Learning Uncertainty from Sequential Internal Dispersion in Large Language Models

Conference: ACL 2026
arXiv: 2604.15741
Code: GitHub
Area: Uncertainty Estimation / Hallucination Detection
Keywords: Uncertainty Estimation, Hallucination Detection, Hidden State Variance, Sequence Aggregation, Internal Representation Dispersion

TL;DR

Ours proposes the SIVR framework, which computes internal variance (generalized variance, circular variance, token entropy) across LLM hidden layers as token-level features. A lightweight Transformer encoder aggregates full sequence patterns to estimate uncertainty and detect hallucinations, significantly outperforming baselines with stronger generalization.

Background & Motivation

Background: Uncertainty estimation is a critical means for detecting LLM hallucinations. Existing methods include sampling consistency (e.g., Semantic Entropy), output probability methods (e.g., Entropy), and internal state probing.

Limitations of Prior Work: (1) Sampling methods incur high computational overhead; (2) methods like CoE rely on overly strict assumptions regarding layer-wise evolution that do not hold across models/tasks; (3) using only the last or average token loses temporal patterns.

Key Challenge: CoE compresses information into a single score, ignoring variance patterns at different token positions. For example, in "Praia is in Portugal", a variance spike at "Portugal" can flag an error, but mean aggregation would mask it.

Goal: To design internal state features based on relaxed assumptions while preserving complete sequence information.

Key Insight: Uncertainty is reflected in the "dispersion" of hidden states across layers—representations are more concentrated when correct and more dispersed when incorrect.

Core Idea: Use three dispersion statistics (generalized variance, circular variance, and token entropy) to describe the cross-layer dispersion of each token, and learn full sequence patterns using a Transformer encoder to predict hallucinations.

Method

Overall Architecture

For each generated token, all hidden states across layers are extracted to compute three internal variance features \(\bm{v}_t = [v_t, c_t, e_t]\). These are then fed as a sequence into a lightweight Transformer encoder for binary classification.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400, 'subGraphTitleMargin': {'top': 8, 'bottom': 16}}}}%%
flowchart TD
    A["Each generated token<br/>Take all layer hidden states"]
    subgraph FEAT["Three Cross-layer Dispersion Features"]
        direction TB
        B1["Generalized Variance<br/>logdet of covariance measures point cloud volume"]
        B2["Circular Variance<br/>Normalized mean vector length measures directional divergence"]
        B3["Token Entropy<br/>Standard output entropy"]
    end
    A --> FEAT
    subgraph SEQ["Sequence Aggregation Transformer Classifier"]
        direction TB
        C1["Arranged as token sequence → 128-d embedding"]
        C2["Single-layer Transformer encoder<br/>Perceives temporal variance spikes"]
        C3["Linear classification head"]
    end
    FEAT --> SEQ
    SEQ --> D["Binary Classification: Hallucination / Correct"]

Key Designs

1. Generalized Variance: Characterizing "Volume" Dispersion with a Scalar

Methods like CoE only consider differences (step sizes) between adjacent layers, an assumption that often fails across models and tasks. Generalized variance adopts a fundamental perspective: treating the hidden states of a token across all layers as a point cloud and measuring its "volume" via the log-determinant of the regularized covariance matrix \(v_t = \log\det(\Sigma') = \sum_i \log \lambda_i\).

This is effective because the log-determinant aggregates the entire feature spectrum (all eigenvalues \(\lambda_i\)) rather than local differences between two layers, providing a comprehensive cross-layer dispersion measure. Furthermore, it directly relates to differential entropy; greater dispersion corresponds to higher uncertainty, aligning with the hypothesis that representations are more dispersed when the model is incorrect.

2. Circular Variance: Providing Complementary "Directional" Signals

While generalized variance captures magnitude/volume, two point clouds with the same volume can have entirely different directional distributions. Circular variance first normalizes the hidden states of each layer onto a unit sphere and then examines the magnitude of their mean vector:

\[c_t = 1 - \Big\|\frac{1}{L+1}\sum_l \hat{\bm{h}}_t^l\Big\|\]

The more consistent the directions across layers, the closer the mean vector is to unit length, resulting in a smaller \(c_t\). Conversely, divergent directions yield a larger \(c_t\). This naturally complements generalized variance by encoding pairwise directional relationships across all layers.

