{"id":"383dc633-a7ff-4519-80f0-75ee147049a2","arxiv_id":"2504.19622","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Language models follow Bayesian confirmation with golden evidence but fail to follow Bayesian disconfirmation and irrelevance assumptions, and they are biased toward golden evidence.","lead":"This paper tests whether large language models update their confidence like Bayesian reasoners when given evidence of different quality, and finds they only partly do. It introduces a new evidence dataset and shows that models grow confident with correct evidence but treat contradictory and coincidental evidence much like correct evidence.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central negative claims rest on low-power statistics: non-significant n=6 tests are treated as failure to disconfirm, and Section 5's cross-domain ablation sits in tension with the Section 7 irrelevance conclusion.","rationale":"The reader's chosen weakest assumption—coincidental evidence leakage—is a genuine flaw, and I agree it undermines the paper's claims about handling unreliable evidence. However, it is not the most load-bearing concern for the paper's stated central claim, which is about confirmation, disconfirmation, and irrelevance. The coincidental evidence category supports a secondary analysis; the headline negative claims rest on the conflicting-evidence and irrelevant-evidence results. The statistical issue is more fundamental: the paper infers 'failure to disconfirm' from non-significant p-values computed with only six aggregated data points. This is a logical error that directly affects the main conclusion. The irrelevance claim also faces an internal tension: Section 5's cross-domain ablation suggests that when evidence is truly irrelevant, LLM behavior approaches the no-evidence baseline, which is what the irrelevance assumption predicts. The paper even acknowledges the 'possibility' that LLMs satisfy the irrelevance assumption, yet Section 7 states categorically that they do not. These are addressable issues—sample-level statistics with confidence intervals and a carefully scoped conclusion would fix them—so the verdict remains CONDITIONAL. The paper does have independent value: the new evidence dataset, the multi-method confidence elicitation, and the gradient ablation are useful contributions, and the confirmation result appears robust across models and methods. My concern is that the negative half of the central claim is currently overstated relative to the statistical evidence.","tokens_in":34395,"tokens_out":10567,"duration_ms":103991,"concrete_test":"Recompute the NO_EVI vs. CONFLICT confidence comparison at the sample level for each model and dataset (e.g., all 1095 SciQ, 1000 TriviaQA, 622 GSM8K samples for GPT-3.5; 200 for GPT-4o). Report a paired bootstrap 95% confidence interval for the mean confidence difference and run a two one-sided t-test (TOST) equivalence test with a prespecified bound such as Δ=0.05. If the CI is wide and includes zero and equivalence is not rejected, the Section 7 disconfirmation-failure claim is unsupported; if the CI excludes zero, the claim survives this critique.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's core negative claim—that LLMs 'fail to adhere to disconfirmation and irrelevance assumptions' (Section 7)—is not supported by its own statistical analysis. Appendix H.2 states that p-values come from two-sided paired t-tests on dataset-level metrics, comparing six aggregated results (three datasets × two models). With n=6, power is extremely low. Section 4.1 interprets the non-significant confidence difference for conflicting evidence (e.g., p=0.99 for verbal confidence in Table 4) as evidence that LLMs fail Bayesian disconfirmation. This is a classic error: absence of evidence is not evidence of absence. The same low-power analysis underlies the irrelevance claim, where p-values are only marginal (0.059 and 0.012 in Tables 4–6). Moreover, Section 5's ablation with cross-domain irrelevant evidence shows that confidence, accuracy, and ECE 'approached closer to the baseline no evidence case,' and the authors write 'there is a possibility that the LLMs satisfy the irrelevant assumption.' That statement is in direct tension with the Section 7 conclusion that LLMs fail the irrelevance assumption. The central negative conclusions are therefore either statistically unfounded or internally hedged to the point of contradiction.