{"id":"302dfb35-482c-46e0-adbf-c936692503df","arxiv_id":"2412.06033","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The paper introduces a p-value computed by resampling datasets from a conditional generative model's predictive distribution, and shows it can flag tasks the model cannot solve in-context.","lead":"Researchers propose a statistical test, the generative predictive p-value, that uses only a generative model's own generated examples and response probabilities to tell whether the model can reliably solve a given in-context learning task. It extends classic Bayesian posterior predictive checks to black-box models such as large language models, with experiments on tabular, image, and language tasks.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central theorem assumes the CGM's predictive distribution is exchangeable; for LLMs this is false, and the paper's 'abuse of notation' does not bridge the gap. The finite-N estimator has no error control, so the practical claim rests on an untested premise.","rationale":"Reader's weakest_assumption is correct: the theorem is only defined relative to an exchangeable model. I considered whether the uncontrolled finite-N error is the more critical gap, but that is secondary: even with a perfect infinite-N oracle, the equality would not apply to a non-exchangeable LLM, and the finite truncation is explicitly acknowledged. The empirical evaluations are real and suggestive, but they cannot validate the theoretical claim because the ground-truth 'capability' labels are task-level and the p-values are computed under the very assumption in question. The paper should be conditional: require either a permutation-invariance test for the deployed CGMs, or a restatement of the contribution as a heuristic with no Bayesian guarantee.","tokens_in":19036,"tokens_out":12565,"duration_ms":120401,"concrete_test":"Check exchangeability directly: take 100 pairs of in-context examples from SST2 and MQP, and for each pair compute log pθ(x_1,x_2) and log pθ(x_2,x_1) under Llama-2 7B with the same prompt format and tokenization. If the absolute log-probability difference exceeds 0.1 nats for more than 5% of pairs, pθ is not exchangeable and the de Finetti step in Section 3 fails. Then recompute pgpc (Algorithm 1) on these tasks after randomly permuting the n in-context examples; if the estimated p-value crosses α=0.05, the method's output is not permutation-invariant.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing premise is exchangeability of the CGM's predictive distribution. Theorem 1 (Section 6.1; proof in Appendix C) and Lemma 3 require a latent explanation F with X_i i.i.d. given F; this representation exists only if pθ(x) is exchangeable (de Finetti). Section 3 asserts 'if pθ(x) approximates an exchangeable distribution p(x), as is the case with ICL problems' with no evidence for LLMs. For transformer LMs, pθ(x) is not permutation invariant: changing the order of in-context examples changes next-token probabilities, and even the marginal probability of a set of examples depends on its ordering. Hence Condition 3 (identifiability) has no well-defined f, and the equality pppc = pmpc has no Bayesian target for the actual CGM. The 'convenient abuse of notation' is doing load-bearing work. Separately, pgpc (Eq. 3) truncates x∞ to finite x_N with no error bound (Section 6.2: 'formal analysis ... left to future work'), and the LLM experiments use only N−n=10 generated examples; without a bound, empirical success is not explained by Theorem 1.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper addresses the problem of deciding when a conditional generative model (CGM) can solve an in-context learning (ICL) problem. It assumes a Bayesian interpretation of ICL in which the CGM's predictive distribution pθ(x | xn) is the posterior predictive of some latent-variable model pθ(x, f). The main theoretical result (Theorem 1, proved in Appendix C via Doob's theorem) states that, under measurability and identifiability conditions (Conditions 1-3) and an integrability condition, the posterior predictive p-value pppc (Eq. 1) equals a martingale predictive p-value pmpc (Eq. 2) that depends on an infinite dataset x∞ rather than on the latent explanation f. The paper then introduces the generative predictive p-value pgpc (Eq. 3), which truncates x∞ to a finite completion x_N, gives Algorithm 1 to estimate it, and evaluates it as a capability predictor on tabular, natural-language, and imaging ICL tasks with Llama-2 and Gemma-2. The central practical claim is that pgpc, computed only from CGM predictive samples and log-probabilities, accurately predicts whether the model can solve the ICL problem.","tokens_in":19306,"tokens_out":10931,"duration_ms":92629,"significance":"The elegance of the proposal is that it reduces Bayesian model criticism for black-box CGMs to operations that are available in practice: ancestral sampling from pθ and scoring with log-probabilities. The proof of Theorem 1 via Doob's martingale theorem is a clean extension of the martingale posterior literature (Fong et al., 2023; Lee et al., 2023; Falck et al., 2024), and the paper is honest about the finite-N gap in Section 6.2. If the exchangeability premise were established for the target CGMs, the method would be a useful diagnostic for assessing ICL suitability. However, the current manuscript does not establish that premise, does not quantify the finite-N error, and does not connect pgpc to the formal capability definition in Section B; the empirical evidence, while suggestive, is not yet strong enough