SCOPE-RL improves average accuracy by up to 11.2 pp and reduces reasoning tokens by up to 27.1% over outcome-only GRPO, indicating that reward-signal densification is complementary to policy-update-level RLVR advances.
Abstract
Reinforcement learning with verifiable rewards (RLVR) optimizes LLMs using sparse verifiable final-answer rewards. This sparse anchor reliably verifies whether a trajectory succeeds but provides no direct feedback on the reasoning path that produced it. Before success, prerequisite progress on hard problems receives no reward signal; after success, outcome rewards cannot distinguish well-organized correct trajectories from redundant or locally flawed ones. We introduce SCOPE-RL (Scaffolded Chain Optimization with Process Efficiency), a two-stage framework that densifies this anchor while retaining the GRPO update: Adaptive Scaffolded RL adds prefix-decomposed verifiable rewards on answer-hidden sub-question chains before success, and Quality-Aware Process RL applies correctness-gated process-shape rewards to refine correct trajectories after success. An expert-validated Step-Quality Evaluation Protocol evaluates useful-step density, error localization, and token efficiency beyond final-answer accuracy. On Qwen3-8B-Instruct trained on DAPO-Math and Big-Math, SCOPE-RL improves average accuracy by up to 11.2 pp and reduces reasoning tokens by up to 27.1% over outcome-only GRPO; the gains hold under GSPO and on Qwen3-0.6B-Instruct, indicating that reward-signal densification is complementary to policy-update-level RLVR advances. Code and data are available at https://github.com/tokencraft-lab/SCOPE-RL.
Reinforcement learning (RL) has become one of the primary paradigms for reasoning enhancement of large language models (LLMs). In particular, Group Relative Policy Optimization (GRPO) and related algorithms have demonstrated strong performance with outcome-level rewards. However, these methods depend solely on the final answer, without feedback regarding which intermediate steps contribute to success or failure. As task complexity and reasoning trajectory length increase, such sparse final-answer rewards become increasingly insufficient. To address this limitation, we introduce ConsensusBench, a novel dataset designed to provide rule-based process-level signals. We posit that a correct final answer relies on a small set of intermediate conclusions throughout the reasoning process, which can be seen as a verifiable sub-outcome. We identify these sub-outcomes by filtering correct trajectories from N rollouts and clustering semantically equivalent intermediate statements. We call these clustered statements as Consensus Nodes. By integrating a rule-based process reward derived from these nodes into GRPO-style algorithms, we develop a new reinforcement learning signal named ConsensusPR. It directly reduces the reward sparsity of outcome reward across long reasoning trajectories. To facilitate systematic process-level evaluation, we introduce three metrics to our benchmark: Final Answer Accuracy (Acc), Node Coverage Rate (NCR), and Tokens per Node (TPN). Experiments across AIME 2024, AIME 2025, GSM8K, MATH-500, and our ConsensusBench demonstrate that the proposed method consistently surpasses GRPO-style approaches, highlighting the practical value of consensus nodes in guiding reasoning.
Shi-Qi Yan, Chao-Hong Tan, Qian Chen et al.· 0 citations
This work introduces StructReward, a compute-efficient framework that provides dense reinforcement signals through structured step-level reward alignment and substantially reduces the computational overhead of multimodal reinforcement learning.
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.
Le-Qi Zheng, Jin-Bo Su, Fang Niu et al.· 2 citations
It is shown that on-policy reinforcement learning with verifiable rewards (RLVR) can improve the current objective while making successful behaviors for later objectives too rare to sample and reinforce, and effective rewardable support is defined as successful trajectories reachable within a fixed rollout budget.
Shaohang Wei, Z.Y. Su, Feifan Song et al.· 0 citations
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), $N_{\mathrm{Base}} \approx \alpha N_{\mathrm{RL}}^{\beta}$, 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.
Wen-He Sun, Cun-Xiang Wang, Zijun Yao et al.· 0 citations
This work reformulates the implicit reward of sampled-token OPD based on trajectory correctness, then applies a ReLU gating mechanism to ensure that correct trajectories receive non-negative rewards and incorrect ones receive non-positive rewards, making it readily combinable with any policy gradient algorithm, such as GRPO.
Wenze Lin, Jiale Zhao, Xi-Tai Jiang et al.· 0 citations
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