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 the internal variance of LLM hidden states across layers (Generalised Variance, Circular Variance, and Token Entropy) as token-level features. These features are then processed by a lightweight Transformer encoder to aggregate full-sequence patterns for uncertainty estimation and hallucination detection, significantly outperforming baselines with stronger generalization.

Background & Motivation

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

Limitations of Prior Work: (1) Sampling-based methods incur high computational overhead; (2) Methods like CoE (Consistency of Evolution) impose overly strict assumptions on layer-wise evolution that do not hold across different models or tasks; (3) Relying solely on the last or average token loses temporal patterns.

Key Challenge: Compressing internal signals into a single score (as in CoE) ignores variance patterns at different token positions. For instance, in the phrase "Praia is in Portugal," a variance spike at "Portugal" can signal an error, but simple mean aggregation would mask this signal.

Goal: Design internal state features based on more relaxed assumptions while preserving full sequence information.

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

Core Idea: Use three dispersion statistics (Generalised Variance, Circular Variance, and Token Entropy) to describe the cross-layer dispersion of each token, and employ a Transformer encoder to learn full-sequence patterns for hallucination prediction.

Method

Overall Architecture

For each generated token, the hidden states from all layers are extracted. Three internal variance features \(\bm{v}_t = [v_t, c_t, e_t]\) are calculated to form a sequence, which is then fed into a lightweight Transformer encoder for binary classification.

Key Designs

1. Generalised Variance:

   • Function: Measures "volume" dispersion across layers.
   • Mechanism: Computes the log-determinant of the regularized covariance matrix \(v_t = \log\det(\Sigma') = \sum_i \log \lambda_i\), aggregating the entire feature spectrum.
   • Design Motivation: Unlike CoE which only considers differences between adjacent layers, Generalised Variance is directly related to differential entropy and provides a more comprehensive measure of dispersion.

2. Circular Variance:

   • Function: Measures "directional" dispersion across layers.
   • Mechanism: Calculates the magnitude of the mean vector after normalizing hidden states at each layer: \(c_t = 1 - \|\frac{1}{L+1}\sum_l \hat{\bm{h}}_t^l\|\).
   • Design Motivation: Complementary to Generalised Variance—one captures magnitude while the other captures direction. It implicitly considers all pairwise relationships between layers.

3. Sequence Aggregation Transformer Classifier:

   • Function: Learns hallucination detection from full-sequence dispersion patterns.
   • Mechanism: Consists of an embedding layer (128 dimensions), a single-layer Transformer encoder, and a linear classification head.
   • Design Motivation: Preserves sequential order to capture temporal patterns like "variance spikes," which is more effective than mean or last-token aggregation.

Loss & Training

Binary Cross-Entropy with \(l_2\) regularization. Only a few hundred to a few thousand labeled samples are required.

Key Experimental Results

Main Results

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

Method	TriviaQA	SciQ	MedMCQA	MATH	Avg 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	Avg AUC	Description
Token Entropy Only	71.2	Basic effectiveness but insufficient
Generalised Variance Only	72.8	Complementary signal
Triple Combination (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 compared to mean or last-token aggregation, proving the value of temporal patterns.
• OOD (Out-Of-Distribution) generalization is significantly better than CoE, requiring only minimal training data.

Highlights & Insights

• "Dispersion" assumption is more robust than "step size": CoE's assumption of consistent layer-wise evolution varies across models, whereas SIVR's dispersion assumption is more fundamental and universal.
• Transferable sequence-structure paradigm: Any task requiring the inference of sequence-level properties from token-level signals can benefit from this approach.
• Lightweight yet effective: Using only 3 statistics and a single-layer Transformer, the inference overhead is nearly negligible.

Limitations & Future Work

• Requires labeled data; although the amount is small, new domains require additional annotations.
• Only validated on greedy decoding; performance under sampling-based decoding remains to be evaluated.
• Insufficient validation on large-scale models (70B+).
• Did not explore using SIVR for active hallucination mitigation.

Related Work & Insights

• vs CoE: CoE has overly strong assumptions that fail across tasks; SIVR uses a more relaxed dispersion assumption.
• vs Semantic Entropy: SE requires multiple samples and is computationally expensive; SIVR only requires a single forward pass.
• vs Lookback Lens: Focuses on specific layers or attention patterns, whereas SIVR provides a more global perspective.

Rating

• Novelty: ⭐⭐⭐⭐ The concept of internal variance features is clear, and while components are simple, the combination is effective.
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ Comprehensive ablation studies across 7 datasets and multiple models.
• Writing Quality: ⭐⭐⭐⭐ Clear motivation and effective visualizations.
• Value: ⭐⭐⭐⭐⭐ High practicality with direct value for hallucination detection applications.

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