to support the broad 'can it solve your ICL problem' claim.","major_comments":[{"comment":"The equality pppc = pmpc is proved for a Bayesian model (F, X1, X2, ...) with X_i conditionally i.i.d. given F. By de Finetti's theorem, such a representation exists only if the joint distribution of every finite collection of observations is exchangeable. For pretrained LLMs, pθ is not permutation invariant: changing the order of in-context examples changes next-token probabilities, and the joint probability of a set of examples is order-dependent. The paper's assertion in Section 3 that one can treat pθ(x, f) as 'a convenient abuse of notation' when pθ(x) approximates an exchangeable distribution is unsupported with respect to ICL; no evidence is given that transformer LMs have approximately exchangeable predictive distributions in the ICL settings of Section 7. Consequently, the latent explanation f in Condition 3 may not exist for the actual CGM, and the equality pppc = pmpc has no well-defined Bayesian target. This is load-bearing because it is the theoretical justification for interpreting pgpc as a posterior predictive check.","section":"Section 3 and Theorem 1"},{"comment":"pgpc truncates the infinite dataset x∞ to a finite completion x_N, but no bound or rate is given for |pgpc - pppc|; the paper explicitly states in Section 6.2 that a formal analysis of this error is left to future work. The practical estimator also has Monte Carlo error from M replicates, and in the natural-language experiments N - n = 10 and M = 20. Without an error analysis, the empirical agreement in Figures 8 and 9 cannot be attributed to Theorem 1; the finite-N truncation is particularly delicate because Algorithm 1 generates completions sequentially from pθ(z, y | x_N), and this sequential procedure may not converge to the exchangeable posterior predictive at practical values of N when the model is not exchangeable.","section":"Section 6.2, Eq. (3), Algorithm 1"},{"comment":"The paper defines model capability through Eq. (5) but never establishes a formal relationship between pgpc and this definition. The empirical ground truth in Section 7 is based on the model's own ICL error rate (Figure 4), so the reported 'accurate predictor' results measure correlation between two model-derived quantities. A low posterior predictive p-value indicates that the holdout data are surprising under the model's predictive distribution; it does not by itself imply that the model fails Definition 1. To support the central claim, the authors should either prove (or precisely state conditions under which) small pgpc implies low capability, or validate against an independent, non-model-derived capability measure with appropriate baselines.","section":"Section B and Section 7"},{"comment":"The natural-language and imaging evaluations contain only two in-capability and two out-of-capability tasks per model, and the reported precision, recall, F1, and accuracy curves are presented without error bars or confidence intervals. With such a small number of tasks, the curves in Figures 8 and 9 may be driven by task-specific effects; no baseline (e.g., random guessing or thresholding a simple model-confidence score) is reported. This weakens the empirical claim that pgpc accurately predicts model capability and should be addressed with more tasks, repeated subsampling, or at least a bootstrap analysis.","section":"Section 7.1, Figures 8 and 9"}],"minor_comments":[{"comment":"The symbol θ is used both for the CGM and for the Bayesian model; using distinct notation (e.g., θ for the CGM and M for the Bayesian model) would reduce confusion.","section":"Sections 2-3"},{"comment":"The notation gθ(x, ·) is overloaded; the text does not specify which discrepancy function (NLML or NLL) is being used in the generic definition of pppc.","section":"Section 5, Eq. (1)"},{"comment":"There is a typo: 'nuber' should be 'number' in the description of Algorithm 2.","section":"Appendix D"},{"comment":"The caption says 'Transformer models (pink)' but the figure appears to show fitted Bayesian linear and polynomial models; the caption should be made consistent with the figure contents.","section":"Figure 2 caption"},{"comment":"Gemma-2 9B results are reported only in an appendix; a one- or two-sentence summary in Section 7 would help readers understand the qualitative difference from Llama-2 7B without consulting the appendix.","section":"Appendix H"}],"recommendation":"major_revision","confidential_remarks":"The manuscript fits the journal's scope and builds on a credible line of work. The main risk is that the theoretical theorem is presented as applying to LLMs when the exchangeability condition is not established; I would encourage the editor to require the authors to either prove approximate exchangeability for an ICL-relevant class of models, or explicitly frame the method as a heuristic with finite-N and exchangeability caveats, and strengthen the empirical evaluation. I do not see a fundamental error requiring rejection, but the current version overclaims relative to its assumptions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a useful practical estimator with a clean theoretical core, but the theory's scope is narrower than the paper's claims, because the exchangeability assumption is untested for LLMs and the finite-N approximation has no error analysis.