CLUE: Non-parametric Verification from Experience via Hidden-State
  Clustering
Authors: name: Zhenwen Liang; name: Ruosen Li; name: Yujun Zhou; name: Linfeng Song; name: Dian Yu; name: Xinya Du; name: Haitao Mi; name: Dong Yu
Published: 2025-10-02 02:14:33

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).