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HalluField detects hallucinations by measuring how an LLM's token-level free energy and entropy respond to temperature changes, using the change in internal energy as a hallucination score.

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2026-08-04 17:34 UTC pith:O7IQE3Q4

load-bearing objection A genuinely fast, auxiliary-free hallucination detector, but the paper's own appendix contradicts its central theoretical mechanism, and the weights are tuned on the test benchmarks. the 3 major comments →

arxiv 2509.10753 v1 pith:O7IQE3Q4 submitted 2025-09-12 cs.LG cs.AI

HalluField: Detecting LLM Hallucinations via Field-Theoretic Modeling

Minh Vu , Brian K. Tran , Syed A. Shah , Geigh Zollicoffer , Nhat Hoang-Xuan , Manish Bhattarai This is my paper
classification cs.LG cs.AI
keywords hallucination detectionlarge language modelsthermodynamicsvariational principlesfree energysemantic entropylogit-based uncertaintytemperature perturbation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

HalluField treats an LLM's answer as a thermodynamic system: each token is assigned a free energy and an entropy from the model's own logits, and the change in internal energy under a temperature shift becomes a hallucination score. The paper's hypothesis is that hallucinated responses already occupy high-energy, unstable states, so heating them barely changes their energy, whereas correct low-energy responses jump to higher energy when heated. This total variation is computed as a weighted sum over several temperature perturbations using a parametrized discrete variational principle, with no auxiliary LLM, fine-tuning, or hidden-state probing. The authors report that HalluField outperforms semantic entropy and kernel language entropy in AUC/accuracy across several open-domain QA datasets and multiple model families, with near-instant runtime. A variant that adds semantic entropy, HalluFieldSE, is the strongest detector overall.

Core claim

On the paper's own terms, the central discovery is that the change in internal energy δU_Q = δF_Q + δ(TH_Q) — computed as a weighted sum of a base free-energy variation, a potential-change term, and a temperature-entropy variation — cleanly separates hallucinated from correct responses. The free energy is the negative log-likelihood of the generated token path, the entropy is the per-token Shannon entropy over the likelihood-ranked vocabulary, and the weighted sum over perturbations in generation temperature operationalizes the first law of thermodynamics. The paper argues that this physically motivated quantity captures semantic stability better than single-measure uncertainty scores, and t

What carries the argument

The parametrized discrete variation of a functional on token paths, defined as a weighted sum over temperature increments ΔT of the difference of the functional evaluated at T0+ΔT and at T0. The functionals are the free energy F_Q(τ) = −Σ_i log P(τ_i | τ_<i, Q) and the temperature-entropy product T·H_Q, where H_Q is the token-level Shannon entropy summed over likelihood ranks. The weights are hand-set to w_B = T0+ΔT, w_P = 1/(T0+ΔT)^2, w_TH = 1/(T0+ΔT)^2, and the final score is δU_Q plus (optionally) 2·SE_Q. This machinery lets the method stay entirely within the model's logits, avoiding auxiliary LLMs.

Load-bearing premise

The load-bearing assumption is that the hand-picked weight functions (w_B = T0+ΔT, w_P = w_TH = 1/(T0+ΔT)^2) and the mixing constant λ = 2, chosen after inspecting how the individual signals separate hallucinated from correct answers on the same datasets later used for evaluation, will transfer to new models, datasets, and temperature ranges; if they don't, the reported advantage over semantic entropy can disappear.

