{"id":"69568836-6787-434f-8dfd-31c61fd0a3d0","arxiv_id":"2506.07448","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Bayesian Modeling of Experiments is proposed as a unifying framework for quantifying and reducing the many sources of uncertainty in LLM deployments, beyond abstention.","lead":"This position paper argues that uncertainty in large language models should be treated as a resource to actively reduce, not just a reason to refuse answering. It recommends a Bayesian framework that lets models ask for clarification, refine prompts, or fetch information, and shows how existing reliability heuristics fit this view.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. 10 measures output/context sensitivity, not reducible uncertainty about a true answer; the claimed BME unification is therefore not established.","rationale":"The reader's weakest assumption (simulator fidelity) is real but downstream: even with a perfect P(C|X) and P(Y|X,C), Eq. 10 can recommend actions that do not reduce epistemic uncertainty about the task. The paper's BME foundation in Section 2.2 is about learning a fixed parameter; Section 3.2 silently replaces that parameter with the model's own predictive distribution Y. This is the load-bearing conceptual move. A high I(Y;C|X) can arise purely from prompt sensitivity (e.g., formatting bias) and is then misdescribed as reducible epistemic uncertainty. The synthetic counterexample makes this precise without relying on any empirical claim. Therefore the assertion that the heuristics 'unify' under BME as reducers of epistemic uncertainty is not established; at best they unify as maximizers of conditional mutual information. The Section 4.2 acknowledgement of unreliable simulators does not repair the target-variable issue. I would keep the conditional verdict: the paper needs to clarify and justify the target variable (true answer/intent versus model output), or the framework's recommendations must be recast as sensitivity-based rather than epistemic. This is not an objection to BME as mathematics; it is an objection to the mapping claimed in Section 3.2.","tokens_in":24155,"tokens_out":11682,"duration_ms":152116,"concrete_test":"Analytic check: instantiate the toy model above (T, C independent Bernoulli(1/2), Y = C with probability 0.9 and Y = 1-C otherwise, independent of T) and evaluate Eq. 10. It returns approximately 0.531 bits of claimed reducible uncertainty while H[T|X,C] - H[T|X] = 0, falsifying the interpretation of Eq. 10 as reducible epistemic uncertainty about the answer. Empirical follow-up: on a dataset of questions with known ground-truth answers and a real LLM, generate candidate clarifications C from P(C|X), compute the predicted information gain from Eq. 10 for each C, then measure the actual expected reduction in error rate (or calibration) after conditioning on C. If the predicted gains do not rank-order the actual error reductions, the central claim is unsupported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that BME unifies clarification, templating, and in-context demonstration as instances of one reducible-epistemic-uncertainty quantity. The load-bearing step is Section 3.2's definition I[Y|X;C] = H[P_LM(Y|X)] - E_{P(C|X)} H[P_LM(Y|X,C)], which makes the LLM's own output Y the 'parameter of interest'. In the BME setup of Section 2.2, the quantity of interest is a fixed unknown state of the world whose value the experiment reveals; the paper never bridges this gap. If Y is merely the model's predictive distribution, then I(Y;C|X) is conditional mutual information between output and context, and it measures sensitivity to prompt perturbations, which can be positive even when the context provides zero information about the correct answer. Example: true answer T ~ Bernoulli(1/2), context C ~ Bernoulli(1/2) independent of T, and P(Y|X,C) = 0.9 when Y=C and 0.1 otherwise. Then H[Y|X] = 1 bit, H[Y|X,C] = H(0.9), so Eq. 10 declares roughly 0.53 bits of reducible epistemic uncertainty, yet H[T|X,C] = H[T|X] = 1 bit: no epistemic uncertainty about the answer is reducible by C. The framework would recommend asking/clarifying even though the true target remains completely uncertain. Thus the 'unification' in Section 3 relabels prompt-sensitivity as epistemic reducibility. The Section 4.2 caveat about unreliable simulators is a separate, downstream issue; even with a perfect simulator, the objective is not an estimate of uncertainty about a true target.