{"id":"eeac5069-c044-49d2-88ad-f8e17b51a11a","arxiv_id":"2502.00290","paper_version":5,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"LogTokU splits token uncertainty into aleatoric and epistemic components from the top-K logits, enabling single-pass hallucination detection and uncertainty-guided decoding.","lead":"This paper proposes LogTokU, a method for reading a large language model's raw pre-softmax scores, or logits, to estimate whether the model is unsure, knows several valid answers, or is confidently repeating a memorized phrase. It reports large gains over probability-based and sampling-based baselines for detecting unreliable answers and for deciding when to generate a second answer, using only one generation instead of many.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Appendix G's proof that CE training accumulates top-K evidence is formally incorrect, so the paper's central premise that raw logits encode evidence strength is unsupported; the Dirichlet parameterization also fails for negative logits.","rationale":"The reader's weakest_assumption identifies the same underlying vulnerability: raw top-K logits are treated as Dirichlet evidence without the required positivity, and the appendix proof does not establish the evidence-accumulation premise. I agree with that diagnosis and would go further: the proof in Appendix G is not merely incomplete; it is demonstrably wrong because it ignores the changing top-K set and because the single-step CE update conserves the sum of all logits. Thus the central explanatory claim (normalization destroys evidence strength, and logits capture it) is left without valid theoretical support. The paper does have independent empirical value: the AUROC gains are consistent across model sizes and the framework is falsifiable, which is why I would not move to REJECT. The appropriate verdict remains CONDITIONAL, with the condition being a repaired proof or a direct empirical demonstration that top-K logit sums track training evidence frequency. The nonnegativity issue should also be addressed, for example by defining α_k as a positive transform of logits or by restricting the method to tokens where the denominator in Eq. (5) is positive.","tokens_in":17406,"tokens_out":4200,"duration_ms":48557,"concrete_test":"Implement the Appendix G one-step update on a toy softmax vector, e.g., z = (0, 100) with K=1 and label class 0, using η=0.1. If the top-1 logit after the update is smaller than before, the theorem's claimed lower bound is false. Then, on a real LLM such as LLaMA-2-13B, compute the fraction of generated tokens for which Σ_{k=1}^K (α_k+1) ≤ 0 using K=25; a non-negligible fraction would confirm that EU is undefined or negative in the paper's actual operating regime.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The theoretical weight of the central claim rests on Eq. (3) and Theorem 1 in Appendix G, but the theorem is not proved. In the proof the authors write ΔΣ_{τ_i∈T} z_i = η(1-p_k) + Σ_{τ_i∈T, i≠k}(-η p_i) and then lower-bound the second term by extending the sum over all classes, claiming the result is ≥ 0. This only bounds the sum over the old set T, not the new top-K set after the gradient step. The top-K membership can change, and when the correct class is outside the current top-K or has a very low logit, the sum of the top-K logits can decrease. A concrete counterexample: label class k has logit -100 while another class has logit 100; after one small step, the correct logit rises while the top logit falls, so the top-1 evidence decreases. Moreover, for a single CE update the sum over all logits changes by exactly zero: ΔΣ_i z_i = η(1-p_k) + Σ_{i≠k}(-η p_i) = 0. Any apparent accumulation is an artifact of restricting to the top-K subset, and the sign depends on which side of the boundary the correct token lies. Separately, Eq. (3) sets α_k = raw logits without enforcing positivity. Dirichlet parameters must be positive, and EU in Eq. (5) is undefined or negative whenever Σ_k(α_k+1) ≤ 0. Real LLM top-K logits are frequently negative, so the method is applied exactly in a regime where its stated theoretical basis fails. The empirical AUROC gains may still be valuable heuristics, but the central explanatory claim is not established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper argues that probability-based token-level uncertainty in LLMs fails because softmax normalization discards the evidence-strength information carried by raw