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes evaluating whether large language models update their beliefs in accordance with three Bayesian epistemology assumptions (confirmation, disconfirmation, irrelevance) plus an evidence-power assumption. To do so, the authors construct a multi-type evidence dataset from SciQ, TriviaQA, and GSM8K, and measure verbalized confidence, token probability, and sampling-based confidence for GPT-3.5-turbo, GPT-4o, and Gemini-1.5-Flash. They report that golden evidence increases confidence and accuracy (supporting confirmation), that conflicting evidence does not reliably reduce confidence (interpreted as failing disconfirmation), that irrelevant evidence reduces accuracy but not always confidence (interpreted as failing irrelevance), and that stronger evidence raises verbalized and sampling confidence but not token-probability confidence in some conditions. They attribute the deviations to a bias toward golden evidence and to the degree of irrelevance.","tokens_in":34623,"tokens_out":4438,"duration_ms":41826,"significance":"If the findings are robust, the paper offers a philosophically grounded and empirically falsifiable test of whether LLM confidence behaves like Bayesian confirmation, and it ships code and data with explicit prompts, which is a strength. The strongest contribution is the confirmation result, which appears consistent across models, datasets, and confidence elicitation methods, and the systematic comparison of three confidence measures. However, the main negative conclusions about disconfirmation and irrelevance are based on statistical tests with severe power constraints and on evidence-category validity assumptions that are not fully met, so the significance is conditional and will depend on the adequacy of a revised analysis.","major_comments":[{"comment":"The negative conclusions about disconfirmation are inferred from non-significant paired t-tests on only six dataset-level observations (three datasets by two models), as described in Appendix H.2; for example, the verbal-confidence comparison of conflicting evidence against no evidence yields p=0.99 (Table 4), and the token and sampling versions yield p=0.445 and p=0.392 (Tables 5 and 6). With n=6, these tests have very low power, so a non-significant p-value cannot support the paper's claim that conflicting evidence does not have a significant effect on confidence and consequently that LLMs fail the disconfirmation assumption (Section 4.1). A proper analysis using sample-level data, equivalence tests, or at least effect sizes and confidence intervals is needed before the central failure-to-disconfirm claim can be made.","section":"Appendix H.2 and Section 4.1, Tables 4-6"},{"comment":"Section 5's cross-domain irrelevant-evidence ablation reports that confidence, accuracy, and ECE approached closer to the baseline no-evidence case and states that there is a possibility that the LLMs satisfy the irrelevant assumption, which directly contradicts the Section 7 conclusion that LLMs fail to adhere to irrelevance assumptions. If the irrelevance failure applies only to same-domain irrelevant evidence, the conclusion in Section 7 is overgeneralized; if it applies globally, the ablation's finding must be reconciled. The manuscript currently leaves the reader with an internal inconsistency that needs to be resolved, either by a more nuanced conclusion or by additional evidence that the same-domain result is the relevant one.","section":"Section 5 vs. Section 7"},{"comment":"The prompts for generating coincidental evidence (Appendix I.2) embed the correct answer directly in the explanation text (e.g., 'hemoglobin', 'coagulation', 'golden eagles'), so the model can produce the correct answer by extraction even when the reasoning is supposed to be unreasonable or based on epistemic luck. This breaks the intended construct: Section 3.2 defines coincidental evidence as not containing the correct answer, yet the generated examples do. Consequently, the Section 4.1 claim that LLMs cannot handle coincidental evidence well is not a clean measure of whether models capture evidence unreliability; high accuracy and high confidence may simply reflect answer leakage. The dataset construction or the interpretation must be revised.","section":"Appendix I.2 and Section 3.2"}],"minor_comments":[{"comment":"The significance thresholds (p<=0.05 significant, 0.05<p<=0.1 marginal) are used without any correction for the 18 comparisons made in the confirmation task; a multiple-comparison correction or an explicit justification for omitting one would strengthen the statistical claims.","section":"Appendix B, Tables 4-6"},{"comment":"The statement that only GPT-4o with the verbal method exhibited behavior aligned with Bayesian disconfirmation is based on a single model-method combination; given the small number of tests and the