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper is a position paper proposing that Bayesian Modeling of Experiments (BME) be adopted as the conceptual foundation for managing uncertainty in LLM deployments. It reviews the BME framework, defines an information-theoretic quantity I[Y|X;C] intended to capture uncertainty reducible by auxiliary context C, and argues that this quantity unifies existing heuristics for clarification (Zhang and Choi; Hou et al.), prompt template selection (Sorensen et al.), and in-context demonstration selection (Ling et al.). The paper then sketches a research agenda for jointly reducing multiple uncertainty sources via a controllable proxy variable, deriving a lower bound on effective aleatoric uncertainty, identifying or rejecting uncertainty sources a priori, and using experiments to probe latent model properties.","tokens_in":24465,"tokens_out":12816,"duration_ms":147680,"significance":"If the central identification were valid, the paper would provide a useful unifying reframing of several ad hoc uncertainty-reduction methods and a principled justification for active clarification, retrieval, and prompt refinement rather than passive abstention. The paper is clearly written and engages honestly with limitations, explicitly acknowledging in Section 4.2 that simulators are not always available or reliable and in Section 5 the difficulties of priors and Knightian uncertainty. The information-theoretic background in Section 2.2 and the variance-correction calculation in Appendix C are correct as derivations. The research agenda, especially the lower-bound idea based on a controllable proxy variable in Section 4.1, is genuinely interesting. However, the core analogy between BME's parameter of interest and an LLM's predictive output is not established, and one supporting identity in Section 4.1 is incorrect. The paper is therefore more persuasive as an advocacy essay and literature review than as the theoretical unification it claims to provide.","major_comments":[{"comment":"The object I[Y|X;C] is conditional mutual information between the model's own output variable Y and the context C, not expected information gain about a fixed unknown state of the world, which is what BME in Section 2.2 is formulated for. Because Y is the model's random output, Eq. (10) can be positive even when C carries zero information about the correct answer. Concretely, let the true answer T be Bernoulli(1/2), let C be Bernoulli(1/2) independent of T, and let the LLM satisfy P(Y=C|X)=0.9 and P(Y≠C|X)=0.1. Then H[Y|X]=1 bit, H[Y|X,C]=H(0.9), so Eq. (10) reports roughly 0.53 bits of \"reducible uncertainty\" even though H[T|X,C]=H[T|X]=1 bit. The framework would recommend asking a clarification although no clarification can reduce uncertainty about T. The Section 4.2 caveat about unreliable simulators is a separate, downstream issue; even a perfect simulator P(C|X) would not turn I[Y;C|X] into an estimate of I[T;C|X]. The claimed unification of clarification, template, and demonstration heuristics in Section 3 therefore currently relabels prompt-sensitivity as epistemic reducibility. To support the central claim, the authors need to define a latent target variable T (e.g., user intent or a truth value) and either justify that P_LM(Y|X,C) approximates P(T|X,C) or explicitly restrict the claims to reducibility of model-output uncertainty.","section":"§3.2, Eq. (10)"},{"comment":"The reinterpretation of Sorensen et al.'s template-selection score as H[P(Y|X)] - H[P(Y|X,τ_i)] is not justified. If X denotes the original input and τ_i is a deterministic template transform, then the pair (X, τ_i(X)) generates the same information as X alone, so H[Y|X,τ_i]=H[Y|X] and the proposed difference is identically zero. The positive quantity estimated by Sorensen et al. is, on its face, a mutual information between the transformed input and the output, H[Y]-H[Y|τ_i(X)], not a reduction in conditional entropy given the original input. Moreover, Appendix C shows only that the entropy of the empirical mixture H[1/N Σ_j P(Y|x_j)] equals the conditional entropy plus a variance-correction term; it does not establish the equality to H[P(Y|X)] used in the surrounding text. This weakens the BME-unification claim for prompt templating and should be repaired or removed.","section":"§3.3.2, Eq. (12) and Appendix C"},{"comment":"The additivity decomposition I(Y;(A,B,E)|X)=I(Y;A|X)+I(Y;B|X)+I(Y;E|X) does not follow from the stated conditional independence of A, B, and E given X. The chain rule gives I(Y;A,B,E|X)=I(Y;A|X)+I(Y;B|X,A)+I(Y;E|X,A,B); additional assumptions such as Y⊥B|X,A and Y⊥E|X,A,B are required. The data-processing bound in Eq. (14) is correct, but Eq. (13) is a false identity in a section that proposes this decomposition as the starting point for jointly managing uncertainty