logits. It proposes LogTokU, which interprets the top-K logits as Dirichlet evidence parameters and computes two uncertainty components (aleatoric and epistemic) in a single forward pass. The estimated uncertainty is applied to dynamic decoding on SemEval and to response-reliability estimation (AUROC against correctness) on TruthfulQA, across LLaMA-2 and LLaMA-3 models of several sizes. The theoretical justification is presented in Section 3.5 and Appendix G, where a theorem claims that cross-entropy training accumulates top-K evidence.","tokens_in":17813,"tokens_out":6379,"duration_ms":66150,"significance":"If the central claim held, LogTokU would be a practically attractive contribution: it gives token-level uncertainty without sampling, distinguishes \"I do not know\" from \"I know more than one answer,\" and supports downstream hallucination-related applications. The four-quadrant framing is intuitive, and the experiments cover a useful range of model sizes with several sampling-based baselines. The appendix also provides implementation details for the baselines and an honest limitations section. However, the core theoretical result is not established: the proof in Appendix G concerns direct logit updates rather than trained network parameters, and the Dirichlet parameterization in Eq. (3) is invalid for ordinary negative logits. The empirical gains are suggestive but currently best interpreted as evidence for a heuristic; the reported AUROC and decoding improvements also lack error bars and rely on parameters selected on the evaluation data.","major_comments":[{"comment":"The proof analyzes gradient descent on the logits themselves (update rules z_k := z_k + eta(1-p_k) and z_i := z_i - eta p_i), not on the network parameters of M, so the conclusion does not apply to an LLM trained by optimizing weights. It also assumes the correct class tau_k lies in the top-K set T; for a misclassified sample with tau_k not in T, the change in the top-K sum is -eta sum_{i in T} p_i < 0, directly contradicting the claimed accumulation. Because top-K membership can change across gradient steps, the fixed-set inequality in Eq. (16) cannot establish the theorem as stated.","section":"Appendix G, Theorem 1 and Eq. (16)"},{"comment":"Setting alpha_k = M(tau_k) to raw logits violates the requirement that Dirichlet parameters be strictly positive, since real LLM top-K logits are frequently negative. When sum_k (alpha_k + 1) <= 0, the epistemic uncertainty EU = K / sum_k(alpha_k + 1) is undefined or negative. The \"Bridging the positivity gap\" paragraph in Section 3.5 argues via the softmax exponential that negative logits behave like weak evidence, but Eq. (3) still uses raw logits rather than exponentials or ReLU, so the implementation is run precisely in a regime where the stated Dirichlet justification fails.","section":"Eq. (3), Eq. (5), and Section 3.5"},{"comment":"The headline results are reported without error bars or significance tests, and the main free parameters are selected on the evaluation data. Appendix C.1 chooses K by best AUROC on LLaMA2-13B, and Figure 4 selects the decoding threshold at the best accumulated-score point on the same test set; no validation split or sensitivity analysis is provided. As a consequence, the magnitude of the claimed improvements over the baselines is not established by the current experimental protocol.","section":"Tables 1-3 and Figure 4"},{"comment":"Appendix F states that distilled models cannot be handled because they \"lose the strength of evidence in their logits,\" but Theorem 1 claims evidence accumulation for any LLM trained with cross-entropy. Distillation is typically trained with distribution-matching losses that are cross-entropy-like, so the scope of the theoretical claim needs to be reconciled with this self-reported limitation, or the theorem must be restricted accordingly.","section":"Appendix F vs. Theorem 1"}],"minor_comments":[{"comment":"The abstract says the code is available at \"link\"; this placeholder should either contain a working repository or be removed before publication.","section":"Abstract"},{"comment":"The symbol K is used both for the number of top logits in Eq. (3) and for the number of lowest-reliability tokens aggregated in Eq. (7); using distinct symbols would remove ambiguity.","section":"Eq. (3) and Eq. (7)"},{"comment":"Equation (8) defines R(at) = -AU(at) * EU(at), while Appendix A defines unrel(word) = AU(word) * EU(word) with lower values