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LLM Hallucination Detection via Low-rank Multilinear Decomposition

Devansh Sharma, Faizul Rakib Sayem, Shahana Ibrahim

arXiv:2610.36191v1cs.CLcs.LG

TL;DR

Detecting hallucinations from LLM hidden states is challenging because the representations are high-dimensional, variable-length, and model-specific. LOTUS learns compact Tucker-2 subspaces from unlabeled hidden states for a lightweight classifier, and across two LLMs and four QA benchmarks it outperformed HARP in all eight pooled-AUROC settings by 7.10 points on average.

  • Problem

    Using LLM hidden states for hallucination detection remains challenging because they are high-dimensional, token lengths vary, and layer and feature dimensions differ across models.

    Source: §2 · p. 3

  • Method

    LOTUS summarizes variable-length hidden states into fixed-size representations, learns label-free Tucker-2 projections over layer and feature modes, and trains a lightweight hallucination classifier.

    Source: §3 · p. 3

  • Results

    Across two LLMs and four QA benchmarks, LOTUS outperformed HARP in all eight pooled-AUROC settings by 7.10 AUROC points on average.

    Source: §4.2 · p. 6

  • Takeaways & Limitations

    LOTUS reduces representation size and supports transfer across models with different internal dimensions.

    Source: §5 · p. 9

Abstract

from arXiv · show

Large language models (LLMs) frequently generate fluent yet factually incorrect responses, raising concerns about their reliability. Recent hallucination detectors increasingly exploit internal representations, but extracting informative signals from high-dimensional hidden states remains challenging. Existing approaches often rely on selected activations or pooling-based compression, potentially overlooking discriminative information distributed across Transformer layers, feature modes, and tokens. We propose LOTUS (Low-rank Order-statistic TUcker-based Subspace learning), a multilinear low-rank decomposition framework for hallucination detection that extracts compact representations from LLM hidden states while reducing dependence on labeled data. Our approach first summarizes variable-length token representations using complementary statistical descriptors that capture peak activations, activation distributions, and cross-layer changes. We then leverage low-rank multilinear decomposition to extract compact representations that capture the underlying structure of LLM hidden states, which are subsequently used to train a lightweight hallucination classifier. Experiments across multiple LLMs and question-answering benchmarks demonstrate improved hallucination detection performance over recent state-of-the-art baselines.

1 INTRODUCTION

Hallucination detection is difficult because fluent, coherent, and even logically structured responses can be factually wrong. LOTUS addresses challenges in using LLM hidden states by compressing them with unsupervised low-rank multilinear decomposition before lightweight classification.

Motivation

  • Hallucinated responses can remain fluent and coherent, while reasoning models may produce plausible traces that reach incorrect conclusions.This makes hallucinations difficult to distinguish from correct responses using surface form alone.Source: §1 · p. 1

Existing methods

  • Prior detectors use output uncertainty or consistency signals, or train supervised classifiers on internal representations.Output-based methods do not use the internal representations underlying generated outputs.Source: §1 · p. 1

Challenges

  • Hidden states are high-dimensional, variable-length, and model-specific; compression can discard information, while full-tensor learning raises computational cost and overfitting risk.Differences in layer counts and hidden dimensions also make detectors defined in the original hidden space difficult to transfer across LLMs.Source: §1 · pp. 1–2

Contributions

  • LOTUS summarizes variable-length tokens into complementary layer-by-feature representations, then applies unsupervised Tucker-2 projection across layer and feature modes while preserving multilinear structure.The summaries capture order statistics, and the decomposition follows Tucker (1966) and Kolda & Bader (2009).Source: §1 · p. 2
  • LOTUS learns its representation from unlabeled hidden states, uses hallucination labels only for a lightweight classifier, and maps model-specific states to fixed-dimensional cores to reduce size and memory cost and facilitate reuse across LLMs.The fixed-dimensional cores address differences in models' internal dimensions.Source: §1 · p. 2

Evaluation

  • LOTUS is evaluated on two LLMs and four question-answering benchmarks, with ablations covering summaries, Tucker ranks, projection design, limited labeled data, and cross-model transfer.The introduction reports strong and consistent detection performance but provides no quantitative results here.Source: §1 · p. 2

2 PROBLEM STATEMENT

The problem is to detect hallucinated responses from LLM hidden states by assigning higher scores to responses labeled hallucinated using similarity to a reference answer. Hidden-state cues vary across layers, tokens, and feature dimensions, while variable token lengths and model-specific dimensions complicate efficient, label-efficient detection.

