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Life sciences · Preprint
arXiv · September 3, 2026
Early or partial results. Treat as a signal, not a conclusion.
This preprint introduces Gradient-Aligned Reward (GAR), a novel dense reward method for reinforcement learning in large language models that uses cosine similarity of gradient vectors to enable fine-grained signal during chain-of-thought reasoning. The authors report improvements over baselines (GRPO) on competition math benchmarks and transfer to knowledge tasks, but the work is unrefereed, lacks independent validation, and does not report sample sizes or statistical significance.
Preprint. Qwen3-4B and Qwen3-8B language models evaluated on competition-level math benchmarks, GPQA Diamond, and MMLU-Pro.. Intervention: Gradient-Aligned Reward (GAR): dense reward computed via cosine similarity of truncated backpropagation gradient vectors to expert-anchor gradient.. Compared with: GRPO and other baselines (names not detailed); no explicit control condition described..
GAR incurs less than 9% wall-clock overhead compared to baseline methods GAR consistently improves over GRPO on competition-level math benchmarks (specific improvement magnitudes not reported) GAR transfers to GPQA Diamond and MMLU-Pro without domain-specific data (transfer success not quantified)
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This is a preprint describing a novel method for reward design in reinforcement learning applied to LLM reasoning, demonstrated on benchmark tasks without peer review or independent external validation.
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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.
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