low power, this should be hedged as exploratory rather than presented as a settled finding.","section":"Section 4.1"},{"comment":"The captions of Tables 2 and 3 are identical; they should clearly distinguish that Table 2 reports token probability and Table 3 reports the sampling method.","section":"Table captions (Appendix A)"},{"comment":"The definition of conflicting evidence states that all sentences are replaced with conflicting counterparts, but some of the negation examples in Appendix I.2 may still contain the original answer or close variants; a systematic check that the golden answer is absent from generated conflicting and coincidental evidence would improve construct validity.","section":"Section 3.2"},{"comment":"The Limitations section notes that conflicting evidence is heterogeneous in whether it is entirely incompatible or merely obstructive; this heterogeneity weakens the disconfirmation analysis and should be analyzed separately or used to refine the evidence taxonomy, as the authors themselves suggest.","section":"Section 8 (Limitations)"}],"recommendation":"major_revision","confidential_remarks":"The paper's central confirmation result appears solid and the dataset/prompt release is a strength. However, the load-bearing negative claims need re-analysis or substantial hedging, and the coincidental evidence leakage is a data-construction issue that the authors should be able to fix. The paper is within the journal's scope and could be a contribution after revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the quick take: the evidence taxonomy and the confirmation result are genuinely useful additions to the LLM evaluation toolbox, but the paper's central negative claims — that LLMs fail disconfirmation and irrelevance — are not supported by its own statistics, and the authors hedge one of them away in Section 5.\n\nWhat's actually new: a dataset with six evidence types (golden, conflicting, contradictory, coincidental, irrelevant, incomplete) plus four reliability dimensions (source credibility, specificity, timeliness, experimental vs. observational), tested across three confidence elicitation methods. That mapping from Bayesian epistemology to LLM confidence behavior is new, as far as I know. The core confirmation finding holds up: golden evidence consistently raises confidence and accuracy across models and datasets. That alone is worth having as a baseline result. The code and data are public, which makes the resource usable.\n\nThe soft spots are real and center on the statistics. Appendix H.2 is explicit: p-values come from two-sided paired t-tests on dataset-level metrics, comparing six aggregated results (three datasets × two models). With n=6, the power is very low. So reading p=0.99 for conflicting evidence as 'LLMs fail to disconfirm' is a textbook absence-of-evidence error. The same issue dogs the irrelevance claim, which rests on p=0.059 and p=0.012. You cannot conclude the null holds from a failed significance test at n=6. The fix is straightforward: report sample-level statistics with proper mixed-effects models or expand the dataset/model grid, and show confidence intervals.\n\nSecond, the coincidental evidence category has answer leakage. Appendix I.2's examples embed the exact answer in the explanation text ('hemoglobin,' 'coagulation,' 'golden eagles'). The model can answer by extraction rather than by updating on unreliable evidence, so part of the coincidental finding may be an artifact.\n\nThird, Section 5 actively undercuts the Section 7 conclusion. The cross-domain ablation shows confidence, accuracy, and ECE 'approached closer to the baseline no evidence case,' and the authors write 'there is a possibility that the LLMs satisfy the irrelevant assumption.' That is in direct tension with the abstract and conclusion claiming LLMs 'fail to adhere to the irrelevance assumption.' The paper needs to reconcile that, or the claims need to be softened to match what the cross-domain result suggests.\n\nThere's also a measurement caveat, acknowledged implicitly: P(H|E,theta) is operationalized as model confidence. That's a defensible assumption but worth stating as a construct-validity limitation.