{"id":"2ca9fcfe-fb8f-46c5-86a8-17b39baa2d7b","arxiv_id":"2506.10268","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Large language models can behave deterministically at standard settings, so iterated-learning priors may be artifacts, and varying the starting point can reveal which models are truly sampling.","lead":"The paper argues that some language models make near-deterministic decisions, such as always predicting the most likely number, even when the model is set to sample with randomness. This matters because a popular method for reading a model's hidden beliefs may instead be measuring an artifact of these deterministic choices.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The initial-condition diagnostic is not validated against known stochastic processes: finite-chain dependence can masquerade as determinism, and Section 6's sufficiency claim does not establish non-stochasticity.","rationale":"The theoretical MLE false-prior construction in Section 3.1 is internally coherent, and the observation that a deterministic MLE rule can produce a spurious bimodal prior is valuable. The load-bearing weakness is not the algebra but the proposed diagnostic: the paper's headline experiment depends on classifying each model's decision pattern by whether empirical stationary distributions vary with Ω0. That classification is only as good as the assumption that a stochastic process cannot produce such variation in finite samples. The paper neither proves nor tests this assumption, and Section 6's sufficiency claim only rescues the weaker statement 'initial dependence implies not Gibbs-sampling,' which does not imply deterministic. The reader identified the same gap (finite chains, multimodality, slow mixing), and the missing stochastic baseline experiment is the natural next step. Because the paper's central contribution is conditional on this unvalidated premise, the CONDITIONAL verdict is appropriate; my analysis does not move it.","tokens_in":10035,"tokens_out":6266,"duration_ms":80936,"concrete_test":"Run a synthetic Gibbs-sampler control: choose a known bimodal posterior (e.g., Beta(0.1,0.1) prior with Binomial likelihood), N=10, and the same chain length and number of seeds as in the paper; apply the Section 3.2 test across Ω0 ∈ {0,...,10}. If a true stochastic sampler is flagged as deterministic in a substantial fraction of repeated runs (e.g., by a chi-square or KS test on the empirical θ-distributions), the diagnostic has an unacceptable false-positive rate. Also run a deterministic constant-output rule (always predict 50 heads); if it is classified as stochastic, the converse failure is confirmed. Reporting these two baselines would settle whether the diagnostic distinguishes stochastic from deterministic decision patterns at all.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.2's criterion assumes that a genuine stochastic Gibbs sampler has a stationary distribution invariant to the initial value ω0. That is an asymptotic property of an irreducible, aperiodic finite chain; it does not hold for the finite chains used in the experiments (N=10, no reported burn-in or convergence diagnostics), for multimodal targets, or under slow mixing. A stochastic process can therefore produce the very pattern the paper labels deterministic: empirical distributions that vary with Ω0. The paper provides no baseline on a known stochastic process to quantify this false-positive rate, and no code. Section 6 claims the approach is a sufficient condition to detect non-Gibbs-sampling processes; even if true, non-Gibbs is not the same as non-stochastic, so the leap to 'non-stochastic decision processes' is unsupported. Conversely, Section 3.2 concedes that some deterministic processes converge to the same distribution across initial values, so initial invariance is not sufficient evidence of stochasticity. The empirical classifications (e.g., gpt-4o-mini as deterministic in CoinFlip) therefore rest on an unvalidated premise.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper revisits the question of whether LLMs make stochastic decisions during iterated-learning prior elicitation. It analyzes a deterministic MLE decision rule for a coin-flip proportion-estimation task, derives the stationary distribution of the induced Markov chain (Eq. 4), and shows that this distribution is bimodal and depends on the initial value. It then proposes that varying the initial value ω0 can distinguish deterministic from stochastic decision processes, reports experiments on six LLMs, and concludes that some models (notably gpt-4o-mini) behave as MLE decision makers while others behave stochastically. The theoretical derivation in Section 3.1 is