sources. The equation should be corrected or explicitly labeled as an idealized extra assumption.","section":"§4.1, Eq. (13)"}],"minor_comments":[{"comment":"The notation in Eq. (10) uses E_{P(C)} but the surrounding discussion treats X as fixed; the expectation should be over P(C|X) or this should be stated explicitly. Section 3.3.1 writes H[P(Y|x,C)] without an expectation over C, which is inconsistent with Eq. (10).","section":"§3.2, Eq. (10) and §3.3.1"},{"comment":"The Bayes-net diagram \"A↗ ↘X→B→Ψ→Y↘ ↗E\" is difficult to interpret as a standard DAG and should be redrawn with explicit nodes and edges. The sentence \"We acknowledge that while this setting is oversimplistic, unlikely to occur in the real world, and do not lead to uncertainty reduction\" also appears to contain a grammatical error.","section":"§4.1"},{"comment":"The notation H[P(Y|X)] is used ambiguously to mean both the conditional entropy and the entropy of the marginal distribution in different places; this ambiguity is material in the discussion of Sorensen et al. and should be resolved with consistent notation.","section":"§3.3.2 and Appendix C"},{"comment":"The reference list for the Phan et al. entry appears to contain an extremely long author list that is likely intended for a different paper (Humanity's Last Exam); the citation should be checked and brought into line with the text.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is a position piece with a potentially valuable agenda, but the central unification claim currently rests on identifying model-output entropy with uncertainty about a true target. That identification needs to be made explicit with a latent target variable or the scope of the claims needs to be substantially narrowed. The false additivity identity in Section 4.1 should also be corrected. These are conceptual repairs rather than new experiments, so they are feasible within revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper is a well-written position paper advocating Bayesian Modeling of Experiments as a unifying framework for LLM uncertainty. The exposition in Section 2.2 is correct, the critique of Hou et al. and Ling et al.'s labeling is genuinely clarifying, and the paper is honest about its idealizations. But the central claim has a load-bearing gap: Eq. 10 defines I[Y|X;C] with the model output Y as the quantity of interest, which is conditional mutual information between output and context, not the expected reduction in uncertainty about a true state of the world. The stress-test counterexample is decisive: you can have positive I(Y;C|X) even when context provides zero information about the correct answer, so Eq. 10 would recommend clarifying when no clarification can reduce the relevant epistemic uncertainty. The paper never bridges the gap between the fixed unknown state of the world in Section 2.2 and the LLM's own predictive distribution in Section 3.2. What the paper does well: the derivation in Section 2.2 is standard but clean, and the point that Hou et al. call their information gap 'aleatoric' while also proposing to reduce it is a real internal inconsistency worth naming. The re-reading of Sorensen et al. and Ling et al. is thoughtful and may be useful as a design heuristic, even if the unification claim needs scope revision. The paper is also notable for flagging its own limitations: Section 4.2 acknowledges simulators are not always reliable, and the Bayes net in Section 4.1 is explicitly admitted to be oversimplistic and not leading to uncertainty reduction. That kind of candor is rare. The soft spots are not minor. The central issue is not the simulator reliability, which is downstream; even with a perfect simulator, the objective is not an estimate of uncertainty about a true target unless Y is a sufficient statistic for that target. The abstract overclaims 'enablement' without empirical demonstration, and there are notational slips (Eq. 10 uses E_{P(C)} while Section 3.3.1 writes H[P(Y|x,C)] without an expectation). These are fixable, but the scope claim has to change. Who is this for? Researchers thinking about uncertainty decomposition and active clarification in LLMs. Practitioners will not find actionable tools, as there are no experiments. It deserves a serious referee, but the unification claim needs to be either scoped down to 'output sensitivity' or explicitly bridged to a true target by adding an assumption about the relationship between Y and the user intention. I would send it to review, with a request to address the target-of-inference issue.","headline":"A clean and honest position paper that mislabels output sensitivity as reducible epistemic