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.
Learning theory — why learning generalizes and how it proceeds — compression and description length, Kolmogorov complexity and sufficient statistics, rate–distortion and PAC-style bounds, model selection; and training dynamics: solvable models of learning trajectories, stages, plateaus and phase transitions in training, and the implicit bias of optimisation. A work whose subject is how to train a model better is ML practice and goes to the anthology (ADR-036).
51 of 371 QUESTION documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| QUESTION-039 v2 | What sets the order and the moment, in training time or in examples, at which a network acquires a structure, and is acquisition one kind of event or several? | Filed in the fourth synthesis pass to give readings no question asked for a place in the argument. It bears on CLAIM-164. THEORY-086, THEORY-187, THEORY-200, THEORY-204 and THEORY-039 answer it in part; the body gives each one’s limit. | Open |
| QUESTION-040 v4 | When the reification rule prices a candidate found in the same data, among many directions the data only partly determine, what must its Occam term count, and how far does the search inflate the candidate’s d’? | Filed in the fourth synthesis pass to give readings no question asked for a place in the argument. It bears on CLAIM-154, CLAIM-188, CLAIM-152 and CLAIM-164. THEORY-080 and THEORY-028 answer it in part; the body gives each one’s limit. | Open |
| QUESTION-051 v2 | What structure does training for one classification task leave in a network’s last layers, and what does that structure cost for decisions and distributions the network was not trained on? | Filed in the fourth synthesis pass to give readings no question asked for a place in the argument. It bears on QUESTION-010 and CLAIM-164. THEORY-083, THEORY-104 and THEORY-085 answer it in part; the body gives each one’s limit. | Open |
| QUESTION-058 | When a trained network’s representation carries a group’s structure, how much of it comes from the task, the architecture, the training set’s relations and the symmetry of the update, and how much can be read off the network without supplying the group? | Filed in the fourth synthesis pass to give readings no question asked for a place in the argument. It bears on QUESTION-036, CLAIM-137, CLAIM-132, CLAIM-148, CLAIM-135 and CLAIM-193. THEORY-022, THEORY-181, THEORY-021 and THEORY-184 answer it in part; the body gives each one’s limit. | Open |
| QUESTION-069 | Is the connectedness of trained solutions a property of the solutions, or of the path family searched, the shared history that produced them and the regime they were trained in? | Filed in the fourth synthesis pass to give readings no question asked for a place in the argument. It bears on CLAIM-187 and CLAIM-142. THEORY-105, THEORY-107, THEORY-108, THEORY-109, THEORY-110 and THEORY-114 answer it in part; the body gives each one’s limit. | Open |
| QUESTION-080 | When a trained network’s parameters keep moving after its loss has converged, what about the network stays fixed, and is the last-layer geometry of neural collapse among the things that do? | The record holds two pictures of the end of training. In one, the last layer converges to a fixed geometry through the terminal phase (THEORY-083, neural collapse). In the other, the parameters never stop: they sample a stationary distribution at constant speed (THEORY-209). The two may describe different regimes. The terminal phase of neural collapse is cross-entropy training past zero error, with no finite minimum, while the limiting dynamics assume a quadratic minimum. Nothing in the record relates them. Drawn by the assistant from the reading of Kunin et al., and filed at the owner’s request. | Open |
| QUESTION-081 | When the relative scale of a network’s layers sets its learning regime under gradient flow, does that regime survive SGD, whose minibatch noise drives the relative scale toward balance, and on what timescale compared with learning? | Two readings meet here. Under gradient flow, the relative scale of adjacent layers is conserved and sets whether learning is rich or lazy (THEORY-212, Dominé et al.). Under SGD, that scale is not conserved: minibatch noise drives it toward the point where the layers’ gradient noise balances, at a rate set by η/S (THEORY-211, Ziyin et al.). If the drift is fast compared with learning, an unbalanced start chosen to be lazy would drift toward balance and richness. If it is slow, the regime set at initialization stands. Neither paper addresses the other. Drawn by the assistant from reading both, and filed at the owner’s request. | Open |