mathematically correct, but the proposed diagnostic and the empirical support have substantial gaps, and the final limitation section overclaims the method's sufficiency.","tokens_in":10268,"tokens_out":6439,"duration_ms":80802,"significance":"The paper's main strength is the clean martingale derivation in Section 3.1: the MLE decision rule combined with binomial resampling yields a Markov chain whose absorption probabilities are given exactly by Eq. (4), producing a bimodal 'false prior' that can mimic Bayesian prior-elicitation results. This is a credible, concrete challenge to prior work that infers LLM priors from iterated in-context learning, and the paper explicitly identifies a failure mode that should be taken seriously. If the empirical classification were validated, the paper would be a useful cautionary result for the behavioral ML community. However, the significance is currently conditional: the diagnostic used to classify models is not validated against known stochastic processes, the experimental evidence is largely qualitative, and the manuscript does not provide code or full experimental protocol. The paper deserves credit for stating its limitations explicitly, but the limitation section's claim of 'universal applicability' and sufficiency is not established.","major_comments":[{"comment":"The proposed initial-condition test is not a valid discriminator between stochastic and deterministic decision processes as stated. Invariance of the stationary distribution to the initial value is an asymptotic property of an irreducible, aperiodic finite chain; for the finite chains used in the experiments (N=10, no convergence diagnostics or burn-in reported), a stochastic Gibbs sampler can exhibit initial-value dependence due to slow mixing or multimodality. Conversely, Section 3.2 concedes that some deterministic processes converge to the same distribution across initial values, and this caveat is dismissed only by an appeal to 'empirical evidence' without reporting a test. The manuscript needs a positive control on a known stochastic process to measure the false-positive rate before any model can be classified as deterministic on the basis of this test.","section":"3.2, 6"},{"comment":"The empirical classifications are made by visual inspection. The manuscript does not report the number of chains, iterations per chain, burn-in, repeated seeds, or any quantitative comparison of the empirical distributions across initial ω0. For example, the claim that claude-3-haiku, claude-3-5-sonnet and LLaMA-3.1-70B-Instruct produce 'consistent distributions regardless of the initial values' is not backed by a test statistic, divergence measure, or error bars. Without this, the main empirical contrast between deterministic and stochastic models is not established, and the paper is not reproducible.","section":"4.2, Figures 1-3"},{"comment":"The final limitation section claims that 'our proposed identification approach is a sufficient condition to detect non-Gibbs-sampling processes, which further indicates non-stochastic decision processes.' This is a non sequitur: observing initial-value dependence can indicate non-convergence or non-stationarity of a stochastic process, not necessarily non-stochasticity. In addition, non-Gibbs is not equivalent to non-stochastic, because many stochastic decision rules are not Gibbs samplers. This claim should be either removed or proved under explicit assumptions about the chain and the number of iterations.","section":"6"},{"comment":"The evidence that gpt-4o-mini is an MLE decision maker rests on 'the black dotted line ... which we fit featuring p(θ=1|Ω0) with respect to Ω0' coinciding with Eq. (4). It is unclear what was fitted: if the line is the theoretical curve from Eq. (4), it has no free parameters and the word 'fit' is misleading; if it is a fitted line, the fitted parameters and goodness of fit should be reported. Relatedly, the interpretation of gpt-4o and Gemma-2-2b-it as 'near-deterministic, except under certain conditions' is presented without a testable model or statistical comparison to an alternative stochastic prior.","section":"4.2, Eq. (4)"}],"minor_comments":[{"comment":"The displayed computation of E[ω_i] is difficult to read; it should be written cleanly as E[ω_i] = E[E[ω_i | ω_{i-1}]] = E[ω_{i-1}].","section":"3.1, Eq. (2)"},{"comment":"The paper uses 'stationary distribution' to describe the empirical distribution of finite simulation runs; please distinguish the asymptotic stationary distribution from the empirical distribution over the finite number of iterations actually run.","section":"4.2"},{"comment":"The figure captions appear garbled (the text contains unicode token