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This paper introduces Gradient-Aligned Reward (GAR), a novel reinforcement learning approach that enhances chain-of-thought reasoning in large language models by utilizing a dense reward mechanism based on gradient alignment with expert solutions. GAR leverages truncated backpropagation to extract compact gradient vectors, which are then compared to expert-anchor gradients to produce reasoning-aware rewards with minimal computational overhead. The method outperforms existing baselines, such as GRPO, on competitive math benchmarks and demonstrates effective transferability to other tasks without requiring additional domain-specific data.
Gradient-Aligned Reward transforms how we leverage expert knowledge in reinforcement learning, enabling LLMs to achieve superior reasoning performance with minimal overhead.
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.
