Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Mathematical statistics — the theory of statistical inference read for itself — comparison and sufficiency of experiments (Blackwell, Le Cam deficiency), statistical decision theory, the sufficiency theorems (Fisher–Neyman, Basu, Bahadur) and bounds on estimation. Bayesian modelling is probabilistic-modeling (ADR-031).
11 of 371 QUESTION documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| QUESTION-027 v3 | Is there a relational signature of a communicative kind that is stable under admissible transformations, sufficient for a family of decisions and discriminating on designated contrasts, and can it be identified from the available probes, for decisions outside them, when the full latent model cannot? | The assistant’s “central construction problem” (A203 §36) joined to its question of sufficiency without full identification (A214 §7, A218 RQ3 and Part III). The exchange calls it the central unresolved problem twice. Its unrestricted form is answered by standard results, so it is filed narrowed: it has content only for decisions about unobserved probes, interventions and transported targets. As A203 states it, it is not well posed. | Open |
| QUESTION-112 v3 | How should the sufficiency of a retained state be judged when the family of future decisions can itself change in response to what the inquiry finds? | The owner asked at U10 to “double click” on A8’s closing question: when does justificatory history add value beyond a sufficient current state? A10 answered that, so posed, it never does (CLAIM-300). What is left is this question. Sufficiency is relative to a decision family, and inquiry changes its own family. | Open |
| QUESTION-163 | Do Blackwell-equivalent representations of trained networks carry different stitching penalties under the paper’s own protocol, by more than the spread across stitching seeds and top networks, or does an independent treatment relate stitching to the comparison of experiments? | The promotion condition formerly on THEORY-176, moved here unchanged when THEORY-176 was promoted on 2026-10-19. That Blackwell-equivalent representations can stitch differently is shown by a constructed example. Whether they do, by a measurable margin, in trained networks under the paper’s protocol is untested. | Open |
| QUESTION-168 | Does the ℓ₁ recovery transition of some non-Gaussian measurement ensemble provably converge to the Gaussian curve ρ(δ) as N → ∞, or do simulations an order of magnitude beyond N = 1600 keep the gap shrinking as N^(−1/2) for an ensemble not used to choose that exponent? | Filed when the promotion audit (batch 025, ADR-047 v3) narrowed and promoted THEORY-391 to what Donoho and Tanner measured. In 2,948,000 optimizations at N = 200, 400 and 1600, eight non-Gaussian ensembles approached the Gaussian curve, consistent with N^(−1/2) gaps. Whether that agreement is a limit theorem is THEORY-391’s former promote_when, moved here unchanged. | Open |
| QUESTION-177 | Do the semantic rate–distortion frameworks beyond Zhao et al. and Chai et al., Liu, Zhang and Poor’s among them, also treat meaning as a latent variable with a known joint law with the observation, or does any limit depend on a property of meaning beyond that law? | Filed when the promotion audit (batch 037) narrowed and promoted THEORY-161 to the two semantic rate–distortion frameworks the record has read in full, Zhao et al. (2025) and Chai et al. (2023), with its two identities re-derived. The former title spoke of the frameworks of 2021–2025 as a class, and the former promote_when asked for Liu, Zhang and Poor’s framework and one further framework to be read directly. This question holds that wider reading. | Open |
| QUESTION-190 | Is the ε⁻² sample complexity of estimating the bisimulation metric between finite Markov chains from occupancy samples optimal, and does an estimator keep a polynomial guarantee on samples from one running trajectory? | Filed when the promotion audit (batch 042, ADR-047 v2) narrowed and promoted THEORY-280. Theorem 1 of Calo et al. (LIT-948) was re-checked: an ε-accurate estimate from O((|X||Y|(|X|+|Y|) + (|X|+|Y|)log(1/δ))/((1−γ)²ε²)) independent occupancy samples per chain. That the ε⁻² rate is optimal was part of the former promote_when, and this question holds it, with the single-stream case the authors expect but do not test. | Open |
| QUESTION-196 | Does Thresholdout keep every one of m adaptively chosen statistical queries within τ of its true mean, with probability 1 − β, on a holdout whose size grows only logarithmically in m, as Dwork and co-authors’ Theorem 11 states? | Filed when the promotion audit (batch 044, ADR-047 v2) narrowed and promoted THEORY-318 to the two results the record has re-derived: max-information bounds the chance of overfitting, and ε-differential privacy bounds max-information. The holdout clause, and the former promote_when’s request for the deferred proofs, are held here. | Open |
| QUESTION-272 v2 | When the task’s target and the probes’ outcome laws are both linear in one unknown state, as for the pairwise comparisons of actions under partial monitoring and for the authority shares of a mixture of known response profiles, when does a family of probes separate what the task needs told apart? | The part of QUESTION-031 that the readings of 2026-10-25 settle, split off under ADR-049. Both answers are linear: a probe family separates what the task needs exactly when the task’s target lies in the span of what the probes reveal. For pairwise comparisons of actions under partial monitoring, that is the loss difference lying in the probes’ combined signal row space (THEORY-962). For the authority shares of a mixture of known profiles, it is the profiles over the probe contexts being affinely independent (CLAIM-452). The general stochastic, decision-relative case, where the target or the outcome laws are not linear in a common state, stays with QUESTION-031. | Answered |
| QUESTION-288 | Can preserving an inquiry’s justificatory history improve decisions beyond a current state that is sufficient for those decisions, and can such a state stop being sufficient when a source, the model or the decision family changes? | A8’s closing question, the part of QUESTION-112 that A10 answered, split off by the status review of 2026-10-27 under ADR-049, because CLAIM-300 (Active) settles it in full. While a state is sufficient for a decision family under a model, its history cannot improve those decisions. The state can stop being sufficient when a source is discredited, the model is revised or the family changes. | Answered |
| QUESTION-321 | For finitely many states, does “at least as informative in every bounded decision problem” imply simulation by a Markov kernel when the simulated experiment’s outcome space is not standard Borel? | The part of the promotion condition formerly on THEORY-156 that the twelfth status review’s re-derivation does not reach. Blackwell (1953), LIT-781, claims the equivalence for arbitrary outcome spaces through its Theorem 2, quoted from Blackwell (1951), which the record has not read. The record’s proof needs a regular conditional distribution of the simulated experiment’s outcome given its posterior, so THEORY-156 was narrowed to standard Borel spaces and promoted. | Open |
| QUESTION-363 | When does the order in which stochastic gradient descent comes to occupy a network’s organizations over training time follow the order in which they come to dominate the Bayesian posterior as the sample grows, and what fixes the correspondence where it holds: an effective temperature set by learning rate and batch size, the accessibility of regions and the barriers between them, or the time allowed to equilibrate? | The owner’s challenge at U4 of the exchange “Analyze nucleation concepts” (2026-10-31). A3 had said that “Bayesian posterior dominance as sample size n changes is not the same process as gradient-based optimization as training time advances”. The owner: “Isn’t it? I think there’s a David M Blei paper that discusses this.” The paper is Mandt, Hoffman and Blei 2017 (LIT-1898). A4 conceded the separation was “too strong” and kept a narrower one, which is this question. It refines QUESTION-039, which asks what sets the order and moment of acquisition. | Open |