| QUESTION-120 v5 | Beyond distances and sparse recovery, whose thresholds share a sufficiency proof and not a necessity proof, when the record meets a random linear map that keeps what a later stage needs, in random features for kernels, the superposition toy model’s bound and phase changes, and the expand-and-threshold codes of sparse distributed memory and the fly, is it one concentration-of-measure fact applied to different families, and does each threshold count the same thing? | Filed when a survey of the record found random projections in three places and the Johnson–Lindenstrauss lemma in none. The three uses carry three thresholds: ε⁻² log n for distances, k log(n/k) for sparse recovery, and 2N = n for random-features regression. The question is whether these are one union bound over different families or different phenomena that share a tool. Six anchor works are now read. They show the distance and sparse-recovery thresholds share a sufficiency proof, but not a necessity proof, and that part is QUESTION-251, Answered. They give nothing that reaches random features or expand-and-threshold. For SDM and the fly, the record’s SDM recall account and its LSH account offer candidate thresholds of a different shape. | Open |
| QUESTION-122 | Can a deep network during training have meaningful affect-like states, such as frustration of its demands, and to which unit, the network, the network–optimizer pair or the training process, would they belong? | The owner’s, U30 of the exchange of 2026-10-17: “the possibility of meaningful affective states attributable to a deep neural network specifically during training”. A30: the framework supports “a meaningful, qualified notion of training-time affective organization” and not “the conclusion that a neural network feels distress”. U31 added the bearer half, and CLAIM-367 answers it for conventional training, in part. U33 moved the primitive from distress to frustration (CLAIM-368). An answer says what training-time condition, if any, is affect-like, and whose. Organizational-affect is the natural line, set aside; whether it reopens is the owner’s decision, not made here. | Open |
| QUESTION-133 | Can a population of operators whose demands are jointly infeasible under one functional organization develop a differentiated or compositional repertoire that makes them jointly feasible, without suppressing, weakening or deleting any of those demands? | From the synthesis the owner relayed on 2026-10-18, which called it the most conceptually interesting new connection. CLAIM-347 defines structural frustration as joint infeasibility and relief as enlargement of the compatibility complex under fixed demands. CASE-119 shows relief by enlarging the attainable set, with every pair compatible and the triple not, until a composite policy appears. The question is whether learning, specialization or recomposition can bring this about endogenously. An answer is a model that keeps the acceptance sets fixed while learning changes what is attainable and strictly enlarges the complex. Apparent relief that comes only from removing a demand or redefining success does not count. | Open |
| QUESTION-134 v2 | When influence decides access to learning opportunities, does the resulting feedback make a marginalized specialist lose its competence, so that it cannot recover influence even when its former niche becomes relevant again? | From the synthesis the owner relayed on 2026-10-18. CLAIM-277’s note of 2026-10-18 records niche exclusion by authority deprivation: low exposure, poor competence estimates, low endorsement, lower exposure. This asks whether the loop goes further and destroys the competence, not just the measurement of it. When training opportunities follow influence, a specialist denied opportunities may become genuinely unable to do its job. An answer separates loss of influence, loss of competence and loss of access to evaluation. That gives an operational test for one mechanism of domination without defining domination as holding less authority. | Open |
| QUESTION-139 | Does the one-hidden-layer lower bound of ∏(rᵢ+1) neurons for the monomial x₁^r₁⋯xₙ^rₙ hold for uniform approximation on a box, and not only for Taylor matching at the origin, and what replaces it when hidden units have biases? | The open half of THEORY-206’s former promotion condition. On 2026-10-19 THEORY-206 was narrowed to the Taylor-matching bound for bias-free networks, which Rolnick and Tegmark prove and the record re-derived, and promoted. Their uniform lower bound rests on a step that fails, and the biased case is untreated. Both are here. | Open |
| QUESTION-155 | Does a lossy-compression bound on generalisation error give a non-trivial value for an algorithm whose output carries infinite information about its sample, such as deterministic training of a network with continuous weights? | The promotion condition formerly on THEORY-248, moved here unchanged when THEORY-248 was narrowed and promoted on 2026-10-19. The bound is proved and finite wherever the output law’s rate-distortion function is. No one has evaluated it for a learned model whose I(S;W) is infinite. | Open |
