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

2025-10-01

AI Summary

Existing LLM output verification methods rely on text-level signals (e.g., reward models) or calibrated token probabilities, suffering from overfitting or sensitivity to calibration quality. This paper proposes CLUE, a non-parametric verification method based on clustering hidden-state trajectories. Its core innovation is the first direct exploitation of the geometric structure of internal model activations: it constructs differential representations of reasoning paths, builds prototypical success/failure experiences in the latent space, and enables unsupervised discrimination via nearest-centroid distance. Experiments show that CLUE outperforms LLM-as-a-judge baselines on AIME 2024/2025 and GPQA, matching state-of-the-art confidence-based methods. On AIME 2024, it lifts the accuracy of a 1.5B-parameter model from 56.7% to 70.0%, empirically confirming that correct reasoning exhibits separable geometric structure in the hidden space.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

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).

Problem

• Verifying LLM output quality using internal hidden states
• Overcoming limitations of text-level and confidence-based verification
• Developing non-parametric verification via hidden state clustering

Innovation

• Uses hidden states as unified verification foundation
• Clusters hidden state deltas from past experience
• Classifies correctness via nearest centroid distance