sequences such as '/uni00000013/...') and do not explain the axes, plotted curves, or the dotted line; the figures are consequently not interpretable from the captions.","section":"Figures 1-3"},{"comment":"The experimental protocol is underspecified: please report the number of chains per initial value, the number of iterations per chain, any burn-in, temperature and decoding parameters, and how the 'single value' response was extracted from each model.","section":"4.1"},{"comment":"The LifeExpectancy MLE comparison (Li = Ai-1) is degenerate and thus not a strong baseline; a sentence explaining why this is still informative would help the reader interpret the stochasticity claim.","section":"4.2, LifeExpectancy"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is currently closer to a workshop contribution than a full journal article: the theoretical example is neat, but the empirical section needs substantial methodological additions. If the authors can add a positive control on a known stochastic process, quantitative convergence diagnostics, and statistical comparisons across initial conditions, the paper could become a solid contribution. The current overclaim in Section 6 should also be corrected."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know up front. The theoretical derivation in §3.1 is correct and genuinely new: for a chain where an MLE decision rule produces θ_i = ω_{i-1}/N and then ω_i ~ Binomial(N, θ_i), the stationary distribution is supported only at 0 and N, with probabilities determined by E[ω_0]/N. That is a clean result and a credible mechanism for the bimodal 'priors' reported in the iterated-learning literature. Second, the paper's proposed diagnostic—vary the initial ω_0 and check whether the empirical distribution shifts—is sensible in the limit but is not validated anywhere in the paper.\n\nThe soft spots are real and proportionate to the paper's claims. The diagnostic assumes that any genuine stochastic Gibbs sampler yields initial-invariant stationary distributions. That is an asymptotic property of an irreducible, aperiodic chain; it fails for finite chains with slow mixing, for multimodal targets, and in practice with N=10 and no convergence diagnostics. The paper provides no baseline on a known stochastic process, so the false-positive rate of the test is unknown. There is also no code and no error bars, and only one model (gpt-4o-mini) matches the MLE prediction; the other models' classifications are eyeballed from figures rather than tested against a stochastic null.\n\nSection 6 overstates the conclusion. It claims the approach is a 'sufficient condition to detect non-Gibbs-sampling processes, which further indicates non-stochastic decision processes.' Even if a process is not this particular Gibbs sampler, that doesn't make it deterministic. The limitation section also says only two tasks were tested, then asserts universal applicability. That should be removed or rewritten.\n\nWhat the paper does well is give a concrete, falsifiable mechanism and a plausible way to test for it. That earns a serious referee. But a referee should demand a validation experiment on a known stochastic process, including slow-mixing and multimodal cases, and a proper quantitative comparison of empirical distributions across initial conditions. With that, the paper could be a useful caution for the prior-elicitation literature. As it stands, the central claim is under-supported.\n\nI'd send it to review, but I'd expect major revision. Worth a reading group slot if you want to argue about what counts as evidence for stochasticity in LLMs.","headline":"The §3.1 MLE chain analysis is correct and new, but the initial-condition diagnostic is unvalidated and the experimental support is thin; send to review conditionally.","tokens_in":10754,"tokens_out":3056,"would_cite":true,"duration_ms":37130,"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":"The paper claims that under some conditions, large language models make near-deterministic maximum-likelihood decisions despite nonzero sampling temperature, so simulated Gibbs sampling can converge to a false prior rather than the…","keywords":["language model priors","iterated learning","Gibbs sampling","maximum likelihood estimation","deterministic decision-making","stochastic decision-making","prior elicitation","Markov chain"],"falsifier":"Run the proposed initial-value test on a controlled stochastic baseline, for instance a synthetic Gibbs sampler targeting a known bimodal distribution, or a language model whose responses are verified to vary across repeated identical prompts at temperature 1.0. If a genuinely stochastic process nevertheless shows starting-value-dependent