| QUESTION-158 | Does gradient descent on a two-layer network, without a spectral initialization or a data split, recover direction k of a scale-free hierarchical multi-index target at n = Θ(a_k^(−2) d) samples and attain the optimal weighted error, and do the same thresholds hold for an input law that is not isotropic Gaussian? | The condition formerly on THEORY-283, moved here unchanged when THEORY-283 was narrowed and promoted on 2026-10-19. The thresholds and rates are proved for the Bayes-optimal and spectral estimators, and for a network whose first layer is the spectral estimator. Whether gradient descent reaches them, or whether they survive a second input law, is open. | Open |
| QUESTION-159 | Does an exact train-then-predict identity, of the kind proved for unnormalized linear attention and for softmax attention, hold for further sequence-layer classes such as delta-rule or mini-batch inner updates, and is there a standard attention layer whose dependence on its context admits no description as any learner’s train-then-predict step? | The scope test formerly in THEORY-169’s promote_when, moved here unchanged when THEORY-169 was narrowed and promoted on 2026-10-19. The identities are proved for unnormalized causal linear attention (one batch gradient step of a linear model from zero) and for softmax attention (kernel regression that stores the context). Whether the pattern reaches other layer classes, or is bounded by one, is open. | Open |
| QUESTION-161 | Do trained language models learn in context by implicit Bayesian inference over a latent concept: do their in-context predictions track the posterior predictive of a latent-concept mixture fitted to their pretraining data, or carry a readable posterior that concentrates as the theorems say? | The promotion condition formerly on THEORY-614, moved here unchanged on 2026-10-19. THEORY-614’s title is a conditional theorem about the pretraining distribution under exact fit, and it says that whether trained networks learn in context this way is not shown. The old condition asked for evidence on exactly that disclaimed point, so it is a question in its own right. | Open |
| QUESTION-164 | Does the law of balance hold in a deep network trained on real data during its limiting dynamics: for parameter groups related by a rescaling symmetry, does the difference of squared norms move toward the value where the groups’ gradient-noise traces are equal, at a rate that scales with learning rate over batch size? | The promotion condition formerly on THEORY-211, moved here unchanged when THEORY-211 was narrowed and promoted on 2026-10-19 to the SDE model in which the law of balance is proved. Whether the law holds for a deep network trained on real data is not shown; the tests are small synthetic networks. | Open |
| QUESTION-165 | On the Random Hierarchy Model, is the number of examples a deep network needs set by when patch-label correlations become detectable, or by the size of the grammar, once the two are separated by moving the correlations with n_c, m and L fixed? | The promotion condition formerly on THEORY-195, moved here unchanged when THEORY-195 was narrowed and promoted on 2026-10-19 to what the experiments measured. In the model as given, the correlation threshold and the grammar’s size are the same expression, n_c m^L, so the measurements cannot say which one sets the number of examples. | Open |
| QUESTION-166 | Does the depth law of deep linear networks hold from starts off the decoupled set: learning time, counted in iterations at the stable step size, bounded in depth when every mode’s initial end-to-end gain is of order one, and growing as a power of 1/ε when it is ε, for random orthogonal or small random weights not aligned with the task’s singular vectors? | The promotion condition formerly on THEORY-187, moved here unchanged when THEORY-187 was narrowed and promoted on 2026-10-19. The depth law is exact for decoupled, balanced starts on whitened inputs. Whether it holds from random orthogonal or small random weights is supported by one MNIST experiment and an argument from dynamical isometry, not derived. | Open |
| QUESTION-174 | Outside finite alphabets, is a variable-rate covering argument, rather than a change of measure alone, what yields data-dependent PAC-Bayes bounds? | Filed when the promotion audit (batch 036, ADR-047 v2) promoted THEORY-263. Its second clause was re-derived in general spaces by the disintegrated change of measure, with no coding argument. The former promote_when also asked for a second source deriving a PAC-Bayes bound from a variable-rate covering outside finite alphabets; this question holds that request. | Open |
| QUESTION-175 | From generic small initialization, does gradient flow on a symmetrized Barlow Twins loss with a linear or fixed-kernel model follow the aligned trajectory, learning the top eigenvectors one at a time in order of eigenvalue? | Filed when the promotion audit (batch 036, ADR-047 v2) narrowed and promoted THEORY-229 to initialization aligned with the top eigenvectors. Simon et al.’s Result 4.6, for generic small initialization, is an informal derivation; the former promote_when asked for its proof, and this question holds it. | Open |
