# CLUE: Non-parametric Verification from Experience via Hidden-State Clustering

arXiv: https://arxiv.org/abs/2510.01591 · HTML: https://mlsanity.com/paper/2510.01591/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 34 references that are in the map.
- First posted on arXiv 2 Oct 2025.

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

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Improving alignment of dialogue agents via targeted human judgements](https://mlsanity.com/paper/2209.14375/) (2022)
- [Persona Vectors: Monitoring and Controlling Character Traits in Language Models](https://mlsanity.com/paper/2507.21509/) (2025)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [General-Reasoner: Advancing LLM Reasoning Across All Domains](https://mlsanity.com/paper/2505.14652/) (2025)
- [Efficient Reasoning with Hidden Thinking](https://mlsanity.com/paper/2501.19201/) (2025)
- [Multiple Choice Questions: Reasoning Makes Large Language Models (LLMs) More Self-Confident, Especially When They are Wrong](https://mlsanity.com/paper/2501.09775/) (2025)
- [Semantic Self-Consistency: Enhancing Language Model Reasoning via Semantic Weighting](https://mlsanity.com/paper/2410.07839/) (2024)
- [Mining Intrinsic Rewards from LLM Hidden States for Efficient Best-of-N Sampling](https://mlsanity.com/paper/2505.12225/) (2025)
- [Momentum Point-Perplexity Mechanics in Large Language Models](https://mlsanity.com/paper/2508.08492/) (2025)

## Built on by (most cited first, 12 of 12)

- [LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals](https://mlsanity.com/paper/2604.05655/) (2026)
- [Hidden States as Early Signals: Step-level Trace Evaluation and Pruning for Efficient Test-Time Scaling](https://mlsanity.com/paper/2601.09093/) (2026)
- [ModeX: Evaluator-Free Best-of-N Selection for Open-Ended Generation](https://mlsanity.com/paper/2601.02535/) (2026)
- [Breaking the Solver Bottleneck: Training Task Generators at the Learnable Frontier](https://mlsanity.com/paper/2606.18284/) (2026)
- [Too Correct to Learn: Reinforcement Learning on Saturated Reasoning Data](https://mlsanity.com/paper/2604.18493/) (2026)
- [Single-Rollout Hidden-State Dynamics for Training-Free RLVR Data Selection](https://mlsanity.com/paper/2605.28631/) (2026)
- [ARBITER: Reasoning Trajectory Basins and Majority Vote Failures in Test-Time Sampling](https://mlsanity.com/paper/2605.26172/) (2026)
- [Reasoning as State Transition: A Representational Analysis of Reasoning Evolution in Large Language Models](https://mlsanity.com/paper/2602.00770/) (2026)
- [Spatiotemporal Hidden-State Dynamics as a Signature of Internal Reasoning in Large Language Models](https://mlsanity.com/paper/2605.01853/) (2026)
- [Reasoning Fine-Tuning Induces Persistent Latent Policy States](https://mlsanity.com/paper/2607.18532/) (2026)
- [HSRM: Hidden-State Reward Models for Test-Time Verification](https://mlsanity.com/paper/2608.30841/) (2026)
- [GLIDE: Generalized Layer-wise Intrinsic Distributional Evaluation for Heterogeneous LLM Agents](https://mlsanity.com/paper/2609.32295/) (2026)

## Abstract (arXiv)

Assessing the quality of Large Language Model (LLM) outputs presents a critical challenge. Previous methods either rely on text-level information (e.g., reward models, majority voting), which can overfit to superficial cues, or on calibrated confidence from token probabilities, which would fail on less-calibrated models. Yet both of these signals are, in fact, partial projections of a richer source of information: the model's internal hidden states. Early layers, closer to token embeddings, preserve semantic and lexical features that underpin text-based judgments, while later layers increasingly align with output logits, embedding confidence-related information. This paper explores hidden states directly as a unified foundation for verification. We show that the correctness of a solution is encoded as a geometrically separable signature within the trajectory of hidden activations. To validate this, we present Clue (Clustering and Experience-based Verification), a deliberately minimalist, non-parametric verifier. With no trainable parameters, CLUE only summarizes each reasoning trace by an hidden state delta and classifies correctness via nearest-centroid distance to ``success'' and ``failure'' clusters formed from past experience. The simplicity of this method highlights the strength of the underlying signal. Empirically, CLUE consistently outperforms LLM-as-a-judge baselines and matches or exceeds modern confidence-based methods in reranking candidates, improving both top-1 and majority-vote accuracy across AIME 24/25 and GPQA. As a highlight, on AIME 24 with a 1.5B model, CLUE boosts accuracy from 56.7% (majority@64) to 70.0% (top-maj@16).