and an exact correction against false-positive self-guidance on rejected responses. On mathematical reasoning, FlowBalance improves average performance over FlowRL on both Qwen3-4B and Qwen3-8B, while also improving training speed and stability, avoiding direct OPSD's response-length collapse, and exhibiting higher correct-strategy diversity in a controlled AIME24 diagnostic.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for large language model (LLM) post-training, but its reliance on coarse outcome rewards leads to limited guidance on intermediate reasoning processes. Existing approaches such as process reward modeling and on-policy distillation introduce additional constraints, such as reliance on a specialized reward model or assuming identical reasoning patterns between teacher and student. Nevertheless, we observe that once a reasoning process first goes wrong, evaluating the subsequent reasoning provides limited additional information, as it is already conditioned on an invalid prefix. Therefore, we propose Cliff, a reward shaping strategy that utilizes an off-the-shelf LLM as a teacher to identify the first mistake in each rollout. As a result, the rollout is naturally decomposed into two parts: a correct prefix and an incorrect suffix. Cliff then converts this signal into token-level advantages, assigning positive advantages for the correct prefix and negative feedback afterward. Experiments across 12 different scenarios demonstrate that Cliff consistently improves reasoning performance, outperforming on-policy distillation by 15% and standard GRPO by 7%, even with teachers of modest capability. Furthermore, we analyse the role of ``ground truth'' in Cliff and investigate its training dynamics. These results establish Cliff as a simple, general and effective approach for improving RLVR with richer, fine-grained supervision.

Reinforcement learning with verifiable rewards (RLVR) and standard benchmark evaluation both rely on an automatic verifier that turns a free text answer into a binary reward. Prior work reports that one evaluation harness accepts only about 94% of its own ground truth answers, blaming LaTeX parsing. That is an aggregate: it does not say which answer forms consume the error budget. We supply the decomposition. We apply metamorphic testing to the verifier rather than the model, generating certified equivalent answer variants, that is, rewrites that preserve mathematical meaning by construction, so that any rejection is a provable false negative needing no human adjudication. We then measure rejection per answer category across four widely used verifiers over 307,420 verdicts. We find three things. (1) Self validation ranges from 53.8% to 95.2% on identical inputs, a spread of 41.3 points. The published figure describes one implementation, not the task; two configurations of the same library disagree on 49.9% of pairs. (2) The residual is not spread across parsing categories but concentrated in whitespace and punctuation, which account for 93.0% of in contract failures for the default LaTeX configuration. A trailing period or newline dominates the budget. (3) Separating rejection from execution failure shows that verifiers with similar aggregate error fail for opposite reasons, and that a reference numeric cascade accepts off by one wrong answers as a step function of magnitude, from 0% below 10^4 to 100% at or above, because its relative tolerance is scale invariant.

Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning, but how these gains relate to inference-time decoding and search remains unclear. Does RL create reasoning the base model lacks, or shift the rollout distribution toward trajectories it can already reach but rarely samples? We study this behaviorally with a Unified Decoding Framework (UDF), which expresses token-level sampling, beam-like search, tree search, and sequence-level resampling as executable policies over a shared budgeted operating space, scored post hoc with pass@$k$, self-consistency, best-of-$N$, and first-finish success. Using paired Base/RL checkpoints from SimpleRL-Zoo, we ask whether an RL default-policy curve can be approximated by a structured path of Base operating points. On Math500, AIME, GPQA, and IFEval, the pass@$k$ recovery path follows a Budgeted Operating-Point Transition Rule (BOPTR), $N_{\mathrm{Base}} \approx αN_{\mathrm{RL}}^β$, with benchmark-conditioned exponents. On Qwen2.5-7B, BOPTR gives the lowest transfer error among the non-oracle rules we test, 3.41 pp (95% CI [2.32, 5.53]); a three-seed replication gives 3.07 $\pm$ 0.39 pp. The rule extends to ten models across four families (3.28 to 4.87 pp on checkpoints added after fitting), to four benchmarks it was never fitted on (5.03 pp vs. 4.44 pp in fit), and holds without an RL checkpoint for the target model (4.19 pp) or without RL supervision of any kind (5.08 pp). These results support a qualified internalized-search reading: under the recipe we test, much of the measured RL gain corresponds to a change in sampling efficiency toward operating points the base model can already reach under search. We treat the scaling patterns as descriptive of this recipe and cohort, report where they break down, and use UDF and BOPTR as behavioral diagnostics rather than evidence of parameter-level equivalence.

