GRAIL: Gradient-Reweighted Advantages for Reinforcement Learning with Verifiable Rewards
Authors: Tej Deep Pala, Vernon Toh, Soujanya Poria
Organizations: DeCLaRe Lab, Nanyang Technological University
Abstract
Reinforcement learning with verifiable rewards (e.g. GRPO) is now a common way to improve mathematical reasoning in Large Language Models (LLMs). However, current methods usually broadcast one sequence-level advantage to all tokens, or use costly process reward models (PRMs) for step-level supervision. Uniform advantage distribution assumes that all tokens contribute equally to the final reward. This dilutes the gradient signal, since flawed reasoning steps and filler words are updated as strongly as valid logical inferences. To address this, we introduce Gradient-Reweighted Advantage (GRAIL), an intrinsic token-wise advantage reweighting method. GRAIL uses gradient-activation saliency to place more weight on tokens that are more locally sensitive to the final answer. Evaluations across five models from the Qwen3, R1-distilled and OctoThinker families show that GRAIL consistently outperforms GRPO. GRAIL achieved an average improvement of 3.60% in accuracy and 3.05% in Pass@3, demonstrating that fine-grained reasoning alignment can be achieved without process-level supervision.
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) 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.
Group Relative Policy Optimization (GRPO) is an effective recipe for training reasoning models with verifier-based outcome rewards, but its supervision is sparse: when all sampled trajectories for a prompt receive the same verifier reward, the group-relative advantage collapses to zero and learning stalls. Outcome-only rewards also provide no step-level credit assignment, limiting exploration and making it harder to learn robust reasoning. We present VeriGate (Verifier-Gated Step-Level GRPO), a verifier-gated extension of GRPO that addresses these limitations with three design choices. First, VeriGate keeps the verifier in charge whenever verifier rewards induce a meaningful preference among sampled trajectories, and uses process supervision only when verifier rewards are degenerate. Second, instead of collapsing Process Reward Model (PRM) step scores into a single trajectory reward, VeriGate converts them into future-cumulated rewards to assign continuation-aware credit. Third, VeriGate transforms these rewards into group-normalized token-level advantages, restoring informative gradients and fine-grained credit assignment while remaining less susceptible to reward hacking than methods that optimize aggregated PRM scores. Empirically, training on MATH with 1.5B and 7B Qwen2.5-Instruct models and evaluating on six reasoning benchmarks, VeriGate improves average accuracy by about 20% and 12% for 1.5B and 7B models respectively, substantially reduces zero-gradient failures, decreases reward-hacking behavior, and improves reasoning quality relative to outcome-only GRPO and PRM-as-outcome baselines.