3. Sequence Aggregation Transformer Classifier: Preserving Temporal Patterns

CoE compresses entire outputs into a single score, smoothing out variance spikes at critical tokens. For instance, a spike at "Portugal" in "Praia is in Portugal" could flag an error, but it disappears when averaged. Ours preserves the full temporal sequence: the triplet features \(\bm{v}_t = [v_t, c_t, e_t]\) for each token are arranged as a sequence, passed through a 128-dimensional embedding layer, and processed by a single-layer Transformer encoder with a linear head for binary classification.

Because the Transformer is aware of token order, it learns temporal patterns such as "sudden spikes in variance," which are lost in mean or last-token aggregation. This explains why sequence aggregation yields a 2–3 point AUC improvement over mean aggregation in ablation studies. The classifier is extremely lightweight and can be trained with only a few hundred to a few thousand labeled samples.

Loss & Training

Binary cross-entropy with \(l_2\) regularization is used, requiring only small-scale labeled data.

Key Experimental Results

Main Results

Comparison of AUC on 7 datasets using Llama-3.1-8B:

Method	TriviaQA	SciQ	MedMCQA	MATH	Average AUC	Rank
Entropy	80.46	72.85	62.76	62.77	67.63	7.96
SE	84.44	79.44	66.88	67.27	68.87	7.13
CoE-C	66.97	75.06	62.14	58.67	61.25	11.08
SIVR	90.75	83.64	68.37	71.22	75.35	1.88

Ablation Study

Configuration	Average AUC	Description
Token Entropy Only	71.2	Basic effectiveness but insufficient
Generalized Variance Only	72.8	Complementary signal
Combined (SIVR)	75.35	Best performance
Mean Aggregation instead of Sequence	72.5	Loss of temporal patterns

Key Findings

• SIVR achieves an average rank of 1.88, significantly outperforming the runner-up, with strong complementarity among the three features.
• Sequence aggregation improves AUC by 2-3 points over mean/last-token aggregation, proving the value of temporal patterns.
• OOD generalization is significantly better than CoE, requiring only minimal training data.

Highlights & Insights

• The "dispersion" hypothesis is more robust than "step size"—whereas CoE assumptions shift between models, SIVR's hypothesis is more fundamental and universal.
• Transferable sequence structure paradigm—any task requiring the inference of sequence-level attributes from token-level signals can benefit from this approach.
• Lightweight yet effective—three statistics plus a single-layer Transformer result in negligible inference overhead.

Limitations & Future Work

• Requires labeled data; although the volume is small, new domains require additional annotation.
• Only verified on greedy decoding; performance under sampling-based decoding remains to be evaluated.
• Insufficient validation on large-scale models (70B+).
• The use of SIVR for active hallucination mitigation has not yet been explored.

Related Work & Insights

• vs CoE: CoE's strong assumptions fail across tasks; SIVR employs a more relaxed and robust hypothesis.
• vs Semantic Entropy: SE requires multiple samples and is computationally expensive; SIVR requires only a single forward pass.
• vs Lookback Lens: While the former focuses on specific layers or attention patterns, SIVR provides a more global perspective across all layers.

Rating

• Novelty: ⭐⭐⭐⭐ The internal variance feature is intuitive; components are simple but combined effectively.
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ Comprehensive ablation across 7 datasets and multiple models.
• Writing Quality: ⭐⭐⭐⭐ Clear motivation and effective visualization.
• Value: ⭐⭐⭐⭐⭐ Highly practical with direct utility for hallucination detection.

Related Papers

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• [ICML 2025] CROW: Eliminating Backdoors from Large Language Models via Internal Consistency Regularization
• [ACL 2026] Multi-component Causal Tracing in Large Language Models