stationary distributions (due to finite chains, slow mixing, or multi-modality), the diagnostic would misclassify it as deterministic; conversely, if a model flagged as deterministic produces multiple distinct estimates on repeated identical prompts, the deterministic label is wrong.","tokens_in":9791,"feed_emoji":"🪙","tokens_out":6281,"duration_ms":62387,"temperature":0.7,"pith_summary":"Large language models are usually treated as stochastic samplers over token distributions, and prior work has used simulated Gibbs sampling to infer their priors on quantities like coin bias. This paper argues that this treatment can be wrong: under certain conditions, models make near-deterministic decisions that match maximum likelihood estimation (MLE), even when the sampling temperature is nonzero. If so, an iterated-learning chain based on such a model does not converge to a prior at all; it converges to a polarization artifact, which can look like a reasonable bimodal prior. The paper derives the stationary distribution of an MLE-driven chain, proposes a simple diagnostic that varies the initial value of the chain, and shows experimentally that some large language models behave deterministically on a coin-bias task while behaving stochastically on a life-expectancy task. The practical stake is that prior-elicitation results from this line of work may be artifacts of the procedure rather than genuine model beliefs.","feed_headline":"LLMs sometimes fake Bayesian priors with deterministic answers","feed_subtitle":"A new initial-value test shows some models converge to maximum-likelihood guesses that look like real beliefs.","key_machinery":"The central object is the Markov chain formed by alternating a model's point estimate with an observation step: in the coin task, the model outputs $\\Omega_i$, the chain updates $\\omega_i \\sim \\mathrm{Binomial}(N, \\omega_{i-1}/N)$, and the estimated bias is $\\theta_i = \\omega_{i-1}/N$. Under an MLE decision rule this chain is absorbed at $0$ or $N$, with the stationary weight at $N$ equal to the expected initial count divided by $N$; this formula is what lets a deterministic process produce an apparent bimodal prior. The paper's diagnostic machinery is the invariance principle: the stationary distribution of a well-mixed stochastic Gibbs sampler is the same for different starting values $\\omega_0$, so comparing stationary distributions across initial values separates stochastic from deterministic decision patterns.","core_discovery":"On the paper's own terms, the central discovery is that deterministic decision-making can masquerade as Bayesian sampling in iterated-learning protocols. For the proportion-estimation task, if a language model replaces posterior sampling with the MLE rule $\\theta_i = \\omega_{i-1}/N$, the induced Markov chain $\\omega_i \\sim \\mathrm{Binomial}(N, \\omega_{i-1}/N)$ has absorbing states at $\\omega = 0$ and $\\omega = N$, and its stationary distribution satisfies $\\hat{p}_{\\mathrm{MLE}}(0) = 1 - \\mathbb{E}[\\omega_0]/N$ and $\\hat{p}_{\\mathrm{MLE}}(N) = \\mathbb{E}[\\omega_0]/N$, concentrated on the extremes. Because this reproduces the bimodal coin-bias prior reported by prior work, the paper argues that the reported prior may be an artifact of deterministic MLE-style behavior rather than evidence of a genuine bimodal belief. The paper's proposed distinction is that a genuine stochastic Gibbs sampler has a stationary distribution invariant to the initial value $\\omega_0$, whereas deterministic processes can show dependence on it; experiments that vary $\\omega_0$ across models and tasks reveal both patterns.","pith_inferences":["One extension the paper does not develop: the same initial-value test could diagnose deterministic behavior in other Markov-chain-with-LLM protocols, such as chain-of-thought or MCMC-based mental-representation recovery, whenever the stationary distribution would be initialization-dependent.","Because the paper tests each model with a single temperature of 1.0, a natural next experiment is to sweep temperature and seed; if deterministic patterns persist at high temperature, that would strengthen the claim that temperature alone does not restore stochastic decision-making.","A calibration baseline using a known stochastic Gibbs sampler (for example, a synthetic posterior with a symmetric bimodal target) would quantify how often the test mislabels slow-mixing chains as deterministic; the paper does not provide that baseline.","The deterministic classification could be checked directly by inspecting repeated responses or logprob distributions on identical prompts, which would offer a complementary within-chain test rather than a