2 PROBLEM STATEMENT

  • The task is to score generated responses so hallucinated answers receive higher scores, with labels defined by whether answer-reference similarity falls below a threshold.A separate decision threshold converts scores into binary hallucination predictions.Source: §2 · p. 2
  • Prior studies indicate that hallucination cues occur across layers and token positions, so relying on a few selected activations can miss useful information (Azaria & Mitchell, 2023; Chen et al., 2024; Orgad et al., 2025; Bar-Shalom et al., 2026).This motivates joint modeling across layers, tokens, and feature dimensions.Source: §2 · p. 2
  • Hidden-state tensors span Transformer layers, token positions, and feature dimensions, but their size, variable token lengths, and model-specific layer and feature dimensions hinder efficient processing and transfer.Direct tensor processing is memory- and computation-intensive and can require substantially more labeled data to avoid overfitting; variable token lengths require fixed-size representations without token alignment.Source: §2 · p. 3
  • The central question is how to extract compact, informative hidden-state representations for computationally efficient, label-efficient hallucination detection.The passage further asks for representations that facilitate transfer across models with differing layer and feature dimensions.Source: §2 · p. 3

3 PROPOSED APPROACH

LOTUS separates hidden-state representation learning from hallucination classification, using fixed-size token summaries and label-free Tucker-2 projections to create compact response features. A lightweight classifier then uses those features to predict hallucinations.

Order statistics over the token mode

  • LOTUS summarizes variable-length token representations with peak, quantile, and cross-layer-change descriptors, capturing activation magnitude, distribution, and layerwise evolution without token alignment.The peak descriptor captures localized activations regardless of position, while quantiles distinguish isolated peaks from sustained patterns.Source: §3 · pp. 3–4

Unsupervised Tucker-2 projection over layer and feature modes

  • Shared label-free Tucker-2 layer and feature bases project each summary into a compact core matrix, preserving layer-feature interactions while compressing only those modes.Summaries are robustly scaled using parameters estimated from training responses only; the layer dimension can be reduced or selected using prior knowledge.Source: §3 · p. 4

Hallucination detector from low-dimensional representations

  • A lightweight classifier is trained on concatenated, vectorized core representations and hallucination labels, then scores unseen responses using the learned projections.The score can be thresholded to produce a binary decision.Source: §3 · pp. 4–5

4 EXPERIMENTS

Across two LLMs and four QA datasets, LOTUS outperforms HARP and label-free baselines in every pooled-AUROC setting and exceeds ACT-ViT in most; further experiments examine within-question discrimination, summary choices, transfer, and low-rank structure.

4.1 EVALUATION SETUP

  • Experiments use two open-weight LLMs, four QA datasets, and question-level splits that keep all responses to a question together.Responses are labeled using ROUGE-L and BLEURT-20 thresholds; only model-known questions are eligible for training, and pooled AUROC is supplemented by within-question AUROC to assess response-level discrimination while controlling for question-specific effects.Source: §4.1 · p. 5