| QUESTION-176 | Do networks trained by gradient descent on a mixture of random facts and a second domain reach the capacity-optimal allocation, so that their threshold size and mixing ratio are the optimal learner’s? | Filed when the promotion audit (batch 036, ADR-047 v2 and v3) narrowed and promoted THEORY-293. The theorem about the optimal capacity-bounded learner was re-derived, and Gu et al.’s Pythia runs were accepted as showing a threshold. That the trained networks’ thresholds are the optimal learner’s was the former promote_when, and this question holds it. | Open |
| QUESTION-179 | Is the latent-variable MDL bound of Theorem 4 in Sefidgaran et al. non-vacuous for a trained encoder, with a type-III symmetric prior that does not use the ghost data? | Filed when the promotion audit (batch 038, ADR-047 v2) narrowed and promoted THEORY-238. The constant in Theorem 4 was re-derived and the bound holds as stated. The former promote_when also asked whether the bound is small for a real network, which the account does not claim. This question holds that request. | Open |
| QUESTION-180 | Does the rate-distortion function of an optimisation trajectory given its sample, with the coupling coefficient M bounded or estimated and the 4Lε term kept, account for the generalisation of trained networks? | Filed when the promotion audit (batch 038) narrowed and promoted THEORY-266, Theorem 7 of LIT-233, on its proof. The former promote_when asked for an evaluation that would settle whether the trajectory’s compressibility given the sample accounts for generalisation. That is more than the theorem says. This question holds it. | Open |
| QUESTION-181 | Do trained networks follow the continually renormalized gradient flow toward neural collapse under MSE loss, and does the classifier stay near the least-squares classifier of its features outside Han, Papyan and Donoho’s settings? | Filed when the promotion audit (batch 038, ADR-047 v2 and v3) narrowed and promoted THEORY-278 to LIT-974’s measured cells and its renormalized model. The former promote_when asked whether ordinary training follows that model’s dynamics, and whether the central path holds in settings the paper did not test. This question holds both. | Open |
| QUESTION-182 | Does the landmark readout of a learned contrastive density ratio keep its 1/m rate under a finite second moment of the ratio alone, without a uniform bound on it? | Filed when the promotion audit (batch 037, ADR-047 v2) narrowed and promoted THEORY-319 to Tosh, Krishnamurthy and Hsu’s redundancy and landmark bounds for the exact density ratio, re-derived step by step. Its former promote_when also asked whether a learned ratio keeps the rate without the uniform bound Theorems 10–11 assume. This question holds that clause. | Open |
| QUESTION-183 | Does the spectral contrastive guarantee hold off a finite augmentation space, and is it non-vacuous on a real augmentation graph? | Filed when the promotion audit (batch 037, ADR-047 v2) narrowed and promoted THEORY-228 to HaoChen et al.’s guarantee on a finite augmentation space, re-derived step by step. Its former promote_when asked for two further results, and this question holds both: a proof off a finite space, and a measurement showing the bound is non-vacuous. | Open |
| QUESTION-189 | Does keeping every earlier round’s data bound the error of a model refit on its own outputs beyond least squares with reused Gaussian covariates, when covariates are regenerated or the model class is nonlinear or over-parameterised? | Filed when the promotion audit (batch 042, ADR-047 v2) narrowed and promoted THEORY-289. The closed form of Gerstgrasser et al. (LIT-971) was re-derived for ordinary least squares on reused isotropic Gaussian covariates. Its extension to other settings was the former promote_when, and this question holds it. | Open |
| QUESTION-192 | Does lazy-regime training leave the within-class variability of a network’s features at its initial value beyond one-dimensional, zero-bias, two-class data, where the tangent and initialization kernels are not proportional? | The promotion condition formerly on THEORY-294. THEORY-294 was narrowed to Kothapalli and Tirer’s Theorem 5.1 and promoted on 2026-10-19 (ADR-047 v2): for a wide two-layer ReLU network with zero bias on one-dimensional data whose classes lie on opposite sides of the origin, the tangent kernel is a constant multiple of the initialization kernel, so NC1 is unchanged. Whether lazy training leaves NC1 in place where the kernels are not proportional is open. | Open |