What would settle it

Run HalluField with the published weights and λ on a held-out set of models and datasets that were not used to tune the weights (for instance, a different model family and a domain like medical or legal QA). If the AUC gap over semantic entropy on those unseen conditions is within noise or negative, the weight selection is overfit to the four QA benchmarks. A second check: deliberately flatten the logits of a known-correct response so that all tokens have nearly equal probability; the energy variation should still classify it correctly if the thermodynamic hypothesis is the real driver.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • HalluField detects hallucinations from a single model's logits in roughly 10^-4 seconds per query, orders of magnitude faster than methods that call an auxiliary LLM.
  • Because it needs no fine-tuning or external verifier, it can be dropped into existing generation pipelines for any autoregressive transformer with exposed logits.
  • The separation between hallucinated and correct responses appears consistently across several open-weight model families and four open-domain QA datasets, suggesting the thermodynamic signature is model-agnostic.
  • Adding semantic entropy to δU further improves detection, meaning the energy-landscape signal is complementary to semantic clustering rather than redundant.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A stress test that freezes the published weights and λ=2 on a development set and evaluates on unseen model families and domains would verify whether the hand-picked weight functions generalize or merely fit the four reported datasets.
  • If the high-energy hypothesis holds, the same δU score could be used at decoding time as a rejection criterion or to guide beam search away from high-energy paths, not just for post-hoc detection.
  • The temperature-perturbation idea extends naturally to other controllable sampling parameters (top-p, repetition penalty, length penalty), potentially yielding a family of variational signatures for different failure modes.
  • Because the entropy term is computed per token over likelihood ranks, the framework could be adapted to quantify uncertainty in structured outputs (e.g., tool calls or chain-of-thought) where semantic clustering is ill-defined.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes HalluField, a hallucination-detection method for LLMs that treats a response as a token path with an associated free energy F and entropy H, both derived from token-level logits. A 'total variation' δU = δF + δ(TH) is computed as a weighted sum of temperature-perturbed differences (Eq. 17), and δU (or δU + λ·SE, called HalluFieldSE) is used as a hallucination score. The method is evaluated on four open-domain QA datasets and multiple open-weight models, reporting AUC/accuracy competitive with or better than Semantic Entropy, KLE, and other baselines, and claiming very low per-query processing time. The paper presents the approach as grounded in a variational principle and the first law of thermodynamics, and claims state-of-the-art performance.

Significance. If the method's claims held, a logit-only hallucination detector requiring no auxiliary LLM and negligible processing cost would be practically valuable. The paper does provide a broad experimental comparison across models and datasets and directly uses token-level probabilities, which is a strength. However, the central theoretical mechanism is contradicted by the paper's own Appendix A, and the key weights and hyperparameters are selected from the same data used for the final evaluation. Consequently, the 'principled physical interpretation' is not established, and the reported performance advantages may not be out-of-sample. The contribution, as it stands, is closer to a heuristic temperature-perturbation score than to a field-theoretic detector.

major comments (3)
  1. [Section 3, Eq. (17), Appendix A] The stated hypothesis and the empirical findings have opposite signs. Section 3 hypothesizes that hallucinated responses have high internal energy, so raising temperature changes their energy little, giving low δU, while correct low-energy responses become high-energy, giving high δU. Appendix A reports the reverse: 'Across different temperatures, models, and datasets, we consistently observe that hallucinated responses yield statistically higher values of all three measures: the base energy variation ΔB_Q, the change in potential ΔP_Q, and the change in entropy Δ(TH_Q).' Since all weights in Eq. (17) are positive for the temperature sets used ({1.0,1.5,2.0} or {1.0,2.0,3.0}), higher ΔB, ΔP, and Δ(TH) imply higher δU. Thus hallucinated responses have higher δU, directly contradicting the proposed mechanism. This is not a tuning or notation issue; it invalidates the 'internal-energy' expl
  2. [Section 4, Eq. (14), Figure 2, Section 5] The weights w_B = T0 + ΔT, w_P = 1/(T0+ΔT)^2, w_TH = 1/(T0+ΔT)^2 and the mixing constant λ = 2 are chosen after inspecting the same data on which the method is later evaluated. The text explicitly says 'Figure 2 shows the advantage of using weighted sums across variations' and that Figure 2 is based on LLaMa-2-7B-Chat across datasets; the experimental section then evaluates on the same datasets and model family. No held-out validation, cross-validation, or sensitivity analysis is provided for these choices, nor for the temperature sets and number of perturbations. Reported margins over baselines are often only 0.01–0.02 AUC, so without out-of-sample selection of these heuristics the 'state-of-the-art' claim is not credible.
  3. [Section B.2, Eq. (30); Section 4, Eqs. (10)–(13)] The 'derivation' of δF is not a variational principle. The theoretical parametrized variation in Eq. (30) requires evaluating the same token sequence at T0+ΔT. In practice, Eq. (11) replaces the unobserved F[τ(r0,T0+ΔT)] with an expectation over independently generated paths, and Eq. (12) introduces a new 'change in potential' term with an indicator I(r ≠ r0). Neither replacement follows from Eq. (30), and Eq. (9) already states that the total variation is 'heuristically defined' as a weighted sum. Consequently, δU is a weighted combination of ad hoc statistics, not a discrete implementation of δU = TδH + W. The thermodynamic vocabulary is used as an analogy and supplies no independent constraint on the weights, so the paper's claim of a 'principled physical interpretation' is overstated.
minor comments (4)
  1. [Section 5, Tables 2–5] Reported AUC differences among methods are often very small (≤0.01–0.02), but no error bars, multiple runs, or significance tests are given. Several rows show KLE or SE matching or exceeding HalluField, so the statement that HalluField 'achieves state-of-the-art ... across models and datasets' is too strong.
  2. [Section 5, Table 6] The runtime of 1×10^-4 seconds for HalluField excludes generation time, yet the algorithm requires generating 50 perturbed responses per temperature. This makes the runtime comparison misleading for end-to-end use.
  3. [Throughout] Notation is inconsistent: 'LLaMa' vs 'LLaMA' appear in different places; Eq. (1) states T ≥ 0 but the softmax with T = 0 is undefined; denominators in Eqs. (14)–(17) implicitly require T0 + ΔT > 0, which should be stated.
  4. [Appendix A] The claim that hallucinated responses yield 'statistically higher' values is not accompanied by error bars, confidence intervals, or a description of the statistical test used.