4.2 EXPERIMENT RESULTS

  • LOTUS beats HARP and all label-free baselines in all eight model–dataset settings, while exceeding ACT-ViT in six of eight pooled-AUROC comparisons.ACT-ViT leads on TriviaQA by 1.08 and 3.11 points; on that dataset, LOTUS uses 28.6–32.7 GB of representation storage versus ACT-ViT's 106–122 GB at the reported token resolution.Source: §4.2 · p. 6, Table 1 · p. 7
  • 5.40–14.95 points is LOTUS’s advantage over HARP in all four within-question AUROC settings; it exceeds ACT-ViT in three of four.Within-question AUROC compares responses from the same question; HARP’s larger pooled-to-within-question gap on TruthfulQA suggests more of its pooled performance comes from between-question differences.Source: §4.2 · p. 6, Table 2 · p. 7
  • 0.74 AUROC points or less separates full LOTUS from the best alternative in six settings, although no summary configuration is best everywhere.Removing summaries generally reduces performance, and using shared bases for S and V underperforms the default in seven of eight settings.Source: §4.2 · pp. 6–7, Table 3 · p. 8
  • 1.78–6.03 points is the range by which aligned cross-model transfer stays below a detector trained directly on the target model across four settings.A lightweight ridge mapping aligns paired unlabeled target responses to the source representation, enabling source-detector use without target hallucination labels; omitting alignment substantially degrades performance, especially on TyDiQA-GP.Source: §4.2 · p. 7, Table 4 · p. 8
  • 64.7–66.4% of correct-response variance, versus 52.3–55.5% of hallucinated-response variance, is captured by the leading 64 directions across LOTUS’s nine layers.Hallucinated responses have effective ranks 2.01–2.22× higher under size-matched sampling and 1.52–1.60× under question-paired sampling. Despite this broader spectrum, blocks 15–23 average 86.8% single-layer AUROC, versus 76.5% for embeddings.Source: §4.2 · p. 8, Figure 2 · p. 9
  • 2.66–3.98 AUROC points is Tucker-2’s gain over equal-dimensional flat PCA on LLaMA-3.1-8B TruthfulQA in every reduced-data regime.The gain reaches 5.06 points on Qwen2.5-7B-Instruct TyDiQA-GP; with full training data, the representations perform similarly, and results in other reduced-data settings are mixed.Source: §4.2 · pp. 8–9
  • 0.37 pooled-AUROC points is the largest improvement of any tested Tucker-3 configuration over Tucker-2 across four settings, despite expanding features from 896 to as many as 7,168.Increasing token rank brings no consistent gain, supporting token aggregation before decomposition for a more compact representation at comparable detection performance.Source: §4.2 · p. 9

5 CONCLUSION

LOTUS learns compact Tucker-2 subspaces from unlabeled LLM activations and uses them for hallucination detection with a lightweight classifier. Across two LLMs and four question-answering benchmarks, it delivers strong, consistent performance while reducing representation size and supporting cross-model transfer.

5 CONCLUSION

  • LOTUS combines complementary layer–feature summaries with low-rank Tucker-2 subspaces to detect hallucinations from LLM hidden representations.It learns the subspaces from unlabeled activations, requiring hallucination labels only for a lightweight downstream classifier; ablations validate the summaries, projection, rank choices, and transfer design.Source: §5 · p. 9

AI USE STATEMENT

  • The authors used a generative AI assistant for code and writing, but not to generate experimental results, data, or labels.Authors reviewed the AI-assisted work and outputs and take responsibility for the paper and artifacts.Source: AI USE STATEMENT · p. 10

ETHICS STATEMENT

  • The work uses public benchmarks and models, with no human subjects or new data collection, and makes no claim of deployment reliability beyond its evaluated benchmarks.Automatic-metric labels inherit metric biases; the authors report agreement with an independently released judge. The detector reduces but does not eliminate risks from incorrect outputs, and the authors report no additional dual-use concerns beyond those of the public models.Source: ETHICS STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

  • A single evaluation harness controls splits, seeds, and metrics, and released scripts cover generation, extraction, evaluation, ablations, and analysis.Generated responses and activations are not released, but can be regenerated exactly from the released configuration using question-specific seeds; the configuration and generation details are specified in Section 4.1 and Appendix D.Source: REPRODUCIBILITY STATEMENT · p. 10

Supplementary Material of “LLM Hallucination Detection via Low-rank Multilinear · A RELATED WORK · B LOTUS WORKFLOW

The related-work discussion distinguishes uncertainty-based detection from approaches using internal representations, while LOTUS’s workflow estimates its scaling statistics and Tucker-2 bases without labels before applying fixed projections at inference.

