Between the Layers Lies the Truth: Uncertainty Estimation in LLMs Using Intra-Layer Local Information Scores

Zvi N. Badash; Yonatan Belinkov; Moti Freiman

cs.LGMar 17, 2026

Between the Layers Lies the Truth: Uncertainty Estimation in LLMs Using Intra-Layer Local Information Scores

Authors: Zvi N. Badash, Yonatan Belinkov, Moti Freiman

Organizations: Faculty of Data and Decision Sciences, Technion — Israel Institute of Technology, Haifa, Israel · Faculty of Computer Science, Technion — Israel Institute of Technology, Haifa, Israel · Faculty of Biomedical Engineering, Technion — Israel Institute of Technology, Haifa, Israel

Abstract

Large language models (LLMs) are often confidently wrong, making reliable uncertainty estimation (UE) essential. Output-based heuristics are cheap but brittle, while probing internal representations is effective yet high-dimensional and hard to transfer. We propose a compact, per-instance UE method that scores cross-layer agreement patterns in internal representations using a single forward pass. Across three models, our method matches probing in-distribution, with mean diagonal differences of at most $-1.8$ AUPRC percentage points and $+4.9$ Brier score points. Under cross-dataset transfer, it consistently outperforms probing, achieving off-diagonal gains up to $+2.86$ AUPRC and $+21.02$ Brier points. Under 4-bit weight-only quantization, it remains robust, improving over probing by $+1.94$ AUPRC points and $+5.33$ Brier points on average. Beyond performance, examining specific layer--layer interactions reveals differences in how disparate models encode uncertainty. Altogether, our UE method offers a lightweight, compact means to capture transferable uncertainty in LLMs.

Figures & tables

Panel of Figure 1 — Figure 1: KL signature maps on MMLU for Mistral-7B-Instruct-v0.3 . Each heatmap shows an $L{\times}L$ matrix of directed divergences computed at task-relevant tokens; warmer colors indicate larger $D_{\mathrm{KL}}$ . Panels (a) and (b) show random examples from incorrect and correct predictions, respectively, highlighting differences in cross-layer agreement patterns.

Figure 2: Pipeline overview. Post-MLP activations are normalized via softmax to distributions $\boldsymbol{p}_{\ell}^{(t)}$ ; pairwise directed KLs produce an $L{\times}L$ signature map per token; after optional contrast correction and flattening, a LightGBM classifier outputs a per-instance score. Stage (1) signifies sampling tokens to perform analysis on. Strategies include looking at exact answer tokens ( Orgad et al., 2025 ) , looking at the last token in the sequence, or aggregating activations over several tokens.

Panel of Figure 3 — Figure 3: Cross- task generalization of uncertainty estimation. Each panel shows the difference (ours minus probing) when training on one task and evaluating on a different task , across all ordered task pairs. Diagonal entries correspond to same-task evaluation, while off-diagonal entries reflect true cross-task transfer. Positive values indicate improved performance of structured layer–layer signatures over probing under task shift.

Model	Metric	Within-dataset (Diagonal, pp)	Across-dataset (Off-diagonal, pp)
Llama-3.1-8B	AUPRC	$-1.80$	$\mathbf{2.86}$
Llama-3.1-8B	Brier	$\mathbf{4.88}$	$\mathbf{21.02}$
Qwen3-14B	AUPRC	$-1.37$	$\mathbf{0.95}$
Qwen3-14B	Brier	$\mathbf{1.52}$	$\mathbf{4.35}$
Mistral-7B-v0.3	AUPRC	$-1.72$	$\mathbf{1.35}$
Mistral-7B-v0.3	Brier	$\mathbf{3.38}$	$\mathbf{4.28}$

Table 1: Comparison of Signatures (ours) versus probing in within-dataset and across-dataset settings. All values are mean absolute differences (ours minus probing), reported in percentage points (pp) . Higher is better; positive values are shown in bold.