Circularity Check

0 steps flagged

No significant circularity; HalluField's score is a heuristic combination of logit-derived features, not a re-statement of its inputs, and the only self-citation is not load-bearing.

full rationale

The derivation chain is: define free energy F and entropy H from token logits (Eq. 7-8), define a heuristic total variation as a weighted sum (Eq. 9), and assemble delta-U in Eq. 17. Hallucination labels are not used in any of these definitions, so the score is not equivalent by construction to the target. The weight functions (Eq. 14) and lambda=2 are chosen heuristically after inspecting Figure 2 on the same benchmarks, which is a legitimate overfitting/selection-on-test-data concern, but it does not make the prediction statistically forced: the weights do not encode the labels, and Appendix A shows the empirical direction of separation (hallucinated responses have higher Delta-B, Delta-P, and Delta(TH), hence higher delta-U) actually contradicts the paper's Section 3 hypothesis that hallucinations have low delta-U. That internal inconsistency is a correctness risk, not a circularity. The only self-citation (Tran & Leok 2025) is cited for background on variational principles and is not load-bearing. The physics analogy does not supply any constraints; it is explicitly labeled heuristic at Eq. 9, so no first-principles claim is being disguised as a fit. Thus no circular step can be exhibited from the paper's own equations.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central computation is the temperature-weighted sum of negative log-likelihood and entropy differences. The weighting scheme, λ, and temperature grid are all chosen by hand using the benchmark data; no first-principles derivation fixes them. The physics vocabulary (energy, entropy, first law) is motivational, and the actual predictive quantities reduce to standard NLL and Shannon entropy.

free parameters (4)
  • weight functions w_B, w_P, w_TH = w_B = T0+ΔT; w_P = 1/(T0+ΔT)^2; w_TH = 1/(T0+ΔT)^2
    Chosen heuristically after inspecting AUC curves in Figure 2, which are computed on the same datasets used for evaluation.
  • λ (HalluFieldSE) = 2
    Set in Section 4 without a validation procedure or sensitivity analysis.
  • temperature perturbation set = {1.0, 1.5, 2.0} or {1.0, 2.0, 3.0}
    Selected per model, e.g., LLaMa-2-7B-Chat uses {1.0, 2.0, 3.0}, based on model temperature scaling.
  • number of perturbations per temperature = 50
    Reported in Section C; no convergence analysis justifies this number.
axioms (5)
  • domain assumption The first law of thermodynamics δU = T δH + W applies to LLM token sequences, with W implicitly defined by the rest of the construction.
    Section 3, Eq. 5. W is never explicitly defined; the identity is used only as an analogy to justify δU = δF + δ(TH).
  • domain assumption Hallucinated responses are high-energy and less coherent; correct low-energy responses become high-energy under temperature increase, while hallucinated ones remain high-energy.
    Section 3 hypothesis. Not derived; supported only by the plots in Figures 1, 2 and Appendix A on the same style of data used for evaluation.
  • domain assumption Token-level Shannon entropy and negative log-likelihood, summed over positions, are the correct analogues of thermodynamic entropy and free energy for hallucination detection.
    Section B.2, B.3. The extensivity and monotonicity properties for F are imposed to force the logarithmic form; no independent evidence links these to hallucination behavior.
  • ad hoc to paper The total variation of a functional is a weighted linear combination of its parametrized discrete variations.
    Defined heuristically in Eq. 9 and Section B.1. The linear form is asserted, not derived.
  • ad hoc to paper The pseudo-distance between token sequences at different temperatures is |ΔT|, and distances between different token paths need not be computed.
    Eq. 26 in Section B.1. This simplification turns the parametrized variation into a plain difference in functional values.