A RELATED WORK

  • Uncertainty-based detectors infer hallucination from lower confidence or greater variability across generations, using token-level scores such as entropy and perplexity (Huang et al., 2025b).Other work aggregates token probabilities or compares sampled generations at the sentence or response level (Malinin & Gales, 2021).Source: A RELATED WORK · p. 15
  • Semantic entropy measures meaning-level consistency across outputs, whereas lexical similarity measures surface-level agreement among sampled answers (Lin et al., 2022b).Source: A RELATED WORK · p. 15
  • Probing methods train classifiers on hidden states, logits, or activations to detect correctness, motivated by evidence that models may encode more knowledge internally than they express (Duan et al., 2024).Studies also report hallucination signals in intermediate layer-wise or token-wise representations (Kim et al., 2025; Bar-Shalom et al., 2026).Source: A RELATED WORK · p. 15
  • HaloScope uses unlabeled embeddings and SVD to identify subspace directions for probing (Du et al., 2024), while EigenScore uses covariance eigenvalues to measure semantic agreement (Chen et al., 2024).Source: A RELATED WORK · p. 15
  • Mechanistic interpretability examines parameters, hidden states, and layer-wise computation; prior work studies weight matrices, attention heads, and feed-forward modules (Hu et al., 2026; Zhang et al., 2025b).In reasoning models, proposed sources of hallucination include shallow pattern matching, unstable reasoning trajectories, incorrect backtracking, and overthinking (Wang et al., 2026).Source: A RELATED WORK · p. 15

B LOTUS WORKFLOW

  • LOTUS estimates scaling statistics and Tucker-2 bases separately for each summary type using training responses without hallucination labels; labels train only the final classifier.At inference, it scales each test response with training statistics, projects onto the same fixed bases, and scores it with two matrix multiplications per summary and one classifier evaluation.Source: B LOTUS WORKFLOW · p. 15

C LAYER WINDOW ANALYSIS

Layer-window analyses find the strongest hallucination signal in intermediate blocks, with the selected blocks 15–23 window performing best and performance generally declining toward the final layers.

C LAYER WINDOW ANALYSIS

  • Across both datasets, earliest layer windows perform worse, while intermediate windows yield consistently strong AUROC with small neighboring-window variations; blocks 15–23 provide the best intermediate-window performance.The nine-block window is selected for both models and indicates a strong hallucination-discriminative signal.Source: C LAYER WINDOW ANALYSIS · pp. 15–16
  • At blocks 16–18, single-layer AUROC reaches 89.0% on TyDiQA-GP and 87.9% on TruthfulQA.For Qwen2.5-7B-Instruct, AUROC rises from the embedding and early blocks, peaks within the selected window, then declines toward the final block.Source: C LAYER WINDOW ANALYSIS · p. 16
  • The range summary matches or exceeds the peak summary in almost every block, suggesting token activation distributions add signal beyond maximum activations.Source: C LAYER WINDOW ANALYSIS · p. 16

D OTHER IMPLEMENTATION DETAILS

The implementation details specify controlled answer generation and evaluation, baseline-specific training and scoring procedures, and robust scaling of LOTUS summaries.

Generation

  • Generation used 10 sampled beam-search answers per question, with fixed seeds, plain-text prompts, and the same responses across methods.Settings were 10 beams, temperature 0.5, top-k 5, top-p 0.99, and at most 64 new tokens; TyDiQA-GP prompts also included the passage and an instruction to answer from it.Source: D OTHER IMPLEMENTATION DETAILS · p. 16

HARP

  • HARP projects final-layer token states onto the 256 smallest-singular-value unembedding directions, applies a two-layer MLP, and scores each answer by its maximum token score.The released implementation was run on the study's answers and labels; performance was reported under question-level and answer-level splits.Source: D OTHER IMPLEMENTATION DETAILS · p. 16

ACT-ViT

  • ACT-ViT was trained for 15 epochs with batch size 128, a three-layer transformer, four attention heads, hidden size 128, and dropout 0.3.Learning rate and weight decay were both 10^-3; released preprocessing max-pooled activations to 8 layers and 20 token positions, with 100 positions also evaluated because responses were short and larger values would mostly add padding.Source: D OTHER IMPLEMENTATION DETAILS · pp. 16–17

Evaluation

  • All experiments ran on one NVIDIA H100 80GB GPU, and every method used identical train/test questions and evaluation procedures across five seeds.The seeds were {42, 0, 1, 2, 3}.Source: D OTHER IMPLEMENTATION DETAILS · pp. 16–17

Summary statistics scaling in LOTUS

  • Before Tucker-2 decomposition, LOTUS scales each summary using training-response statistics, clipping entries to training percentiles, centering by the median, dividing by rescaled interquartile range, and clipping to [−6, 6].Median and interquartile range are used instead of mean and standard deviation because a few residual-stream features have much larger values and could otherwise dominate the objective.Source: D OTHER IMPLEMENTATION DETAILS · p. 17

E EFFECT OF THE DATA SPLIT

Answer-level splitting lets responses to the same question cross training and test sets, inflating AUROC by enabling question-specific recognition. The appendix compares both splits with other factors fixed and finds the answer-level split consistently yields higher AUROC.

