# Silence the Judge: Reinforcement Learning with Self-Verifier via Latent Geometric Clustering

arXiv: https://arxiv.org/abs/2601.08427 · HTML: https://mlsanity.com/paper/2601.08427/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 33 of its 47 references that are in the map.
- First posted on arXiv 13 Jan 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 33)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [Think before you speak: Training Language Models With Pause Tokens](https://mlsanity.com/paper/2310.02226/) (2023)
- [A Study of BFLOAT16 for Deep Learning Training](https://mlsanity.com/paper/1905.12322/) (2019)
- [Platypus: Quick, Cheap, and Powerful Refinement of LLMs](https://mlsanity.com/paper/2308.07317/) (2023)
- [Fast Best-of-N Decoding via Speculative Rejection](https://mlsanity.com/paper/2410.20290/) (2024)
- [Forest-of-Thought: Scaling Test-Time Compute for Enhancing LLM Reasoning](https://mlsanity.com/paper/2412.09078/) (2024)
- [Transformers represent belief state geometry in their residual stream](https://mlsanity.com/paper/2405.15943/) (2024)
- [Reinforcing General Reasoning without Verifiers](https://mlsanity.com/paper/2505.21493/) (2025)
- [PLANNER: Generating Diversified Paragraph via Latent Language Diffusion Model](https://mlsanity.com/paper/2306.02531/) (2023)
- [Latent Space Chain-of-Embedding Enables Output-free LLM Self-Evaluation](https://mlsanity.com/paper/2410.13640/) (2024)
- [Language Models are Hidden Reasoners: Unlocking Latent Reasoning Capabilities via Self-Rewarding](https://mlsanity.com/paper/2411.04282/) (2024)
- [Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers](https://mlsanity.com/paper/2510.00915/) (2025)
- [Knowing Before Saying: LLM Representations Encode Information About Chain-of-Thought Success Before Completion](https://mlsanity.com/paper/2505.24362/) (2025)

## Built on by (most cited first, 7 of 7)

- [The Latent Space: Foundation, Evolution, Mechanism, Ability, and Outlook](https://mlsanity.com/paper/2604.02029/) (2026)
- [GTS: Inference-Time Scaling of Latent Reasoning with a Learnable Gaussian Thought Sampler](https://mlsanity.com/paper/2602.14077/) (2026)
- [Breaking the Solver Bottleneck: Training Task Generators at the Learnable Frontier](https://mlsanity.com/paper/2606.18284/) (2026)
- [Consensus Group Relative Policy Optimization for Text Generation](https://mlsanity.com/paper/2602.03102/) (2026)
- [RRPO: Reference-Relative Policy Optimization with Stratified Conditional Rollouts](https://mlsanity.com/paper/2607.18470/) (2026)
- [Cloud-ScPO: Hidden-State Geometry for Semi-Supervised Preference Optimization in LLM Reasoning](https://mlsanity.com/paper/2608.01014/) (2026)
- [Unsupervised Post-Training of Foundation Models: A Survey](https://mlsanity.com/paper/2608.24982/) (2026)

## Abstract (arXiv)

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. The code will be released soon.