uncertainty; worth reviewing but needs a major scope fix.","tokens_in":797,"tokens_out":1899,"would_cite":false,"duration_ms":49364,"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":"Bayesian Modeling of Experiments, applied to auxiliary context, can turn LLM uncertainty from a reason to abstain into an actionable signal for clarification, retrieval, and prompt refinement.","keywords":["Bayesian Modeling of Experiments","epistemic uncertainty","LLM reliability","expected information gain","clarification","prompt engineering","in-context learning","uncertainty decomposition"],"falsifier":"Fix a set of ambiguous user requests, compute the BME score $I[Y;C|X]$ using the LLM's own sampled clarifications, then collect human clarifications and measure the actual reduction in response entropy or error rate for each request. If the ordering of requests by predicted information gain does not match the ordering by actual improvement—say, a near-zero rank correlation—then the framework's central promise that this quantity identifies reducible uncertainty fails.","tokens_in":23916,"feed_emoji":"❓","tokens_out":5991,"duration_ms":63437,"temperature":0.7,"pith_summary":"This position paper argues that the usual practice of treating LLM uncertainty as a total score and rejecting uncertain outputs misses what is actually reducible. It proposes Bayesian Modeling of Experiments (BME) as a framework in which epistemic uncertainty is, by definition, uncertainty that can be reduced by running an experiment—here, providing a clarification, a different prompt template, or a set of in-context examples. Under this view, the paper claims, several existing heuristics for improving LLM outputs are the same quantity: expected information gain, measured as a drop in predictive entropy. A sympathetic reader would care because, if true, building reliable LLM systems becomes a matter of choosing which experiment to run, not just when to stay silent.","feed_headline":"Bayesian framework turns LLM uncertainty into questions worth asking","feed_subtitle":"The paper argues that clarifications, prompt templates, and few-shot examples all reduce the same expected-information-gain quantity.","key_machinery":"The central object is Bayesian Modeling of Experiments (BME), the classical scheme in which an experiment is a random variable $\\Lambda$, prior knowledge is a distribution over a quantity of interest $\\Xi$, and the value of an experiment is its expected information gain, $H[P(\\Xi)] - \\mathbb{E}_{P(\\Lambda)} H[P(\\Xi|\\lambda)]$, which equals the mutual information $I[\\Xi;\\Lambda]$ and the KL divergence between joint and product distributions. In the LLM setting the paper applies this with the predictive distribution $P(Y|X)$ as the quantity of interest and auxiliary context $C$ as the experiment stimulus, giving $I[Y|X;C] = H[P(Y|X)] - \\mathbb{E}_{P(C|X)} H[P(Y|X,C)]$. The framework does the work of separating reducible from effectively irreducible uncertainty: what counts as reducible depends on which experiment apparatus is available, and the same entropy-difference identity makes clarification, template choice, and in-context demonstrations instances of one mechanism.","core_discovery":"The paper's central claim is that epistemic uncertainty in LLMs should be extended beyond uncertainty about model parameters to any uncertainty reducible by an experiment, and that the Bayesian Modeling of Experiments framework supplies the right quantity for this: the mutual information $I[Y|X;C] = H[P(Y|X)] - \\mathbb{E}_{P(C|X)} H[P(Y|X,C)]$, where $C$ is auxiliary context such as a clarifying question, prompt template, or in-context example. It asserts this quantity unifies the otherwise ad hoc treatments of uncertainty in clarification ensembling, prompt selection, and few-shot demonstration selection, and that it resolves apparent contradictions in prior work where reducible uncertainty was mislabeled as aleatoric. The paper further claims BME supports joint management of multiple uncertainty sources and yields a lower bound on effectively irreducible uncertainty, which can justify conservative abstention when the bound is high.","pith_inferences":["The paper leaves implicit a cost-aware version: when clarification, web retrieval, and re-prompting have different costs, the rational policy is to run the experiment with the highest expected information gain per unit cost, not merely the highest gain.","A natural test is to rank ambiguous prompts by predicted $I[Y;C|X]$ and check whether human-issued clarifications improve response accuracy in that order; the paper motivates but does not run such a validation.","The