HalluSAE: Detecting Hallucinations in Large Language Models via Sparse Auto-Encoders

Boshui Chen; Zhaoxin Fan; Ke Wang; Zhiying Leng; Faguo Wu; Hongwei Zheng; Yifan Sun; Wenjun Wu

cs.CLApr 6, 2026

HalluSAE: Detecting Hallucinations in Large Language Models via Sparse Auto-Encoders

Authors: Boshui Chen, Zhaoxin Fan, Ke Wang, Zhiying Leng, Faguo Wu, Hongwei Zheng, Yifan Sun, Wenjun Wu

Organizations: Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing, School of Artificial Intelligence, Beihang University, Beijing, China. · State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing, China. · Beijing Academy of Blockchain and Edge Computing, Beijing, China. · Renmin University of China, Beijing, China.

Abstract

Large Language Models (LLMs) are powerful and widely adopted, but their practical impact is limited by the well-known hallucination phenomenon. While recent hallucination detection methods have made notable progress, we find most of them overlook the dynamic nature and underlying mechanisms of it. To address this gap, we propose HalluSAE, a phase transition-inspired framework that models hallucination as a critical shift in the model's latent dynamics. By modeling the generation process as a trajectory through a potential energy landscape, HalluSAE identifies critical transition zones and attributes factual errors to specific high-energy sparse features. Our approach consists of three stages: (1) Potential Energy Empowered Phase Zone Localization via sparse autoencoders and a geometric potential energy metric; (2) Hallucination-related Sparse Feature Attribution using contrastive logit attribution; and (3) Probing-based Causal Hallucination Detection through linear probes on disentangled features. Extensive experiments on Gemma-2-9B demonstrate that HalluSAE achieves state-of-the-art hallucination detection performance.

Figures & tables

Figure 1: Illustration of Phase Transition in LLM’s reasoning trajectories. The trajectories in potential energy space reveal three phases: early stability (Phase I), critical transition (Phase II, yellow highlight), and sustained error plateau (Phase III). Factual generation (blue) maintains low energy throughout, while hallucination (gradient color) undergoes abrupt energy increase ( $\Delta E$ ) during the transition zone, entering a persistent high-energy state.

Figure 2: Illustration of the Exploratory Experimental Design. We conduct two complementary experiments: Exp 1 investigates layer-wise energy distribution by dividing 42 layers into Early/Middle/Late groups and comparing GPE differences; Exp 2 identifies microscopic feature-level contributions by analyzing differential features that exhibit high activation in hallucination samples but low activation in factual samples.

Figure 3: Experimental Results on Hallucination Dynamics. (a) Layer-wise energy distribution (grouped analysis). Grouped box plots reveal that hallucination samples’ GPE exhibits significant escalation from Early to Late layer groups (***

p<0.001

). Error bars indicate 95% confidence intervals (bootstrap,

n{=}200

per group). (b) Sparse feature contribution analysis. Cumulative energy contribution curve demonstrates that a small fraction of differential features account for the majority of total energy increase, exhibiting a highly skewed distribution. Gray bars represent individual feature energy contributions.

		In-Distribution (HaluEval)			Out-of-Distribution (TriviaQA)
Category	Method	AUC $\uparrow$	Acc. $\uparrow$	Recall $\uparrow$	AUC $\uparrow$	Acc. $\uparrow$	Recall $\uparrow$
Uncertainty	LN-Entropy	54.93	56.50	65.12	70.94	65.75	66.50
Uncertainty	Semantic Entropy	62.77	67.98	55.45	71.85	69.21	71.88
Consistency	Lexical Similarity	64.25	62.50	59.00	65.40	64.25	53.50
Consistency	SelfCheckGPT	63.78	64.12	56.23	63.53	61.51	57.12
Internal State	EigenScore	60.53	59.50	77.13	61.51	60.25	66.50

Table 1: Comparison Results of Hallucination Detection Performance Across Benchmarks. We compare our method against eight representative baselines spanning four paradigms. Results are grouped by in-distribution (HaluEval) and out-of-distribution (TriviaQA) settings. Best results are highlighted in gray. All metrics are reported as percentages, with AUC as the primary ranking metric.

Figure 4: Examples of Samples with High-Activation on Identified Sparse Features. Each feature exhibits stable and interpretable error patterns: L27-9659 shows fixed year substitution (always outputs “1993”), L28-87984 demonstrates numerical shift patterns (+4 years, -0.2 billion), L23-71479 drives domain-specific entity confusion (Tesla/Edison, Newton/Einstein), and L24-35793 triggers cross-domain celebrity substitution (Tolkien/Rowling, Jobs/Gates).