Overlap between training and test

  • Under answer-level splitting, a question appears in both sets with probability about 94.4%; empirical overlap is 92.6%–95.7% across two models, two datasets, and five runs.Because answers to the same question share a prompt and topic, detectors may recognize question-specific information rather than response factuality.Source: E EFFECT OF THE DATA SPLIT · p. 17, Figure 3 · p. 19

Impact of the splitting protocol

  • Question- and answer-level splits produce nearly identical train/test sizes, so aggregate results alone make the splitting protocol difficult to infer.Answer-level splitting can put responses to the same question in both training and test sets.Source: E EFFECT OF THE DATA SPLIT · p. 17
  • Across HARP, LOTUS, and both ACT-ViT variants, answer-level splitting raises AUROC by less than one to over 13 points, with LOTUS achieving the highest hallucination-detection AUROC.The comparison holds answers, labels, features, and training procedure fixed across the two split settings.Source: E EFFECT OF THE DATA SPLIT · p. 18, Table 7 · p. 18

F COMPARISON WITH ALTERNATIVE REDUCTIONS

Across alternative reductions, Tucker-2 retained comparable detection performance with a more compact representation, while adding explicit token structure yielded little consistent improvement.

Reductions of equal width

  • At equal width, Tucker-2 matched flat PCA and Tucker-3 in accuracy and within-question AUROC with fewer parameters and multiply-adds, while random projection performed worse.All methods used the same random-forest classifier.Source: F COMPARISON WITH ALTERNATIVE REDUCTIONS · p. 19

Single-layer reductions

Tucker-3

  • Explicit token-mode Tucker-3 yielded limited gains: no order-statistic setting beat one bin by more than 0.37% AUROC, and full token rank was usually worse.Average pooling showed a similar pattern, indicating that preserving token structure did not consistently improve detection; Tucker-3 varied token bins and ranks while keeping layer and feature ranks fixed.Source: F COMPARISON WITH ALTERNATIVE REDUCTIONS · pp. 19–20, Table 10 · p. 20

G PERFORMANCE WITH LIMITED TRAINING DATA … J TRANSFER ACROSS MODELS

The sections show Tucker-2’s advantage with limited training data, describe classifier and rank sensitivity, and specify an unlabeled ridge-alignment procedure for cross-model transfer. The supplied passages report the transfer setup but no transfer outcome.

H LOGISTIC REGRESSION CLASSIFIER

  • Logistic regression on standardized features was particularly competitive on TriviaQA, showing that classifier choice affects the relative performance of the six configurations.The comparison replaces the random forest with logistic regression.Source: H LOGISTIC REGRESSION CLASSIFIER · p. 20, Table 12 · p. 21

G PERFORMANCE WITH LIMITED TRAINING DATA

  • 5.06% AUROC improvement on Qwen2.5-7B-Instruct with TyDiQA-GP and 3.98% on LLaMA-3.1-8B with TruthfulQA were reported using 5%–10% of training data.The test sets stayed fixed; at very small training sizes, flat PCA may not supply all 896 features because its components are limited by the number of training samples.Source: G PERFORMANCE WITH LIMITED TRAINING DATA · p. 20, Table 11 · p. 21

I RANK SENSITIVITY

  • Performance remained relatively stable as layer rank k varied from 1 to 9, and the reported setting k = 5 and rF = 64 remained competitive across settings.Peak and range summaries used rL = k, while the update summary used rL = max(1, k−1) to account for its eight-layer structure.Source: I RANK SENSITIVITY · p. 21, Table 13 · p. 22