pith-pipeline@v1.3.0-alltime-deepseek · 17355 in / 10683 out tokens · 105734 ms · 2026-08-04T17:34:47.330780+00:00 · methodology

0 comments
read the original abstract

Large Language Models (LLMs) exhibit impressive reasoning and question-answering capabilities. However, they often produce inaccurate or unreliable content known as hallucinations. This unreliability significantly limits their deployment in high-stakes applications. Thus, there is a growing need for a general-purpose method to detect hallucinations in LLMs. In this work, we introduce HalluField, a novel field-theoretic approach for hallucination detection based on a parametrized variational principle and thermodynamics. Inspired by thermodynamics, HalluField models an LLM's response to a given query and temperature setting as a collection of discrete likelihood token paths, each associated with a corresponding energy and entropy. By analyzing how energy and entropy distributions vary across token paths under changes in temperature and likelihood, HalluField quantifies the semantic stability of a response. Hallucinations are then detected by identifying unstable or erratic behavior in this energy landscape. HalluField is computationally efficient and highly practical: it operates directly on the model's output logits without requiring fine-tuning or auxiliary neural networks. Notably, the method is grounded in a principled physical interpretation, drawing analogies to the first law of thermodynamics. Remarkably, by modeling LLM behavior through this physical lens, HalluField achieves state-of-the-art hallucination detection performance across models and datasets.

Figures

Figures reproduced from arXiv: 2509.10753 by Brian K. Tran, Geigh Zollicoffer, Manish Bhattarai, Minh Vu, Nhat Hoang-Xuan, Syed A. Shah.

Figure 1
Figure 1. Figure 1: Schematic of the HalluField framework for analyzing LLM responses: The change [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Differences (top) and the AUCs (bottom) of the base energy variation [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Summary of comparison between our HalluField-based methods (HalluField and Hallu [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Behaviors of the base energy variation ∆BQ, the change in potential ∆PQ, and the change in entropy ∆(THQ) between non-hallucinated and hallucinated responses of LLaMa-2-7B-Chat in triviaQA dataset B VARIATIONAL PRINCIPLE ON SEQUENCES OF TOKENS This appendix provides our formulation of the variation of a functional defined on the space of se￾quences of tokens; we will subsequently define in Section B.1 a pa… view at source ↗
Figure 5
Figure 5. Figure 5: Behaviors of the base energy variation ∆BQ, the change in potential ∆PQ, and the change in entropy ∆(THQ) between non-hallucinated and hallucinated responses of LLaMa-3.2-3B in triv￾iaQA dataset [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Behaviors of the base energy variation ∆BQ, the change in potential ∆PQ, and the change in entropy ∆(THQ) between non-hallucinated and hallucinated responses of Phi-3 Mini-Inst in triviaQA dataset 14 [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Behaviors of the base energy variation ∆BQ, the change in potential ∆PQ, and the change in entropy ∆(THQ) between non-hallucinated and hallucinated responses of LLaMa-2-7B-Chat in squad dataset [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Behaviors of the base energy variation ∆BQ, the change in potential ∆PQ, and the change in entropy ∆(THQ) between non-hallucinated and hallucinated responses of LLaMa-3.2- 3B in squad dataset 15 [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Behaviors of the base energy variation ∆BQ, the change in potential ∆PQ, and the change in entropy ∆(THQ) between non-hallucinated and hallucinated responses of Phi-3 Mini-Inst in squad dataset of tokens χ = {χi} N i=1, we define the discrete variation of this functional from τ to χ by ∆AQ[τ ; χ] = X N i=1 AQ(τi) − AQ(χi) d(τi , χi) ∆i , (19) where d : T × T → R is a pseudo-distance function between tokens… view at source ↗

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Cited by 1 Pith paper

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Reference graph

Works this paper leans on

27 extracted references · 2 canonical work pages · cited by 1 Pith paper

  1. [1]

    Textbooks are all you need ii: phi-1.5 technical report.arXiv preprint arXiv:2309.05463,

    Marah Abdin, Jyoti Aneja, Shobhit Babbar, Evelina Bakhturina, Aditya Barua, S ´ebastien Bubeck, Ronen Eldan, Sivakanth Gopi, Suriya Gunasekar, Eric Horvitz, et al. Textbooks are all you need ii: phi-1.5 technical report.arXiv preprint arXiv:2309.05463,

    Pith/arXiv arXiv

  2. [3]

    Each GPU is equipped with 96GB of HBM2 memory, ideal for handling large models and datasets

    C EXPERIMENTAL SETTINGS Our experiments were conducted on a cluster with nodes featuring four NVIDIA Hopper (H100) GPUs each, paired with NVIDIA Grace CPUs via NVLink-C2C for rapid data transfer essential for intensive computational tasks. Each GPU is equipped with 96GB of HBM2 memory, ideal for handling large models and datasets. For each dataset, we fol...

