@inproceedings{zhang-etal-2026-silence,
title = "Silence the Judge: Reinforcement Learning with Self-Verifier via Latent Geometric Clustering",
author = "Zhang, Nonghai and
Ma, Weitao and
Ma, Zhanyu and
Xu, Jun and
Gao, Jiuchong and
Hao, Jinghua and
He, Renqing and
Xu, Jingwen",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.2569/",
pages = "58355--58373",
ISBN = "979-8-89176-459-0",
abstract = "Group Relative Policy Optimization (GRPO) significantly enhances the reasoning performance of Large Language Models (LLMs). However, this success heavily relies on expensive external verifiers or human rules. Such dependency not only leads to significant computational costs and training latency, but also yields sparse rewards that hinder optimization efficiency. To address these challenges, we propose Latent-GRPO, a framework that derives intrinsic rewards directly from latent space geometry. Crucially, our empirical analysis reveals a compelling geometric property: terminal token representations of correct reasoning trajectories form dense clusters with high intra-class similarity, whereas incorrect trajectories remain scattered as outliers. In light of this discovery, we introduce the Iterative Robust Centroid Estimation (IRCE) algorithm, which generates dense, continuous rewards by mitigating magnitude fluctuations via spherical projection and estimating a robust ``truth centroid'' through iterative aggregation. Experimental results on multiple datasets show that our method maintains model performance while achieving a training speedup of over 2x compared to baselines. Furthermore, extensive results demonstrate strong generalization ability and robustness."
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<abstract>Group Relative Policy Optimization (GRPO) significantly enhances the reasoning performance of Large Language Models (LLMs). However, this success heavily relies on expensive external verifiers or human rules. Such dependency not only leads to significant computational costs and training latency, but also yields sparse rewards that hinder optimization efficiency. To address these challenges, we propose Latent-GRPO, a framework that derives intrinsic rewards directly from latent space geometry. Crucially, our empirical analysis reveals a compelling geometric property: terminal token representations of correct reasoning trajectories form dense clusters with high intra-class similarity, whereas incorrect trajectories remain scattered as outliers. In light of this discovery, we introduce the Iterative Robust Centroid Estimation (IRCE) algorithm, which generates dense, continuous rewards by mitigating magnitude fluctuations via spherical projection and estimating a robust “truth centroid” through iterative aggregation. Experimental results on multiple datasets show that our method maintains model performance while achieving a training speedup of over 2x compared to baselines. Furthermore, extensive results demonstrate strong generalization ability and robustness.</abstract>
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%0 Conference Proceedings
%T Silence the Judge: Reinforcement Learning with Self-Verifier via Latent Geometric Clustering
%A Zhang, Nonghai
%A Ma, Weitao
%A Ma, Zhanyu
%A Xu, Jun
%A Gao, Jiuchong
%A Hao, Jinghua
%A He, Renqing
%A Xu, Jingwen
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F zhang-etal-2026-silence
%X Group Relative Policy Optimization (GRPO) significantly enhances the reasoning performance of Large Language Models (LLMs). However, this success heavily relies on expensive external verifiers or human rules. Such dependency not only leads to significant computational costs and training latency, but also yields sparse rewards that hinder optimization efficiency. To address these challenges, we propose Latent-GRPO, a framework that derives intrinsic rewards directly from latent space geometry. Crucially, our empirical analysis reveals a compelling geometric property: terminal token representations of correct reasoning trajectories form dense clusters with high intra-class similarity, whereas incorrect trajectories remain scattered as outliers. In light of this discovery, we introduce the Iterative Robust Centroid Estimation (IRCE) algorithm, which generates dense, continuous rewards by mitigating magnitude fluctuations via spherical projection and estimating a robust “truth centroid” through iterative aggregation. Experimental results on multiple datasets show that our method maintains model performance while achieving a training speedup of over 2x compared to baselines. Furthermore, extensive results demonstrate strong generalization ability and robustness.
%U https://aclanthology.org/2026.emnlp-main.2569/
%P 58355-58373
Markdown (Informal)
[Silence the Judge: Reinforcement Learning with Self-Verifier via Latent Geometric Clustering](https://aclanthology.org/2026.emnlp-main.2569/) (Zhang et al., EMNLP 2026)
ACL
- Nonghai Zhang, Weitao Ma, Zhanyu Ma, Jun Xu, Jiuchong Gao, Jinghua Hao, Renqing He, and Jingwen Xu. 2026. Silence the Judge: Reinforcement Learning with Self-Verifier via Latent Geometric Clustering. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 58355–58373, Budapest, Hungary. Association for Computational Linguistics.