Training open-ended agents via reinforcement learning (RL) is hindered by the lack of verifiable gold answers and scalable rubrics. Moreover, even near the model's capability boundary, long-horizon open-ended agentic tasks often yield brittle and unstable rewards, resulting in weak or noisy rollout contrast that obscures fine-grained optimization signals for group-based policy learning. To address these challenges, we propose ARISE-RL, a novel full-cycle self-evolution framework that couples a task/rubric Generator and a reasoning Solver through rubric-mediated co-evolution. The Generator grounds tool-related rubric criteria in real tool observations and is rewarded for producing valid, intermediate-difficulty tasks aligned with the Solver's evolving capability boundary. The Solver, in turn, learns from fine-grained rubric satisfaction signals through multi-step reasoning and tool use. We further introduce Reward-Gated Self-Evolution Distillation (RG-SED), which selectively distills a memory-augmented variant of the same policy back into itself only when the memory yields empirical reward improvement, thereby reducing distribution mismatch and avoiding blind imitation of noisy guidance. Finally, to support rigorous evaluation, we present ECR-Bench, an expert-calibrated rubric benchmark suite covering single-tool deep research and multi-tool travel planning. Extensive experiments demonstrate that ARISE-RL consistently achieves robust and stable overall state-of-the-art performance across all evaluated benchmarks.

Group relative policy optimization for reinforcement learning with verifiable rewards (RLVR) typically uses a fixed importance-sampling (IS) ratio clipping boundary across all rollouts. We identify a key limitation: rare correct rollouts on harder problems and abundant correct rollouts on easier problems are clipped at comparable rates, despite contributing very different learning signals. Rollouts with low group success exhibit larger IS ratios and carry stronger gradient signal for exploration and solving new problems, yet are disproportionately suppressed by fixed clipping. To address this, we propose Group Adaptive Clipping Policy Optimization (GAPO), a plug-in modification to GRPO methods that adapts the clipping boundary to the rollout advantage. GAPO is motivated by a reverse-KL trust-region perspective, which suggests that rollouts with larger learning signal should receive proportionally greater update headroom. GAPO requires no reward shaping and preserves the standard PPO/GSPO surrogate while adapting only the clipping threshold. Across Qwen and Llama models, GAPO consistently improves both Pass@1 and Pass@k over fixed clipping and advantage-shaping baselines on math reasoning and coding benchmarks where the pass rates by the base model are relatively low.

Outcome-based reinforcement learning provides verified feedback for language-model agents, but assigns trajectory-level advantage uniformly to all decisions, yielding coarse credit over long-horizon interactions. On-policy self-distillation offers finer supervision by re-evaluating sampled behavior with privileged information (PI) available only during training. However, fine-grained supervision is not necessarily fine-grained credit: PI-induced likelihood changes describe how additional information alters policy preference, but do not directly determine how an executable action should inherit the verified task outcome. This creates a supervision-credit gap. Privileged signals may be irrelevant to the current interaction state, operate at a token granularity misaligned with executable decisions, and lack the outcome semantics required for reinforcement. We introduce TASPO, which converts privileged supervision into outcome-grounded action credit. TASPO constructs decision-applicable PI from verified successful experience, aggregates PI-induced likelihood shifts at the executable-action level, and converts relative action support into positive, bounded, mean-preserving weights on the original trajectory advantage. Thus, the verified outcome determines the update direction and average scale, while PI only redistributes credit across actions. Across three agentic benchmarks, TASPO improves over GRPO by 10.6% and generalizes better to unseen tasks. Further analysis indicates that TASPO reduces supervision mismatch and that action-level assignment stabilizes the policy optimization process. These findings offer the community another interesting perspective.

Recent advances in large reasoning models (LRMs) have shown that reinforcement learning with verifiable rewards (RLVR) can substantially improve reasoning in mathematics and code, where outcomes can be checked automatically. Extending this progress to open-ended and agentic tasks remains difficult because reliable rewards are harder to obtain and direct human supervision cannot keep pace with the scale and complexity of model-generated experience. This paper studies how LRMs can continue to improve as human supervision gradually recedes from the learning loop. We examine two connected dimensions of this problem. The reward axis traces the development from per-instance human judgments to reusable verifiers and rewards that operate even without human feedback. The experience axis examines how learning can progress from human-curated tasks and environments toward self-generated curricula, constructed environments, and autonomous co-evolution. We connect these dimensions through a five-level ladder from L0 to L4 that identifies which parts of the learning process remain under continued human control. Our analysis further highlights the risks introduced by increasingly autonomous rewards and experience generation, including reward hacking, feedback drift, curriculum collapse, and environment errors. Consequently, we also provide the evaluation around three complementary objects: policy capability, feedback fidelity, and experience quality. This analysis provides a structured account of current approaches to scaling LRMs beyond human supervision and the open problems involved in developing self-sustaining learning systems toward superintelligence. Furthermore, we maintain a continuously updated GitHub repository to track the latest advances.