    2024

  3. [8]

    Ganguli, A

    D. Ganguli, A. Askell, N. Schiefer, T. I. Liao, K. Luko ˇsi¯ut˙e, A. Chen, A. Goldie, A. Mirhoseini, C. Olsson, D. Hernandez, et al. The capacity for moral self-correction in large language models. arXiv preprint arXiv:2302.07459,

    Pith/arXiv arXiv

  4. [9]

    Jiang, Alexandre Sablayrolles, Arthur Mensch, Chris Bamford, Etienne Chapuis, Diego de Las Casas, Fabian Gloeckle, Felix Ho, Huu Nguyen, Guilherme Penedo, et al

    Albert Q. Jiang, Alexandre Sablayrolles, Arthur Mensch, Chris Bamford, Etienne Chapuis, Diego de Las Casas, Fabian Gloeckle, Felix Ho, Huu Nguyen, Guilherme Penedo, et al. Mistral 7b. arXiv preprint arXiv:2310.06825,

    Pith/arXiv arXiv

  5. [11]

    URLhttps://arxiv.org/ abs/2207.05221. K. Kang, E. Wallace, C. Tomlin, A. Kumar, and S. Levine. Unfamiliar finetuning examples control how language models hallucinate.arXiv preprint arXiv:2403.05612,

    Pith/arXiv arXiv

  6. [12]

    doi: 10.1038/s41597-023-02155-3. L. Kuhn, Y . Gal, and S. Farquhar. Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation.arXiv preprint arXiv:2302.09664,

    Pith/arXiv arXiv

  7. [14]

    S. Lin, J. Hilton, and O. Evans. Teaching models to express their uncertainty in words.arXiv preprint arXiv:2205.14334,

    Pith/arXiv arXiv

  8. [15]

    S. Liu, L. Xing, and J. Zou. In-context vectors: Making in-context learning more effective and controllable through latent space steering.arXiv preprint arXiv:2311.06668,

    Pith/arXiv arXiv

  9. [18]

    URLhttps: //openreview.net/forum?id=j2wCrWmgMX. Guilherme Penedo, Quentin Malartic, Daniel Hesslow, Ruxandra Cojocaru, Alessandro Cappelli, Hamza Alobeidli, Baptiste Pannier, Ebtesam Almazrouei, Julien Launay, Abdulaziz Alhammadi, et al. The falcon series of open language models.arXiv preprint arXiv:2306.01116,

    Pith/arXiv arXiv

  10. [19]

    SQuAD: 100,000+ Questions for Machine Comprehension of Text

    Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. SQuAD: 100,000+ Questions for Machine Comprehension of Text. arXiv preprint arXiv:1606.05250,

    Pith/arXiv arXiv

  11. [21]

    K. Tian, E. Mitchell, A. Zhou, A. Sharma, R. Rafailov, H. Yao, C. Finn, and C. D. Manning. Just ask for calibration: Strategies for eliciting calibrated confidence scores from language models fine-tuned with human feedback.arXiv preprint arXiv:2305.14975,

    Pith/arXiv arXiv

  12. [22]

    Llama 2: Open founda- tion and fine-tuned chat models.arXiv preprint arXiv:2307.09288,

    Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Niko- lay Bashlykov, Siddharth Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open founda- tion and fine-tuned chat models.arXiv preprint arXiv:2307.09288,

    Pith/arXiv arXiv

  13. [23]

    We call this thefree energyF Q :T ∗ →Rand define it as a map such thatF Q is continuous, monotonic, and a thermodynamically extensive function of the token sequence

    In thermodynamics, such a quantity is called an extensive property. We call this thefree energyF Q :T ∗ →Rand define it as a map such thatF Q is continuous, monotonic, and a thermodynamically extensive function of the token sequence. We derive the functional form of this energy from the following statistical arguments (see also Landau & Lifshitz (1980)). ...

    1980

  14. [27]

    For HalluField, we generate 50 perturbations per temperature

    and assess hallucination rates on 500 samples. For HalluField, we generate 50 perturbations per temperature. The benchmark methods use a comparable number of perturbations, namely 50×Number of temperatures. We typically use the temperature set{1.0,1.5,2.0}; for models with different temperature scaling such as LLaMa-2-7B-Chat, we instead use{1.0,2.0,3.0}....