| QUESTION-193 v2 | Does sign descent provably delay each weaker skill until the stronger one is learned when a loss’s eigendirections are misaligned with the coordinates, and does changing only the optimizer turn a trained network’s simultaneous skill onsets into a sequence? | The promotion condition formerly on THEORY-253. THEORY-253 was narrowed to what Liu, Liu, Michaud, Gore and Tegmark measured in their Geometry model and promoted on 2026-10-19 (ADR-047 v3): skills progress together under gradient descent and in sequence under sign descent, with the ratio of onset times saturating at 2, and on a rotated quadratic only when the eigendirections are misaligned with the coordinates. That is simulation. A derivation, and a test on a trained network, are open. | Open |
| QUESTION-195 | Does prior-scored translation without parallel data keep an error bound that falls in the common ground and the size of the source language when the languages are not uniform or the translators are lossy? | Filed when the promotion audit (batch 044, ADR-047 v2) narrowed and promoted THEORY-270 to Goldwasser and co-authors’ common-nonsense theorem, re-derived from its appendix. The former promote_when, a bound outside the uniform, lossless models, is held here. | 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-199 | Does the training fraction at which networks summing two learned embeddings generalise follow the fraction at which the training set’s same-answer equations leave only translation and scale free, across group sizes? | Filed when the promotion audit (batch 043, ADR-047 v2 and v3) narrowed and promoted THEORY-181 to the zero-loss injective model and to the one size Liu et al. measured. The former promote_when asked for the multi-size test; this question holds it. | Open |
| QUESTION-202 | Does neural collapse hold outside its first protocol, under augmentation, label noise, class imbalance and several seeds per setting, and does gradient descent on cross-entropy provably reach it? | The promotion condition formerly on THEORY-083, moved here when THEORY-083 was narrowed to the runs Papyan, Han and Donoho plotted and promoted on 2026-10-20 (ADR-047 v3). Those runs had balanced classes, no augmentation, dropout removed and one plotted run per learning rate. Whether collapse holds outside that protocol, and why training reaches it, is open. | Open |
| QUESTION-206 | Does stochastic gradient noise drive training into a mirror-symmetric subspace where it is a saddle, beyond the second-order, diagonal-Hessian argument, and does a trained network’s distance to that subspace fall to zero past a threshold set by noise and curvature? | The promotion condition formerly on THEORY-213. THEORY-213 was narrowed and promoted on 2026-10-20 (ADR-047 v2) to the exact half of Ziyin’s Theorem 1: a mirror symmetry’s subspace is invariant under gradient training, and weight decay above half the lower bound on the Hessian puts every minimum in it. The SGD half, attraction to the subspace even at a saddle, rests on a diagonal approximation and is open. | Open |
| QUESTION-208 | Does the expected structure function of a computable i.i.d. source match its distortion-rate function, with the right-hand step of Grünwald and Vitányi’s Theorem 6.27 filled in? | Filed when the promotion audit (batch 050, ADR-047 v2) narrowed and promoted THEORY-244 to the entropy and mutual-information bridges, which it re-derived. The distortion-rate bridge rests on a step in Theorem 6.27 that the reading found asserted, so it left the title. The former promote_when’s clause for it is held here. | Open |
| QUESTION-217 v2 | When a learning system is said to go from coarse to fine, do the order in which its representations refine one another, the order of their relevance to a task and the order in which training acquires them admit one common chain, and under what conditions on the learning operator? | A1 and A2 of the exchange of 2026-10-19 on coarse-to-fine processes. The record already holds that “coarse to fine” names different things: an order in training time by singular value (THEORY-186), an order in noise (THEORY-199), and a sample-complexity result in which every level arrives at once (THEORY-195). No entry separates refinement, relevance and acquisition as three relations and asks when they agree. An answer is a theorem giving sufficient conditions for a common chain, or a minimal family of counterexamples. | Open |
| QUESTION-220 v3 | Given that information-bottleneck optima at two budgets need not be nested, what condition on P(X, Y), beyond Y a function of X or X and Y both binary, guarantees that the coarser optimum is a (possibly noisy) function of the finer, X → Z₂ → Z₁, and how much is lost by forcing nesting when it fails? | A2 of the exchange of 2026-10-19 on coarse-to-fine processes, which called it “the most consequential missing bridge”. A hierarchy of optimal abstractions needs more than an optimum at each budget: it needs the optima to be compatible. NOTE-676 gets nesting by restricting the encoder to prunings of a fixed tree; nothing in the record says when it holds without that restriction. Rate–distortion theory’s answer is successive refinability (Equitz and Cover, registered unread). | Open |