\n\nWhat's actually new: the generative predictive p-value (Algorithm 1) is a concrete way to do posterior predictive checks on black-box CGMs by sampling dataset completions instead of explanations. That's new relative to the cited prior work, which establishes the martingale-posterior machinery but doesn't give this specific estimator or the ICL application. Theorem 1 is a correct-looking application of Doob's theorem; the proof follows the standard martingale-posterior argument, and the paper is honest that the formulation aligns with Fong et al., Lee et al., and Falck et al. The empirical work is reasonable: the interpolation between NLML and NLL p-values in Section 7.3 is a nice sanity check, and the tabular/language/imaging examples give some evidence that the method can flag out-of-capability tasks.\n\nSoft spots, in order of importance. First, the exchangeability assumption in Section 3 is load-bearing: Theorem 1 needs a latent explanation F with i.i.d. data given F, which de Finetti only guarantees if pθ(x) is exchangeable. For transformer LMs this is false, and the paper's 'if pθ(x) approximates an exchangeable distribution p(x), as is the case with ICL problems' is asserted without evidence. The 'abuse of notation' is doing real work; the equality pppc=pmpc is not established for the actual CGM on real prompts. This doesn't mean the method fails, but it does mean the theory doesn't cover the main application. Second, the finite-N clipping in Equation 3 has no error bound, and Section 6.2 says so explicitly. With N-n=10 for the LLM experiments, the empirical success isn't explained by the asymptotics. Third, the experiments lack error bars and baselines; the ground truth is the model's own accuracy, which is fine but a bit circular. These are genuine gaps, but they're not fatal if scoped as practical heuristics. The self-citation is heavy but to relevant prior work.\n\nWho should read this: anyone building deferral or model-selection systems for LLMs, and people working on Bayesian model criticism for black-box models. It deserves a serious referee; I'd send it out, with the expectation that the authors either validate or relax the exchangeability condition and add the missing error analysis and baselines. My own verdict is a cautious conditional accept.","headline":"Useful practical estimator with a clean Doob core, but the exchangeability assumption is untested for LLMs and the finite-N error is unquantified.","tokens_in":19803,"tokens_out":2917,"would_cite":true,"duration_ms":26753,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62F15","62F03","60G42","62G10"],"pacs":[],"model":"deepseek-v4-flash","headline":"A p-value computed from a model's own generations can predict whether it can solve an in-context learning task.","keywords":["in-context learning","posterior predictive checks","generative predictive p-value","martingale predictive p-value","conditional generative models","Bayesian model criticism","Doob's theorem","model capability"],"falsifier":"Construct an ICL problem whose context order is known to change the answer distribution (violating exchangeability), fit an explicit Bayesian model to the same data, and compare the generative predictive p-value to the exact posterior predictive p-value; systematic divergence as $N$ grows would show the paper's equality does not hold for that CGM.","tokens_in":18870,"feed_emoji":"🎯","tokens_out":6036,"duration_ms":49905,"temperature":0.7,"pith_summary":"The paper aims to show that you can decide whether a generative model can solve an in-context learning (ICL) problem using only the model's own predictive outputs, without access to its internal likelihood or posterior. It proves that the standard posterior predictive p-value equals a martingale predictive p-value defined over infinitely many generated datasets, then introduces the generative predictive p-value, a finite-dataset approximation that any conditional generative model can estimate. The practical payoff is a statistical capability test: generate query-response completions from the model, score them under the model's log probability, and treat a small p-value as evidence the model is not appropriate for the problem. The paper verifies this test on synthetic tabular, natural-language, and imaging tasks with two large language models.","feed_headline":"P-value test flags when generative AI can't learn in context","feed_subtitle":"Proves the Bayesian check equals a martingale version using the model's own outputs, giving a practical capability test.","key_machinery":"The load-bearing object is Doob's theorem for estimators, applied through a martingale argument. It says that under identifiability, the posterior expectation of a function $h(F)$ converges almost surely to $h(F)$ as observations accumulate; this lets the discrepancy $g_\\theta(x, f)$, which depends on an unseen explanation $f$, be replaced by $g_\\theta(x, x_\\infty)$, which depends only on an infinite dataset and hence on the CGM's predictive distribution. The generative predictive p-value then replaces $x_\\infty$ by a finite completion $x_N$, sampled ancestrally from $p_\\theta(z, y \\mid x_n)$, so that the discrepancy can be evaluated from generated completions and response log probabilities.","core_discovery":"On the paper's own terms, the central discovery is Theorem 1: under standard regularity conditions (complete and separable spaces, a measurable family of likelihoods, identifiability, and an integrability condition), the posterior predictive p-value $p_{\\mathrm{ppc}}$ equals the martingale predictive p-value $p_{\\mathrm{mpc}}$, so posterior predictive checks can be carried out using only the predictive distribution $p_\\theta(x \\mid x_n)$. Since infinite completions are impossible, the paper defines the generative predictive