between-chain test."],"forward_implications":["Prior-elicitation studies that use simulated Gibbs sampling on large language models should treat reported priors as provisional until they check whether the chain's stationary distribution depends on initialization.","A deterministic MLE-style model can produce the same extreme, bimodal-looking output as a supposedly Bayesian model, so observing a bimodal distribution is not evidence for a bimodal prior.","Models can switch decision patterns by task: the paper finds deterministic behavior in coin-bias estimation and stochastic behavior in life-expectancy estimation, so a single 'stochastic vs deterministic' label for a model is too coarse.","The proposed initial-value test is a sufficient condition for detecting non-Gibbs processes: if distributions diverge across starting values, the process is not posterior Gibbs sampling.","Behavioral conclusions about language model priors drawn from iterated learning should be re-examined, because the apparent prior may instead reflect the iterative prompting dynamics."],"supporting_citations":[{"why":"It supplies the iterated in-context learning protocol and the bimodal proportion-estimation result that this paper reinterprets.","marker":"[18]"},{"why":"It defines Gibbs sampling, the stochastic process whose convergence properties ground the invariance diagnostic.","marker":"[6]"},{"why":"It provides the human iterated-learning result with a bimodal prior that prior work compared against and that MLE can mimic.","marker":"[13]"},{"why":"It shows the same iterated-learning and MCMC approach applied to recovering mental representations, extending the class of results at stake.","marker":"[19]"}],"fun_headline_variants":["LLMs may fake Bayesian priors with deterministic outputs","Deterministic LLM decisions can masquerade as Bayesian sampling","False priors: when LLMs choose MLE over sampling","Initial-value test exposes deterministic LLM patterns","Bimodal 'Bayesian' priors in LLMs may be deterministic artifacts"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The diagnostic relies on the premise that a genuinely stochastic Gibbs-sampling process always yields a stationary distribution that is independent of the starting value, so any observed dependence on the starting value can only mean deterministic behavior.","fun_headline_variants_meta":{"raw":{"variants":["LLMs may fake Bayesian priors with deterministic outputs","Deterministic LLM decisions can masquerade as Bayesian sampling","False priors: when LLMs choose MLE over sampling","Initial-value test exposes deterministic LLM patterns","Bimodal 'Bayesian' priors in LLMs may be deterministic artifacts"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000971,"raw_usage":{"total_tokens":4163,"prompt_tokens":1016,"completion_tokens":3147,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":632,"completion_tokens_details":{"reasoning_tokens":3062}},"tokens_in":632,"tokens_out":3147,"duration_ms":27806,"temperature":1.0,"reasoning_tokens":3062,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T04:30:18.067914+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the proposed initial-value test on a controlled stochastic baseline, for instance a synthetic Gibbs sampler targeting a known bimodal distribution, or a language model whose responses are verified to vary across repeated identical prompts at temperature 1.0. If a genuinely stochastic process nevertheless shows starting-value-dependent stationary distributions (due to finite chains, slow mixing, or multi-modality), the diagnostic would misclassify it as deterministic; conversely, if a model flagged as deterministic produces multiple distinct estimates on repeated identical prompts, the deterministic label is wrong.","supporting_citations":[{"cited_title":"Stochastic relaxation, gibbs distributions, and the bayesian restoration of images.IEEE Trans","cited_arxiv_id":null,"evidence_quote":"It defines Gibbs sampling, the stochastic process whose convergence properties ground the invariance diagnostic."},{"cited_title":"The evolution of frequency distributions: Relating regularization to inductive biases through iterated learning.Cognition, 111(3):317–328, 2009","cited_arxiv_id":null,"evidence_quote":"It provides the human iterated-learning result with a bimodal prior that prior work compared against and that MLE can mimic."},{"cited_title":"Recovering Mental Representations from Large Language Models with Markov Chain Monte Carlo","cited_arxiv_id":"2401.16657","evidence_quote":"It shows the same iterated-learning and MCMC approach applied to recovering mental representations, extending the class of results at stake."}],"review_version":1}