Metric	Method	Math	MMLU	Movies	WinoBias	WinoGrande	Mean
AUPRC ( $\uparrow$ )	Signature	0.9385	0.7303	0.9599	0.9151	0.5552	0.8198
AUPRC ( $\uparrow$ )	Probing	0.9033	0.6594	0.9733	0.9171	0.5486	0.8004
Brier score ( $\uparrow$ )	Signature	0.2445	0.4061	0.1837	0.3755	0.6406	0.3701
Brier score ( $\uparrow$ )	Probing	0.0438	0.1743	0.4542	0.3088	0.6029	0.3168

Table 2: Quantization shift (trained on full-precision, tested on 4-bit): Signature vs. Probing on Qwen3-14B (Instruct). Brier score is reported as

1-\mathrm{Brier\ loss}

, hence higher is better.

Model	$n_{\text{layers}}^{2}$ Ours	$d_{\text{hidden}}$ Probing	$n_{\text{layers}}\times d_{\text{hidden}}\times T$ ACT-ViT	$K\times T$ LOS-NET
HeRo BERT $\dagger$	$\mathbf{144}$	$3{,}072$	$3{,}686{,}400$	$100{,}000$
GPT-OSS 20B $\ddagger$	$\mathbf{576}$	$2{,}880$	$6{,}912{,}000$	$100{,}000$
Llama 3.1 8B $\star$	$\mathbf{1{,}024}$	$4{,}096$	$13{,}107{,}200$	$100{,}000$
Phi-4 Mini $\diamond$	$\mathbf{1{,}024}$	$3{,}072$	$9{,}830{,}400$	$100{,}000$
Mistral 7B $\triangle$	$\mathbf{1{,}024}$	$4{,}096$	$13{,}107{,}200$	$100{,}000$
Qwen3 14B $\times$	$\mathbf{1{,}600}$	$5{,}120$	$20{,}480{,}000$	$100{,}000$

Table 3: Representation dimension that uncertainty estimation methods can use. The representation used by our method (Signatures) is consistently the most compact. We assume

K=1{,}000

and

T=100

\dagger

( Shalumov and Haskey, 2023 ) ;

\ddagger

( OpenAI et al., 2025 ) ;

\star

( Grattafiori et al., 2024 ) ;

\diamond

( Microsoft et al., 2025 ) ;

\triangle

( Jiang et al., 2023 ) ;

\times

( Yang et al., 2025 ) .

Panel of Figure 4 — Figure 4: Performance (AUC) as a function of UE method complexity, measured by the number of model parameters accessible to the method. Across both LLM backbones, our method achieves comparable performance to prior approaches while using several orders of magnitude fewer parameters.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Dataset	$D_{\text{KL}}$	$D_{\text{JS}}$
Llama-3.1-8B	IMDB	0.8752	0.8719
Llama-3.1-8B	TriviaQA	0.4912	0.4958
Mistral-7B-Instruct-v0.3	HotpotQA	0.7471	0.7461
Mistral-7B-Instruct-v0.3	TriviaQA	0.4604	0.4578
Qwen3-14B	HotpotQA	0.8135	0.8131
	IMDB	0.4614	0.4906

Appendix

Table B1 : Comparison of PRAUC (test) between asymmetric KLD and symmetric JSD distance formulations across models and datasets. Best performance per model–dataset pair is bolded;

Train	Method	HotpotQA	Movies
HotpotQA	Signatures	72.79	61.38
HotpotQA	LOS-NET	58.96	58.98
Movies	Signatures	53.76	66.56
Movies	LOS-NET	58.96	58.98
IMDB	Signatures	59.21	51.72
IMDB	LOS-NET	58.96	58.98

Appendix

Table C1 : Comparison of AUPRC (pp) between our method and LOS-NET on overlapping train–test pairs using Mistral-7B-Instruct-v0.3. Best result per pair is bolded.

Train	Method	HotpotQA	TriviaQA
HotpotQA	Signatures	72.79	58.42
HotpotQA	ACT-ViT	54.34	87.91
TriviaQA	Signatures	63.83	55.01
TriviaQA	ACT-ViT	67.57	82.66
IMDB	Signatures	59.21	71.19
IMDB	ACT-ViT	67.16	62.01

Appendix

Table C2 : Comparison of AUPRC (pp) between our method and ACT-ViT on overlapping train–test pairs using Mistral-7B-Instruct-v0.3. Best result per pair is bolded.