indicating unreliability; the sign convention should be stated consistently in both places.","section":"Eq. (8) and Appendix A"},{"comment":"The first sentence of Appendix C.2 misspells BLEURT as \"BLUERT\".","section":"Appendix C.2"}],"recommendation":"major_revision","confidential_remarks":"For the editor: the manuscript is a preprint with a placeholder code link and a formal claim that the current proof does not support. The empirical setup is best described as a heuristic demonstration; with a careful reframing, a valid positivity-preserving evidence definition, and a validation-based selection procedure, the contribution could become publishable. I see no indication of misconduct, but the \"available at link\" statement should be corrected before any further review stage."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a mixed bag. The LogTokU score—treating top-K logits as Dirichlet evidence and splitting uncertainty into aleatoric and epistemic parts—is a clean, cheap, and empirically promising idea. The four-quadrant framing (\"knows more than one answer\" vs. \"doesn't know\") is genuinely useful, and the authors show consistent AUROC gains over probability and entropy baselines across six LLaMA sizes on TruthfulQA, plus a nice dynamic-decoding application on SemEval. The limitations section is honest: it flags black-box and distilled models as out of scope. That part is good work.\n\nThe soft spots are real and load-bearing. The central premise—that raw logits encode accumulated evidence strength—rests on Theorem 1 in Appendix G, and the proof is wrong as written. The inequality extends the sum over the old top-K set to all classes, but after a gradient step the top-K membership changes; the correct class's rising logit can drop out of the top-K, and the sum can decrease. In fact, for a single CE update the sum of all logits changes by exactly zero, so the claimed \"accumulation\" is an artifact of the top-K selection, not a property of training. Separately, Eq. 3 sets alpha_k = raw logits, which are frequently negative; Dirichlet parameters must be positive, and EU = K / sum(alpha_k + 1) becomes undefined or negative whenever the denominator is not positive. The paper's own \"bridging the positivity gap\" paragraph in Section 3.5 does not fix this—it asserts a logarithmic relationship that does not follow from cross-entropy training. So the theoretical story does not hold up.\n\nThe empirics are better, but not fully convincing: no error bars, no released code (the link is a placeholder), and K is ablated on the evaluation set, with the best K reported. That is fitting, not fatal—the external correctness labels in TruthfulQA give the reliability claim independent grounding—but the magnitude of the gains should be treated with caution until replicated.\n\nWho should read this? Researchers working on efficient hallucination detection or sampling-free uncertainty will find the idea worth building on. It does not deserve desk rejection; the core question—are logit magnitudes a useful uncertainty signal?—is well motivated and the experiments are suggestive. But it needs a serious referee and major revision: fix or remove the theorem, address the Dirichlet positivity issue (e.g., by shifting or using a proper evidence mapping), report variances, and release code. I would not cite the theoretical claim, but I might cite the empirical result if it survives.","headline":"A practically promising token-level uncertainty heuristic whose central theoretical claim is not supported by the proof as written; worth refereeing but not accepting without major revision.","tokens_in":18293,"tokens_out":1854,"would_cite":false,"duration_ms":21893,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Probability-based confidence scores fail for LLMs because normalization erases the evidence strength that raw logits carry.","keywords":["LLM uncertainty estimation","epistemic uncertainty","aleatoric uncertainty","Dirichlet evidence","logits","hallucination detection","token reliability","dynamic decoding"],"falsifier":"Run any real LLM generation and inspect tokens where all top-$K$ logits are negative: Eq. 5 returns a negative epistemic uncertainty, which the Dirichlet interpretation cannot accommodate. Alternatively, fine-tune on samples in which the correct token is not among the top $K$ predictions, for which the paper's Theorem 1 predicts the sum of top-$K$ logits strictly increases while the gradient update actually