effective-aleatoric lower bound could plug directly into risk-controlled abstention rules, giving a principled middle ground between passive rejection and active clarification.","For LLM agents, the same identity suggests a general operating principle: treat tool calls and environment queries as experiments and choose actions that maximize expected reduction in the agent's predictive entropy about the task."],"forward_implications":["If BME is right, uncertainty estimates should be reported per source—ambiguity, template, demonstrations—rather than as one total score.","Clarification systems can stop approximating ambiguity heuristically and instead pick the question with maximum expected information gain.","Prompt engineering and in-context example selection become optimization of the same mutual-information objective, allowing shared methods across tasks.","The distinction between epistemic and aleatoric uncertainty becomes relative to the available experiments, yielding an 'effective aleatoric uncertainty' bound that can govern when to abstain.","LLMs that can simulate clarifications can bypass arbitrary priors for sources inside their knowledge, making the framework applicable without hand-specified priors."],"supporting_citations":[{"why":"Supplies the original definition of expected information gain from an experiment.","marker":"Lindley, 1956"},{"why":"Extends the framework to sequential experiments and uncertainty reduction over time.","marker":"DeGroot, 1962"},{"why":"Provides the modern Bayesian experimental design reference from which the paper distinguishes BME.","marker":"Rainforth et al., 2024"},{"why":"Gives the mutual-information and data-processing identities used throughout the argument.","marker":"Cover and Thomas, 2012"},{"why":"Introduces the clarification uncertainty gap that the paper reinterprets as BME.","marker":"Zhang and Choi, 2023"},{"why":"Quantifies reducible uncertainty via input clarification ensembling, which BME subsumes.","marker":"Hou et al., 2024"},{"why":"Introduces mutual-information prompt selection, reinterpreted by the paper as template-induced reducible uncertainty.","marker":"Sorensen et al., 2022"},{"why":"Applies Bayesian experimental design to select clarifying questions, a direct predecessor of the proposed unification.","marker":"Kobalczyk et al., 2025"},{"why":"Studies uncertainty over in-context examples, which the paper recasts as demonstration-induced reducible uncertainty.","marker":"Ling et al., 2024"},{"why":"Introduces context-versus-prior information gain, which BME uses to detect shaky in-weight knowledge.","marker":"Du et al., 2024"}],"fun_headline_variants":["Bayesian modeling unifies LLM uncertainty management","LLM uncertainty: ask, retrieve, refine with expected gain","One information-theoretic rule for all LLM uncertainty","Extend epistemic uncertainty beyond parameters for reliable LLMs","From passive rejection to active resolution of LLM uncertainty"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The framework's useful outputs depend on the LLM being a reliable simulator of the alternative contexts and responses it has not actually observed, so that the information-gain estimates reflect real rather than imagined improvements; the paper itself notes such simulators are not always available or reliable.","fun_headline_variants_meta":{"raw":{"variants":["Bayesian modeling unifies LLM uncertainty management","LLM uncertainty: ask, retrieve, refine with expected gain","One information-theoretic rule for all LLM uncertainty","Extend epistemic uncertainty beyond parameters for reliable LLMs","From passive rejection to active resolution of LLM uncertainty"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000215,"raw_usage":{"total_tokens":1394,"prompt_tokens":875,"completion_tokens":519,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":491,"completion_tokens_details":{"reasoning_tokens":442}},"tokens_in":491,"tokens_out":519,"duration_ms":5792,"temperature":1.0,"reasoning_tokens":442,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T05:33:19.485789+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fix a set of ambiguous user requests, compute the BME score $I[Y;C|X]$ using the LLM's own sampled clarifications, then collect human clarifications and measure the actual reduction in response entropy or error rate for each request. If the ordering of requests by predicted information gain does not match the ordering by actual improvement—say, a near-zero rank correlation—then the framework's central promise that this quantity identifies reducible uncertainty fails.","supporting_citations":[],"review_version":1}