SR-GRPO: Stable Rank as an Intrinsic Geometric Reward for Large Language Model Alignment

TL;DR

This paper introduces stable rank as an intrinsic, annotation-free quality measure derived from model representations, and uses it as a reward signal in reinforcement learning to improve large language model alignment without external supervision.

Contribution

The paper proposes stable rank as a novel intrinsic quality signal and demonstrates its effectiveness in reinforcement learning for LLM alignment, outperforming existing methods.

Findings

Stable rank achieves 84.04% accuracy on RewardBench.

SR-GRPO improves task accuracy by 11.3 percentage points.

SR-GRPO outperforms reward models and self-evaluation baselines.

Abstract

Aligning Large Language Models (LLMs) with human preferences typically relies on external supervision, which faces critical limitations: human annotations are scarce and subjective, reward models are vulnerable to reward hacking, and self-evaluation methods suffer from prompt sensitivity and biases. In this work, we propose stable rank, an intrinsic, annotation-free quality signal derived from model representations. Stable rank measures the effective dimensionality of hidden states by computing the ratio of total variance to dominant-direction variance, capturing quality through how information distributes across representation dimensions. Empirically, stable rank achieves 84.04% accuracy on RewardBench and improves task accuracy by an average of 11.3 percentage points over greedy decoding via Best-of-N sampling. Leveraging this insight, we introduce Stable Rank Group Relative Policy Optimization (SR-GRPO), which uses stable rank as a reward signal for reinforcement learning. Without external supervision, SR-GRPO improves Qwen2.5-1.5B-Instruct by 10% on STEM and 19% on mathematical reasoning, outperforming both learned reward models and self-evaluation baselines. Our findings demonstrate that quality signals can be extracted from internal model geometry, offering a path toward scalable alignment without external supervision.