decreases it; measuring the summed top-$K$ logits over training would settle the claim.","tokens_in":17202,"feed_emoji":"🤔","tokens_out":10721,"duration_ms":92236,"temperature":0.7,"pith_summary":"Large language models often generate fluent answers to questions they know nothing about, and the usual probability-based confidence scores cannot flag this because softmax normalization erases how much evidence the model accumulated for each candidate during training. This paper argues that the raw logits before normalization retain that evidence, and introduces LogTokU, which treats the top $K$ logits as parameters of a Dirichlet distribution and derives two uncertainties for every generated token: aleatoric uncertainty (how torn the model is between candidates) and epistemic uncertainty (how much total evidence it has). The paper uses these signals to decide when a model should volunteer a second answer and to score whole responses for reliability, reporting higher AUROC than probability, entropy, and multi-sample methods on a question-answering benchmark and better multi-label accuracy in dynamic decoding. If the account holds, reliable token-level uncertainty is available in a single forward pass, with no sampling and no extra computation.","feed_headline":"Raw logits, not probabilities, reveal LLM uncertainty","feed_subtitle":"One forward pass tells 'I don't know' from 'I know several answers', improving hallucination checks and decoding.","key_machinery":"The load-bearing machinery is the identification of raw top-$K$ logits with Dirichlet evidence parameters, borrowed from evidential learning. Here $\\alpha_k$ is the $k$-th largest pre-softmax score and $\\alpha_0=\\sum_{k=1}^K \\alpha_k$ is the total evidence; aleatoric uncertainty is the expected entropy of the resulting Dirichlet, and epistemic uncertainty is $K/(\\alpha_0+K)$, so it shrinks as the total logit strength grows. This machinery carries the argument because $\\mathrm{EU}$ depends on logit magnitude rather than normalized probability, which is exactly the information the paper claims softmax destroys. The paper supports the identification with a gradient analysis that treats cross-entropy training as an evidential-learning loss plus an evidence-regularization term.","core_discovery":"The paper's central claim is that probability-based reliability estimation fails because normalization discards the strength of evidence accumulation, and that this information can be recovered from raw logits. Concretely, it sets $\\alpha_k = M(\\tau_k)$ for the $k$-th largest logit, takes the Dirichlet distribution over these evidence parameters, and defines token uncertainty as $\\mathrm{AU}(a_t) = -\\sum_{k=1}^K \\frac{\\alpha_k}{\\alpha_0}(\\psi(\\alpha_k+1)-\\psi(\\alpha_0+1))$ and $\\mathrm{EU}(a_t) = K/\\sum_{k=1}^K (\\alpha_k+1)$. High total evidence spread over several candidates means the model knows more than one valid answer; low total evidence with one dominant candidate means it lacks knowledge but is making a suggestion. This decoupling separates 'I do not know' from 'I know more than one answer', the two cases that probability conflates, and the paper demonstrates the separation through a four-quadrant taxonomy of token states and two downstream uses.","pith_inferences":["Editorial inference: if logit magnitude is a faithful evidence counter, then post-hoc interventions that shift logit scales, such as temperature scaling, calibration layers, or distillation, should degrade LogTokU's uncertainty even when they leave accuracy unchanged; that is a direct, testable consequence the paper does not run.","Editorial inference: the four-quadrant taxonomy suggests that tokens in Quadrant IV (high AU, low EU) should be treated as safe rather than uncertain in hallucination detectors, and comparing $\\mathrm{AU}\\cdot\\mathrm{EU}$ scoring with $\\mathrm{EU}$-only scoring on free-form QA would isolate whether the typology earns its keep.","Editorial inference: the same evidence readout could drive abstention or retrieval decisions during generation, deciding when to look up external knowledge, rather than only rescoring text after it is produced.","Editorial inference: because Eq. 5 uses raw logits directly, a constant added to all logits changes EU without changing the output distribution; probing this sensitivity would test whether the evidence interpretation is intrinsic to the model or an artifact of logit scale."],"forward_implications":["Token-level uncertainty