Reinforcement learning (RL), particularly RL with Verifiable Rewards (RLVR), has recently emerged as a central paradigm for enhancing large language models' (LLMs) reasoning abilities, demonstrating remarkable effectiveness across reasoning tasks. Recent studies suggest that high-entropy tokens play an exceptionally important role in model training, since training with only the highest 20% entropy tokens yields significant performance gains. However, why such high-entropy tokens are beneficial remains insufficiently understood. In this work, we find that although high-entropy tokens within one answer tend to correlate with large gradient magnitude, entropy alone fails to consistently reflect token importance across different answers, considering the variations in the answer-level reward signals. Based on this observation, we introduce the Gradient Magnitude-based Token Selection (GMTS) method to quantify token importance, which leverages the entropy-gradient connection to approximate gradient-magnitude rankings for token selection. We find that training on the top 20% tokens ranked by GMTS consistently outperforms entropy-based token selection across three reasoning domains and various model sizes, suggesting that GMTS provides a more fine-grained estimate of token contribution for RLVR training.

Large reasoning models achieve strong performance on complex tasks by generating extended chain-of-thought (CoT) traces via reinforcement learning with verifiable rewards (RLVR). While current RLVR methods have achieved strong results with correctness-based reward signals, they provide limited guidance on the quality of the reasoning process itself, leaving the internal reasoning structure largely unoptimized. Through empirical analysis across multiple model families, we identify a consistent pattern: correct reasoning trac es exhibit more frequent and larger token-level entropy drops within the thinking phase than incorrect ones. We propose ERR+, a two-phase RLVR framework grounded in this observation. The first phase trains with the Entropy Relief Reward (ERR), a bonus proportional to cumulative token-level entropy drops in the thinking phase, log-normalized by response length. Unlike prior methods that suppress entropy, ERR rewards the resolution of uncertainty while leaving exploratory high-entropy states unconstrained. The second phase introduces the Robust Relative Efficiency Reward, which scores each response's length against co-generated peers via a $\tanh$-transformed within-group $z$-score. We provide a formal analysis showing that joint optimization of the two objectives induces gradient conflict in early training, motivating the sequential design . Experiments on five datasets demonstrate consistent improvements in both accuracy and response conciseness across model backbones. Our code is available at https://github.com/XrkArul/err_response

Post training a language model to reason means updating its weights. Supervised finetuning and reinforcement learning both place the acquired capability inside the model where it cannot be inspected cannot be checked step by step and cannot be moved to another model. We argue that for tasks whose intermediate steps admit verification, reasoning is better placed outside the base models weights as an explicit program composed from deterministic and neural primitives. We introduce PLVR (Program Learning with Verifiable Rewards): a post training method that learns such programs directly from input-output examples. Its mechanism is symbolic backpropagation: each program layer carries a typed ontology a loss is computed at the output against ground truth and required input ontologies are propagated backward by type inference over primitive signatures: an analogue of the chain rule in which credit assignment is a derivation rather than an estimate. Where RLVR verifies a terminal outcome, PLVRs reward is a per step contract verdict dense over program structure. On LiveCodeBench v6 and Tau2Bench, 30B base models with PLVR outperform RL at matched budget by 27.8 points on average and frontier models an order of magnitude larger by 13.6 points. A single primitive library serves two benchmarks, so the marginal cost of a new task is 100 examples of program search and no new finetuning data. Replacing the loss guided search with uniform sampling over the same type admissible space at equal budget collapses the median program from 65.6 to 17.5, identifying the backward pass rather than the type system as the source of the advantage. We release the symbolic backpropagation library and a conformance checker so the method can be applied to primitive libraries other than our own.

Reinforcement Learning with Verifiable Rewards (RLVR) and on-policy distillation (OPD) have become two widely adopted paradigms for post-training large language models. However, RLVR suffers from sparse task-level feedback, while OPD provides dense token-level guidance but ignores trajectory correctness, limiting its performance to that of the teacher. Combining them is a promising direction: OPD supplies dense supervisory signals, while RLVR provides task-level correctness. Nevertheless, existing integrations often rely on weighted combination or heuristic switching, introducing extra hyperparameters and trade-offs. We propose On-policy Distillation with Verifiable Reward (OPDVR), a simple yet effective method that seamlessly combines OPD and RLVR without adding any hyperparameters. We first reformulate the implicit reward of sampled-token OPD based on trajectory correctness, then apply a ReLU gating mechanism to ensure that correct trajectories receive non-negative rewards and incorrect ones receive non-positive rewards---thereby aligning the distillation signal with task success while preserving the teacher's distributional guidance. Furthermore, our modification transforms sampled-token OPD into a proper RLVR method, making it readily combinable with any policy gradient algorithm, such as GRPO. Experiments on six reasoning benchmarks show that OPDVR consistently outperforms standard OPD. Our code is available at https://github.com/LeapLabTHU/OPDVR.