\n\nWho is this for: the LLM trustworthiness and calibration crowd. It does not reshape the field, but the dataset and the framing are a usable contribution. It deserves peer review, not desk rejection — the reviewer's job is to force the fixes above. I'd send it back for major revision with the statistics and the leakage questions flagged first.","headline":"A useful evidence taxonomy and a solid confirmation result, but the negative Bayesian claims rest on n=6 t-tests and a Section 5 that undercuts the irrelevance conclusion.","tokens_in":35136,"tokens_out":3324,"would_cite":true,"duration_ms":30580,"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":"Language models update confidence only when evidence agrees with them, not when it contradicts or is irrelevant.","keywords":["Bayesian epistemology","language model confidence","belief updating","evidence types","irrelevant context","verbalized confidence","calibration"],"falsifier":"Re-run the confirmation experiments with coincidental evidence prompts stripped of any token that can be extracted as the answer, for example by paraphrasing or blanking concrete answer words like hemoglobin, and check whether models still reach high accuracy. If accuracy collapses or confidence drops once answer leakage is removed, the paper's attribution of the deviation to a failure to handle unreliable evidence is called into question.","tokens_in":1635,"feed_emoji":"🧠","tokens_out":2586,"duration_ms":69186,"temperature":0.7,"pith_summary":"This paper asks whether large language models update their confidence the way Bayesian epistemology says a rational agent should: raising belief when evidence confirms a hypothesis, lowering it when evidence disconfirms, and leaving it unchanged when evidence is irrelevant. Probing GPT-3.5 and GPT-4o with seven kinds of evidence built from three question-answering datasets, the authors find that the models raise confidence and accuracy when given correct golden evidence, matching the confirmation assumption. But when evidence conflicts with the correct answer, confidence does not reliably drop, and when evidence is irrelevant, confidence and accuracy fall instead of staying flat. The paper concludes that language models partially align with Bayesian epistemology, following confirmation assumptions but failing to adhere to disconfirmation and irrelevance assumptions, and that their bias toward golden evidence helps explain the deviation. This matters because if model confidence is not a Bayesian posterior over evidence, then high-confidence answers cannot be read as justified beliefs.","feed_headline":"LLMs act Bayesian only when evidence agrees","feed_subtitle":"True evidence raises confidence; conflicting and irrelevant evidence barely move it, so model confidence is not justified belief.","key_machinery":"The load-bearing mechanism is a comparison between the model's probability of a hypothesis without evidence, $P(H|\\theta)$, and its probability given evidence, $P(H|E,\\theta)$, across a designed taxonomy of evidence: golden, conflicting, incomplete, contradictory, coincidental, and irrelevant evidence, together with reliability variations such as source credibility, specificity, timeliness, and experimental versus observational evidence. For each comparison the authors measure confidence three ways, verbalized confidence, token probability, and sampling, plus accuracy and expected calibration error. The taxonomy turns the abstract Bayesian confirmation, disconfirmation, and irrelevance assumptions into concrete, testable predictions: confirmation requires $P(H|E,\\theta) > P(H|\\theta)$, disconfirmation requires $P(H|\\theta) > P(H|E,\\theta)$, and irrelevance requires equality. The paper's evidence-generation prompts, which rewrite correct explanations into negated, coincidental, or out-of-context versions, are what make those predictions operational.","core_discovery":"The central claim is that language models do not possess justified belief in the Bayesian sense: they behave like Bayesian agents only when evidence supports what they already know. Presented with golden evidence, both models show significantly higher confidence and accuracy than with no evidence, satisfying the confirmation assumption. Presented with conflicting evidence, however, they do not consistently lower confidence, with only GPT-4o using verbalized confidence showing a significant drop, while accuracy falls, so the disconfirmation assumption fails. Contradictory evidence containing both correct and wrong sentences is treated almost like golden evidence, and irrelevant evidence decreases accuracy rather than leaving belief unchanged, so the irrelevance assumption also fails. The paper also shows that stronger evidence raises verbalized and sampling confidence but does not always improve accuracy or calibration, meaning high confidence is not a guarantee of correct belief.","pith_inferences":["An untested consequence of the golden-evidence bias is that the same prompting setup should show smaller deviations when questions concern facts absent from the model's training data, because weaker parametric priors