is available in a single forward pass, so hallucination warnings and reliability scores can be computed in real time without sampling.","Dynamic decoding can use epistemic uncertainty to keep sampling diverse when the model knows several answers and to sample cautiously when knowledge is missing, improving multi-label accuracy across several model sizes.","Response reliability can be read from the least reliable tokens, removing the need to hand-assign weights to uncritical tokens such as commas and function words.","The method does not apply to black-box APIs or distilled models, because those settings either do not expose logits or rescale them so that evidence strength is lost."],"supporting_citations":[{"why":"supplies the evidential-learning framework: treating logits as Dirichlet evidence parameters and the closed-form aleatoric and epistemic uncertainty formulas that LogTokU adapts.","marker":"[22]"},{"why":"the semantic entropy sampling-based method that serves as the principal baseline and the main contrast case for the paper's claim that sampling cannot capture inherent uncertainty.","marker":"[15]"},{"why":"provides the critical-token principle that whole-sentence reliability should be aggregated from the least reliable tokens, which LogTokU uses to score responses.","marker":"[19]"},{"why":"provides the multi-label tweet classification benchmark used to evaluate dynamic decoding with and without LogTokU guidance.","marker":"[31]"},{"why":"provides the QA benchmark and the reference-based correctness labels used to compute AUROC for the response-reliability comparison.","marker":"[34]"},{"why":"motivates keeping only the top K logits and discarding the long tail of low-score tokens as noise.","marker":"[28]"}],"fun_headline_variants":["Logits expose LLM uncertainty that probabilities hide","Single-pass uncertainty: evidence from raw logits","Decouple 'don't know' from 'know many' with LogTokU","Raw logits keep evidence: probability methods lose it"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole construction rests on treating the sizes of the raw pre-softmax scores as a faithful measure of how much similar evidence the model saw during training; if logit magnitude is not a reliable evidence counter, the uncertainty formula and both downstream uses lose their foundation.","fun_headline_variants_meta":{"raw":{"variants":["Logits expose LLM uncertainty that probabilities hide","Single-pass uncertainty: evidence from raw logits","Decouple 'don't know' from 'know many' with LogTokU","Raw logits keep evidence: probability methods lose it"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000647,"raw_usage":{"total_tokens":2961,"prompt_tokens":923,"completion_tokens":2038,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":539,"completion_tokens_details":{"reasoning_tokens":1971}},"tokens_in":539,"tokens_out":2038,"duration_ms":14926,"temperature":1.0,"reasoning_tokens":1971,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T19:31:33.783459+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run any real LLM generation and inspect tokens where all top-$K$ logits are negative: Eq. 5 returns a negative epistemic uncertainty, which the Dirichlet interpretation cannot accommodate. Alternatively, fine-tune on samples in which the correct token is not among the top $K$ predictions, for which the paper's Theorem 1 predicts the sum of top-$K$ logits strictly increases while the gradient update actually decreases it; measuring the summed top-$K$ logits over training would settle the claim.","supporting_citations":[{"cited_title":"Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language genera- tion,","cited_arxiv_id":null,"evidence_quote":"the semantic entropy sampling-based method that serves as the principal baseline and the main contrast case for the paper's claim that sampling cannot capture inherent uncertainty."},{"cited_title":"Shifting attention to relevance: Towards the predictive uncertainty quantification of free-form large lan- guage models,","cited_arxiv_id":null,"evidence_quote":"provides the critical-token principle that whole-sentence reliability should be aggregated from the least reliable tokens, which LogTokU uses to score responses."},{"cited_title":"SemEval-2018 task 1: Affect in tweets,","cited_arxiv_id":null,"evidence_quote":"provides the multi-label tweet classification benchmark used to evaluate dynamic decoding with and without LogTokU guidance."}],"review_version":1}