Feature ID	Hal./Fact. Ratio	Top-10 Purity	Mean Activation
L27-9659	22.92	10/10 (100%)	8.03
L28-87984	81.52	10/10 (100%)	8.54
L23-71479	16.57	9/10 (90%)	7.80
L24-35793	12.41	10/10 (100%)	6.86

Table 2: Identified High-Purity Hallucination-Driving Features

Strategy	Layer Range	# Layers	# Feat.	ID AUC	OOD AUC	$\Delta$ vs Ours
Random-13	Random 13 layers	13	100	0.83	0.76	-4.0%
Early-13	L0–12 (Stable)	13	100	0.81	0.73	-7.0%
Late-13	L29–41 (Plateau)	13	100	0.88	0.78	-2.0%
All-42	L0–41 (Full model)	42	420	0.91	0.79	-0.1%
Ours	L23–35 (Transition)	13	100	0.93	0.80	Baseline
Our method achieves comparable OOD performance to All-42 while using 4.2 $\times$ fewer features.

Table 3: Ablation Results on Layer Selection Strategy. Comparison of detection performance across different layer selection strategies using a fixed feature budget of 100 dimensions. The transition zone (L23–35) achieves optimal performance with minimal features, demonstrating the effectiveness of our energy-based localization method.

Figure 5: Illustration of Layer-wise Energy Difference Evolution Across All 42 Layers. Geometric Potential Energy (GPE) difference (Hallucination - Factual) reveals three distinct phases: stable period (L0–22, near-zero difference with random fluctuations), transition zone (L23–35, sharp 20.7-fold escalation highlighted by shaded region), and plateau period (L36–41, sustained high-energy state). Error bars represent 95% confidence intervals (bootstrap, $n$ =900 per group).

Method	Purity	AUC		Accuracy
Method	Purity	ID	OOD	ID	OOD
Wrong-only DLA	73%	0.88	0.79	81.2%	74.5%
Correct-only DLA	68%	0.87	0.77	79.8%	72.1%
Random Selection	51%	0.76	0.68	70.3%	65.2%
C-DLA (Ours)	89%	0.93	0.80	85.6%	78.3%

Table 4: Ablation Results on Feature Attribution Methods. Comprehensive evaluation using Top-100 features in transition zone (L23–35). All methods use identical layer ranges and feature budgets.

Configuration	Layers	# Feat.	AUC
Configuration	Layers	# Feat.	ID	OOD
Baseline	All-42	420	0.63	0.63
+Stage I only	L23–35	130	0.71	0.64
+Stage II only	All-42	420	0.85	0.78
Full (I+II)	L23–35	100	0.93	0.80

Table 5: Results of Joint Ablation Study. Evaluating the synergistic effects of Stage I and Stage II.

Figure 6: Illustration of Cumulative C-DLA Contribution Curve (Pareto Distribution). The top-0.1% features (131 out of 131,072) account for 41.1% of total attribution. The top-1% (1,310) cover 62.5%. The sharp elbow indicates extreme inequality in feature importance (Gini coefficient = 0.912 vs random baseline 0.414). Gray bars represent individual feature contributions, while the red curve shows cumulative percentage.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 7: Data Cleaning Pipeline. Five-stage workflow from raw data to curated dataset.

Attribute	HaluEval	TriviaQA
Total samples	1,800	4,000
Hallucination / Factual	900 / 900	2,000 / 2,000
Question length (avg.)	8.5 words	12.3 words
Answer length (avg.)	4.9 tokens	1.5 words
Initial pool size	1,876	4,092
Removed ambiguous cases	76 (4.0%)	92 (2.2%)

Appendix

Table 6: Dataset Statistics and Comparison

Gemma Scope SAE Details		Hardware Configuration
Dimension	131,072	GPU	8× NVIDIA RTX 4090
Overcompleteness	36.6×	VRAM per GPU	48GB
Activation	JumpReLU	Framework	PyTorch 2.1.0
Sparsity ( $L_{0}$ )	25–42	CUDA Version	12.1
Hook position	resid_post	Precision	Float32 (Gemma) / FP16 (SAE)
Reconstruction MSE	$<$ 0.01	Random Seed	42

Appendix

Table 7: Detailed Hardware and Memory Configuration

Layer Range	Avg. $L_{0}$	Representative Layers
L0–L9	25–42	L0(30), L8(41), L9(42)
L10–L19	27–35	L16(35), L17(35), L18(34)
L20–L29	30–34	L20(34), L23(32), L29(33)
L30–L41	26–32	L30–L39(30), L40(29), L41(26)
Transition Zone (L23–35)	31	Consistent with global mean

Appendix

Table 8: Layer-wise SAE Sparsity (

L_{0}

) Configuration

Panel of Figure 8 — Figure 8: GPT-4o Annotation Prompt. Complete template with explicit grounding, numerical tolerance, structured reasoning, and JSON output.