would let evidence dominate; this can be tested with a held-out corpus of novel facts.","The irrelevance gradient suggests a practical extension: if the degree of distraction tracks semantic or field distance, then retrieval systems could rank context not only by relevance but by predicted distraction, and the paper's within-field versus cross-field comparison provides a template for measuring that.","Bayesian updating is usually about sequential evidence, while this paper tests one-shot evidence; a sequential-evidence version, for example first irrelevant then confirming, could reveal whether model confidence obeys order effects and base-rate neglect, extending the framework without new assumptions."],"forward_implications":["Model confidence cannot be treated as a calibrated probability of being right: golden evidence inflates it, conflicting evidence leaves it nearly unchanged, and stronger evidence can make confidence rise while accuracy stays flat.","When contradictory context is present, a model's parametric prior can outweigh contradictory sentences, so adding a wrong statement to correct evidence need not reduce trustworthiness.","Irrelevant context is more damaging than conflicting context in these experiments, since it lowers accuracy while confidence drops only partially; context selection matters for safe deployment.","Under the paper's Bayesian standard, language models lack justified belief, so their high-confidence outputs should be treated as fluent guesses rather than epistemic commitments."],"supporting_citations":[{"why":"Supplies the SciQ multiple-choice questions with explanations that serve as golden evidence for the confirmation task.","marker":"Welbl et al., 2017"},{"why":"Supplies the TriviaQA context passages used as golden evidence and as raw material for perturbed evidence types.","marker":"Joshi et al., 2017"},{"why":"Supplies the GSM8K math word problems and reasoning explanations used as another evidence source.","marker":"Cobbe et al., 2021"},{"why":"Provides the verbalized-confidence elicitation prompt that the paper uses as one of its three confidence measures.","marker":"Tian et al., 2023b"},{"why":"Supplies the sampling-based confidence measurement approach used alongside verbalized confidence.","marker":"Lee et al., 2023"},{"why":"Defines expected calibration error, the calibration metric used to assess whether confidence matches accuracy.","marker":"Guo et al., 2017"},{"why":"Establishes the prior observation that language models are distracted by irrelevant context, which this paper extends with graded irrelevance and confidence analysis.","marker":"Shi et al., 2023"},{"why":"Provides the primitive conditional-probability treatment that lets the paper apply Bayesian assumptions even to contradictory evidence where the standard ratio formula would break.","marker":"Hájek (2003)"}],"fun_headline_variants":["LLMs ignore Bayes when evidence conflicts","LLM confidence not justified belief","Bayesian LLMs only with agreeable evidence","LLMs fail Bayesian update on conflicting evidence"],"cache_read_input_tokens":37376,"weakest_assumption_plain":"The conclusions stand on the assumption that the automatically generated evidence prompts genuinely instantiate the intended epistemic categories; if coincidental evidence secretly contains the answer in a retrievable form, or if conflicting evidence is not truly contradictory, then the measured deviations from Bayesian assumptions are partly artifacts of data construction.","fun_headline_variants_meta":{"raw":{"variants":["LLMs ignore Bayes when evidence conflicts","LLM confidence not justified belief","Bayesian LLMs only with agreeable evidence","LLMs fail Bayesian update on conflicting evidence"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000123,"raw_usage":{"total_tokens":1045,"prompt_tokens":838,"completion_tokens":207,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":454,"completion_tokens_details":{"reasoning_tokens":155}},"tokens_in":454,"tokens_out":207,"duration_ms":2677,"temperature":1.0,"reasoning_tokens":155,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:47:19.846513+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the confirmation experiments with coincidental evidence prompts stripped of any token that can be extracted as the answer, for example by paraphrasing or blanking concrete answer words like hemoglobin, and check whether models still reach high accuracy. If accuracy collapses or confidence drops once answer leakage is removed, the paper's attribution of the deviation to a failure to handle unreliable evidence is called into question.","supporting_citations":[],"review_version":1}