J TRANSFER ACROSS MODELS

  • The alignment pairs target and source LOTUS representations of the same prompt–response, then fits ridge regression to map target features into the source feature space without hallucination labels.The paired representations are computed using each model’s own hidden states, scaling, and Tucker bases.Source: J TRANSFER ACROSS MODELS · pp. 21–22
  • At test time, target responses are mapped into source space and scored by the fixed pretrained source detector, with no target-model hallucination labels required.For each question-level split, alignment uses source and target training answers for shared questions, with the ridge penalty chosen by question-level five-fold cross-validation.Source: J TRANSFER ACROSS MODELS · p. 22
  • Because scaling statistics and Tucker-2 bases are model-specific and their coordinates are not directly comparable, the paper evaluates scoring target-model responses with a source-model detector.The bases are defined only up to sign, order, and rotation, so the random forest’s feature coordinates have no counterpart across models.Source: J TRANSFER ACROSS MODELS · p. 22

K COMPUTATIONAL COST … Q COVARIANCE SPECTRA

These sections examine LOTUS’s storage and token-budget tradeoffs, performance variability across splits, within-question discrimination, HARP reproduction and label agreement, and covariance spectra of hidden-state summaries.

K COMPUTATIONAL COST

  • On TriviaQA at N=20, LOTUS uses 28.6–32.7 GB versus ACT-ViT’s 106–122 GB; ACT-ViT’s gap reaches about 19× at N=100, while HARP recomputes states.LOTUS stores a fixed-size representation per response, whereas HARP avoids stored activations by recomputing final-layer states during evaluation.Source: K COMPUTATIONAL COST · pp. 22–23, Table 14 · p. 23

L TOKEN BUDGET ANALYSIS OF ACT-VIT

  • Using ACT-ViT with N=100 yields only modest TruthfulQA and TyDiQA-GP improvements but about 5× more activation storage; LOTUS stays ahead under question-level splits at both settings.The main experiments use N=20 because generated responses are short, reducing unnecessary padding and storage.Source: L TOKEN BUDGET ANALYSIS OF ACT-VIT · p. 23, Table 15 · p. 23

M PERFORMANCE ACROSS SPLITTING PROTOCOLS

  • Across most settings, variability over five runs is relatively small, but Qwen2.5-7B-Instruct on question-level NQ-Open has a 5.24% standard deviation.The NQ-Open test set contains only about 280 correct responses; answer-level splits generally have lower standard deviations than question-level splits.Source: M PERFORMANCE ACROSS SPLITTING PROTOCOLS · p. 23, Table 16 · p. 24

N WITHIN-QUESTION AUROC

  • LOTUS beats HARP in all four within-question settings and ACT-ViT in three; single-score baselines yield 50%.HARP has a larger pooled-to-within-question AUROC drop on TruthfulQA, while all three detectors have closer pooled and within-question results on TyDiQA-GP.Source: N WITHIN-QUESTION AUROC · p. 24, Table 18 · p. 25

O REPRODUCTION OF HARP

  • Released HARP results were not consistently reproduced: Qwen runs differed from published scores, while LLaMA draws were lower on every dataset.For Qwen2.5-7B-Instruct, one run differed by −1.83 to +3.47 points (+0.21 average); for LLaMA-3.1-8B, five draws were 0.95 to 4.82 points lower (3.07 average). Under the paper’s question-level split, HARP was 3.75 to 13.30 points lower than under the released split.Source: O REPRODUCTION OF HARP · pp. 24–25, Table 19 · p. 25

P AGREEMENT WITH THE LABELS OF HARP

  • The labeling procedures agree on 99.27%–99.94% of Qwen2.5-7B-Instruct responses, and 44 of 14,827 questions change between known and unknown status.The procedures differ in whether they compare the average or highest ROUGE-L score across reference answers; both use the same BLEURT-20 criterion.Source: P AGREEMENT WITH THE LABELS OF HARP · p. 25, Table 20 · p. 26

Q COVARIANCE SPECTRA

  • Hallucinated responses have higher effective rank, although both classes retain substantial variance in a low-dimensional subspace; the selected layer window has higher single-layer AUROC than the embedding and final block.The covariance-spectrum comparison uses peak summaries from Qwen2.5-7B-Instruct on TyDiQA-GP, averaged over 20 runs.Source: Q COVARIANCE SPECTRA · p. 25, Table 21 · p. 26

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