Uncertainty-based Methods
Method	Samples	Ext. Model	Key Parameters	Training	Cost
LN-Entropy	1	-	Threshold: [0.1, 0.9]	-	1.1×
Semantic Ent.	10	MiniLM-L6	Nucleus p=0.9, T=0.8, clustering=0.75	-	10.8×
Consistency-based Methods
Lexical Sim.	5	-	T=0.7, ROUGE-L, threshold: [0.3, 0.8]	-	5.2×
SelfCheckGPT	5	DeBERTa-XL	Nucleus p=0.95, T=1.0, BERTScore F1 $>$ 0.5	-	6.5×

Appendix

Table 9: Hyperparameter Configuration for Baseline Methods

Config	Start	End Tol.	IoU	Identified	Length
ID	Mult.	(%)		Zone
1	1.0	5	1.000	L23–35	13
7	1.1	5	1.000	L23–35	13
19 (Baseline)	1.3	10	1.000	L23–35	13
31	1.5	25	1.000	L23–35	13
37	1.8	5	0.846	L25–35	11

Appendix

Table 10: Parameter Sensitivity Analysis: Representative Configurations

Layer	Hit Count	Stability	In Ground	Tier
Range	(out of 1000)		Truth?
L0–L22	0	0.000	No	–
L23	998	0.998	Yes	Core (edge)
L24	999	0.999	Yes	Core (edge)
L25–L35	1000	1.000	Yes	Core (perfect)
L36–L39	319	0.319	No	False positive

Appendix

Table 11: Bootstrap Stability Analysis: Layer-wise Results

Comparison	Cohen’s $d$	$t$ -stat	df	$p$ -value	Interpretation
Phase II vs I	1.64	18.32	1798	$<$ 0.001	Very large effect
Phase III vs II	0.12	0.95	1798	0.342	No effect
Phase III vs I	1.71	19.87	1798	$<$ 0.001	Very large effect
Phase I: L0–22 (Stable); Phase II: L23–35 (Transition); Phase III: L36–41 (Plateau)

Appendix

Table 12: Statistical Significance Testing Between Phases

Method	Feature	AUC (ID)	AUC (OOD)	Paired $t$ -test
	Purity			vs C-DLA
Wrong-only DLA	73%	0.88	0.79	$t=8.32$ , $p<0.001$
Correct-only DLA	68%	0.87	0.77	$t=9.14$ , $p<0.001$
C-DLA (Ours)	89%	0.93	0.80	–

Appendix

Table 13: Detailed Comparison of Attribution Methods

Configuration	Layers	# Feat.	AUC (ID)	AUC (OOD)	$\Delta$ OOD
Baseline	All-42	420 (Rand.)	0.63	0.63	–
+Stage I only	L23–35	130 (Rand.)	0.71	0.64	+1.1%
+Stage II only	All-42	420 (C-DLA)	0.85	0.78	+15.0%
Full (I+II)	L23–35	100 (C-DLA)	0.93	0.80	+17.4%

Appendix

Table 14: Joint Ablation: Stage I

\times

Stage II Interaction

Phase	Layer Range	Pearson $r$	$p$ -value	Interpretation
Stable	L0–L22	0.341	0.112	No correlation
Transition	L23–L35	0.990	$<$ 0.001	Very strong
Plateau	L36–L41	0.287	0.581	No correlation
All Layers	L0–L41	0.876	$<$ 0.001	Strong (driven by L23–35)

Appendix

Table 15: Phase-Specific Correlation Between C-DLA and GPE

Component	Configuration
Model Type	Logistic Regression (L1 regularization)
Input Features	100-dim (Top-100 C-DLA from L23–35)
Output	Binary (Hallucination=1, Factual=0)
Regularization $C$	0.1 (selected via 5-fold CV)
CV Search Space	$[10^{-4},10^{4}]$ (20 log-spaced values)
Solver	liblinear

Appendix

Table 16: Complete Detector Configuration

Method	Forward Passes	Relative Cost
Baseline (no detection)	1	1.0 $\times$
Perplexity / Entropy	1	1.1 $\times$
Ours (L23–35)	1	2.3 $\times$
Full-layer Probing (L0–41)	1	7.2 $\times$
SelfCheckGPT (5 samples)	5	5.0 $\times$
SelfCheckGPT (10 samples)	10	10.0 $\times$

Appendix

Table 17: Computational Cost Comparison Across Methods

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