p-value $p_{\\mathrm{gpc}}$ (Equation 3), which uses $N$ ancestrally sampled completions of the observed context as stand-ins for latent explanations. The paper argues that for large enough $N$ this approximates the posterior predictive p-value, with estimation error left to future formal analysis, and it demonstrates empirically that the resulting statistic separates in-capability from out-of-capability ICL tasks.","pith_inferences":["Because the equality theorem rests on exchangeability, the method is on firmest ground for models whose predictive distribution is permutation invariant; for pretrained LLMs this is a working approximation, and a task where order materially changes the answer is where the test would be expected to mislead.","The finite-$N$ gap between $p_{\\mathrm{gpc}}$ and $p_{\\mathrm{ppc}}$ is left unquantified; a practical diagnostic would be to compute the p-value at several $N$ values and check stability before trusting a low p-value.","The same statistic could be used for model selection among several CGMs on a fixed task, by comparing their generative predictive p-values rather than thresholding a single model."],"forward_implications":["Posterior predictive checks become available for any conditional generative model that can output next-token probabilities, including LLMs, without specifying likelihood or posterior.","The same p-value, under the negative log-likelihood discrepancy, also signals whether the number of in-context examples is sufficient: lower p-values correlate with higher response error.","Varying the number of generated completions $N-n$ interpolates the p-value between the NLML and the ideal NLL posterior predictive p-values, so the approximation can be tuned by computational budget.","Thresholding the generative predictive p-value at a significance level yields a binary predictor of model capability that is better than random on all tested synthetic tabular, LLM, and imaging ICL tasks.","The procedure needs only generated queries and responses plus their log probabilities, so it applies broadly to current black-box generative models."],"supporting_citations":[{"why":"Supplies the martingale theorem used to replace functions of latent explanations with functions of infinite observation sequences.","marker":"(Doob, 1949)"},{"why":"Provides the detailed proof of Doob's theorem that the paper invokes.","marker":"(Miller, 2018)"},{"why":"Gives de Finetti's theorem, the basis for representing an exchangeable predictive distribution with a latent explanation.","marker":"(Hewitt & Savage, 1955)"},{"why":"Introduces martingale posterior distributions and predictive resampling, the template for sampling dataset completions.","marker":"(Fong et al., 2023)"},{"why":"Defines holdout predictive checks, the posterior predictive p-value form the paper adapts.","marker":"(Moran et al., 2023)"},{"why":"Establishes posterior predictive checks, the model criticism framework being extended.","marker":"(Rubin, 1984)"},{"why":"Supplies the Llama-2 regression model used in tabular and imaging experiments and the definition of a $(1-\\epsilon)$-likely set used for capability.","marker":"(Jesson et al., 2024)"},{"why":"Provides the Bayesian interpretation of in-context learning that motivates treating CGMs as posterior predictive distributions.","marker":"(Xie et al., 2021)"},{"why":"Provides the Llama-2 architecture and release used for natural language and regression models.","marker":"(Touvron et al., 2023)"}],"fun_headline_variants":["P-value test using AI's own outputs checks ICL capability","Generative AI's in-context learning skill test via its own outputs","Martingale p-value uses model outputs to test ICL ability","Check if AI can learn in context using its own likelihoods","AI's own outputs judge its in-context learning skill"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes the conditional generative model's predictive distribution is exchangeable, or close enough to exchangeable that de Finetti's theorem supplies a latent explanation and Doob's martingale equality holds; the paper asserts this for ICL problems but does not test exchangeability for pretrained language models.","fun_headline_variants_meta":{"raw":{"variants":["P-value test using AI's own outputs checks ICL capability","Generative AI's in-context learning skill test via its own outputs","Martingale p-value uses model outputs to test ICL ability","Check if AI can learn in context using its own likelihoods","AI's own outputs judge its in-context learning skill"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001068,"raw_usage":{"total_tokens":4513,"prompt_tokens":1021,"completion_tokens":3492,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":637,"completion_tokens_details":{"reasoning_tokens":3405}},"tokens_in":637,"tokens_out":3492,"duration_ms":22032,"temperature":1.0,"reasoning_tokens":3405,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T20:04:57.194835+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Construct an ICL problem whose context order is known to change the answer distribution (violating exchangeability), fit an explicit Bayesian model to the same data, and compare the generative predictive p-value to the exact posterior predictive p-value; systematic divergence as $N$ grows would show the paper's equality does not hold for that CGM.","supporting_citations":[{"cited_title":"Holdout predictive checks for [b]ayesian model criticism","cited_arxiv_id":null,"evidence_quote":"Defines holdout predictive checks, the posterior predictive p-value form the paper adapts."}],"review_version":1}