Panel of Figure 11 — Figure E1 : Interpreting layer–layer interactions in Qwen3-14B-Instruct. Top: Feature importance maps over layer–layer KL signatures for three datasets. Compared to Mistral, importance is distributed across a broader set of layer pairs. Bottom: Aggregation by inter-layer distance reveals a flatter profile, with influential interactions persisting across longer distances. This suggests that correctness-relevant information in Qwen is integrated over wider depth spans rather than being dominated by local layer interactions.

Panel of Figure 12 — Figure E2 : Interpreting layer–layer interactions in Mistral-7B-Instruct-v0.3. Top: LightGBM feature importance projected onto the $L{\times}L$ layer–layer signature maps for three datasets. Each cell corresponds to a directed KL divergence between a pair of layers; warmer colors indicate higher contribution to the correctness prediction. Bottom: Feature importance aggregated by inter-layer distance $|i-j|$ , showing a clear decay as distance increases, consistent with predominantly local information refinement across depth.

Uncertainty Quantification

Uncertainty quantification estimates how reliable predictions and scientific inferences are, and how uncertainty propagates into decisions.

See all 647 papers

From Signals to Transfer: A Factorised Study of Probe-Based Uncertainty Estimation in Large Language Models
Jun 26, 2026Ponhvoan Srey, Xiaobao Wu, Cong-Duy Nguyen +3Uncertainty Quantification Hallucination in Language Models
Nanyang Technological University · Shanghai Jiao Tong University · VinUniversity +1
Towards Generation-Efficient Uncertainty Estimation in Large Language Models
May 7, 2026Mingcheng Zhu, Yu Liu, Tingting ZhuLLM Inference Efficiency Uncertainty Quantification
University of Oxford
Improved Confidence Estimates for Black-Box Large Language Models
Aug 19, 2026Sokhna Diarra Mbacke, Mouloud Belbahri, Gabriel Loaiza-GanemConfidence Estimation in Language Models Confidence Estimation
Layer 6 AI · TD Insurance

Jun 26, 2026J/K move · Enter open · S save

From Signals to Transfer: A Factorised Study of Probe-Based Uncertainty Estimation in Large Language Models

Ponhvoan Srey, Xiaobao Wu, Cong-Duy Nguyen, Quang Minh Nguyen+2

Nanyang Technological University · Shanghai Jiao Tong University · VinUniversity+1

Uncertainty Quantification Hallucination in Language Models LLM Uncertainty Estimation Language Model Robustness Language Model Probing

Open paper AskPDF arXiv

Probe-based uncertainty estimation (UE) has emerged as a prominent approach to detect hallucinations in Large Language Models (LLMs) by learning uncertainty from internal model signals. Yet, recent methods vary simultaneously across feature design, training data construction, and evaluation setting, obscuring what actually drives performance. To address this issue, we propose a factorised study of probe-based UE under matched conditions. Our results show that raw hidden states and attention features are difficult to outperform in-domain. However, under distribution shift, structured and compressed features are more robust, suggesting that in-domain performance alone is insufficient to measure progress. Furthermore, prompting and label construction significantly affect probe behaviour. Building on these empirical design principles, we construct benchmark-pretrained probes that retain useful discriminative signal on open-ended factual generation. Their competitive performance relative to limited-label target setting probes and sampling-based estimators suggests that they can provide a practical starting point for subsequent target-domain adaptation. More broadly, our work encourages deployment-oriented evaluation of probe-based uncertainty estimators.

Abstract

Uncertainty Quantification

Explore similar work

From Signals to Transfer: A Factorised Study of Probe-Based Uncertainty Estimation in Large Language Models

Towards Generation-Efficient Uncertainty Estimation in Large Language Models

Improved Confidence Estimates for Black-Box Large Language Models