    2024

  15. [1978]

    doi: 10.1007/978-1-4757-1693-1. A. M. Bloch.Nonholonomic Mechanics and Control. Interdisciplinary Applied Mathematics. Springer New York, NY ,

    doi:10.1007/978-1-4757-1693-1

  16. [2001]

    Maynez, S

    J. Maynez, S. Narayan, B. Bohnet, and R. McDonald. On faithfulness and factuality in abstractive summarization.arXiv preprint arXiv:2005.00661,

    Pith/arXiv arXiv 2005

  17. [2007]

    10 Sebastian Farquhar, Jannik Kossen, Lorenz Kuhn, and Yarin Gal

    doi: 10.1007/s10444-004-4093-5. 10 Sebastian Farquhar, Jannik Kossen, Lorenz Kuhn, and Yarin Gal. Detecting hallucinations in large language models using semantic entropy.Nature, 630:625–630,

    work page doi:10.1007/s10444-004-4093-5

  18. [2010]

    doi: 10.1007/978-3-642-11698-8

    ISBN 978-3-642-11697-1. doi: 10.1007/978-3-642-11698-8. Y . Xiao and W. Y . Wang. On hallucination and predictive uncertainty in conditional language gen- eration.arXiv preprint arXiv:2103.15025,

    Pith/arXiv arXiv

  19. [2015]

    Colin Burns, Hattie Ye, Dan Klein, and Jacob Steinhardt

    doi: 10.1007/978-1-4939-3017-3. Colin Burns, Hattie Ye, Dan Klein, and Jacob Steinhardt. Discovering latent knowledge in language models without supervision.arXiv preprint arXiv:2212.03827,

    Pith/arXiv arXiv

  20. [2016]

    J. Ren, Y . Zhao, T. Vu, P. J. Liu, and B. Lakshminarayanan. Self-evaluation improves selective generation in large language models.arXiv preprint arXiv:2312.09300,

    Pith/arXiv arXiv

  21. [2017]

    doi: 10.18653/v1/P17-1147. Saurav Kadavath, Tom Conerly, Amanda Askell, Tom Henighan, Dawn Drain, Ethan Perez, Nicholas Schiefer, Zac Hatfield-Dodds, Nova DasSarma, Eli Tran-Johnson, Scott Johnston, Sheer El-Showk, Andy Jones, Nelson Elhage, Tristan Hume, Anna Chen, Yuntao Bai, Sam Bow- man, Stanislav Fort, Deep Ganguli, Danny Hernandez, Josh Jacobson, Ja...

    doi:10.18653/v1/p17-1147

  22. [2019]

    doi: 10.1162/tacl a 00276. Lev D. Landau and Evgeny M. Lifshitz.Statistical Physics, volume 5 ofCourse of Theoretical Physics. Pergamon Press, 3rd edition,

    doi:10.1162/tacl

  23. [2020]

    The llama 3 herd of models.arXiv preprint arXiv:2407.12345,

    Meta AI. The llama 3 herd of models.arXiv preprint arXiv:2407.12345,

    Pith/arXiv arXiv

  24. [2022]

    Chen and J

    J. Chen and J. Mueller. Quantifying uncertainty in answers from any language model via intrinsic and extrinsic confidence assessment.arXiv preprint arXiv:2308.16175,

    Pith/arXiv arXiv

  25. [2023]

    Cohen, M

    R. Cohen, M. Hamri, M. Geva, and A. Globerson. Lmvslm: Detecting factual errors via cross- examination.arXiv preprint arXiv:2305.13281,

    Pith/arXiv arXiv

  26. [2024]

    Paul Feldman, James Robert Foulds, and Shimei Pan

    doi: 10.1038/ s41586-024-07421-0. Paul Feldman, James Robert Foulds, and Shimei Pan. Trapping llm hallucinations using tagged context prompts.arXiv preprint arXiv:2306.06085,

    Pith/arXiv arXiv

  27. [2025]

    Friedrich Sauvigny Ulrich Dierkes, Stefan Hildebrandt.Minimal Surfaces

    doi: 10.1142/S2972458925500042. Friedrich Sauvigny Ulrich Dierkes, Stefan Hildebrandt.Minimal Surfaces. Grundlehren der math- ematischen Wissenschaften. Springer Berlin, Heidelberg,

    work page doi:10.1142/s2972458925500042

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.