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

TL;DR

This work tackles the verification of LLM outputs by arguing that correctness is encoded in the model's hidden-state dynamics rather than surface text or final probabilities. The authors introduce CLUE, a training-free verifier that summarizes each reasoning trace with the activation delta $Δh(T)$ between the start and end of a reasoning block and classifies trajectories by nearest-centroid distance to success and failure centers. Empirical results across AIME, GPQA, and WebInstruct show that CLUE matches or exceeds LLM-based judges and confidence-based reranking, with notable gains for smaller, less-calibrated models; e.g., on AIME 24 with a $1.5$B model, accuracy rises from $56.7 imes$ to $70.0 imes$. Layer-wise analysis reveals that separability grows in deeper layers, and RL-tuned models provide stronger internal distinctions than SFT models, suggesting training signals shape the geometry of reasoning. Overall, the paper demonstrates that hidden-state geometry offers a robust, transferable signal for verification and motivates training objectives that cultivate clearer internal representations.

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).

Figures (4)

• Figure 1: Visualization of hidden state trajectories for correct (blue) and incorrect (orange) solutions from our experience set, projected to 2D using PCA. Each panel displays data from a different base model. Across all models, a geometric separation is visible.
• Figure 2: Overview of Clue. Left (Learning): Labeled historical trajectories are summarized by their activation deltas and aggregated into success and failure centroid matrices. Right (Verification): A new trajectory is summarized by its activation delta and classified by the layer-averaged Euclidean distance (Eq. \ref{['eq:layeravg']}) to the two pre-computed centroids. The underlying LLM remains frozen throughout.
• Figure 3: Cross-model reranking performance on AIME 24. The results show that RL-trained models (Nemotron-1.5B, Polaris-4B) are not only effective at self-verification but are also superior verifiers for trajectories generated by SFT-trained models (Deepseek-7B, Qwen3-4B).
• Figure 4: Layer-wise separability. Each row shows PCA projections from a shallow, a middle, and the final layer, plus a curve of the centroid distance $d^{(\ell)}$ across all layers. The centroid-distance curve increases with $\ell$, indicating stronger correctness signals at deeper layers.