| QUESTION-233 | Do language models show the data-limited exponent γ/(2β) because data limits the usable horizon: does the exponent track γ/(2β) when one corpus statistic is moved and the other held, and does the match survive at horizons of thousands of tokens with γ estimated outside the model class? | Filed when the promotion audit (batch 062, ADR-047 v2 and v3) narrowed and promoted THEORY-204. That the fitted data-limited exponent matches γ/(2β) on TinyStories and WikiText-103, and that assumed per-lag scaling forms give min(δ, γ/(2β)), is settled. Whether real learners show the exponent for the horizon reason was the old promote_when, and it moves here. | Open |
| QUESTION-236 | Does fixed-feature transfer to new classes fall as penultimate class separation rises outside ImageNet-trained ResNet-50s, and does it move with within-class spread when the loss is held fixed? | The promotion condition formerly on THEORY-246, moved unchanged when that account was narrowed to what Kornblith et al. (2021) measured and promoted on 2026-10-20 (ADR-047 v3). Open: whether the inverse relation between penultimate class separation and new-class transfer holds in other pretraining settings, and whether separation, rather than the loss, is what moves transfer. | Open |
| QUESTION-244 | Must the optimal representations of an information-bottleneck objective at two budgets be nested, so that the coarser optimum is a (possibly noisy) function of the finer? | The yes-or-no part of QUESTION-220, split off under ADR-049. No, for deterministic encoders (CLAIM-387) and for stochastic ones (CLAIM-392), on one four-state source with binary Y. Raising the budget can reorganize the optimum rather than split it. What condition on P(X, Y) guarantees nesting stays with QUESTION-220. | Answered |
| QUESTION-251 | Do the Johnson–Lindenstrauss threshold for distances and the k log(N/k) threshold for sparse recovery rest on one concentration-of-measure argument, a tail bound for each fixed vector’s norm with a union bound over a family, both for sufficiency and for necessity? | The part of QUESTION-120 its readings on distances and sparse recovery settle, split off under ADR-049. For sufficiency, yes: one per-vector tail and a union bound give both, over pairs for distances (THEORY-397) and over net points on every sparse support for recovery (THEORY-390). For necessity, no: the distance lower bounds are encoding and bit-counting arguments (THEORY-395, THEORY-399), recovery’s rests on Gelfand widths, and its sharp location on face counting (THEORY-391). Random features, superposition and expand-and-threshold stay with QUESTION-120. | Answered |
| QUESTION-271 v3 | How can an organization evaluate its own processes so that the evaluation decides authority without being captured by it: when wins among the processes cycle, when no common scale scores them all, when the processes in charge can add, filter or duplicate the tests, and when only the processes heeded are evaluated? | Filed at the owner’s direction, 2026-10-24, with the registration of works from multi-agent reinforcement learning and learning in games, after the owner asked how the record stands on MARL. The governance line keeps returning to one gap: the scoring that allocates authority is itself governed. The replicator construction makes that gap a lock-in threshold, and BoostTheVote assumes it away with an objective metric. The question asks what evaluation procedures resist capture, and in which of four senses. | Open |
| QUESTION-275 | Can the development of a transformer’s circuits in training be described as organizational regimes forming over shared, overlapping latent features, so that a model coupling feature allocation to circuit interaction, fitted to early checkpoints, predicts the effects of held-out training interventions that feature-only and circuit-only descriptions fitted to the same checkpoints miss? | The owner, at T24: “could we potentially apply this setup as an interpretive framework for understanding the learning dynamics of transformers?” “This setup” is the dynamic latent-feature model of T23 (CASE-165). The reply answered with a test: “Can the emergence, specialization, overlap, and persistence of transformer circuits be explained by modeling them as developing organizational regimes over shared latent features—and does that description predict training responses that existing feature- or circuit-based analyses miss?” It is the second time the owner has applied the record’s frameworks to a network in training. The first was CASE-113 and CLAIM-367, and CASE-117 is the population form. The sharp edge is CLAIM-427’s third grade: positive results would have to be prospective, against strong conventional baselines at matched complexity. Nothing here says that a circuit is a perspective. | Open |
| QUESTION-291 | For finite X and Y, does every finite-budget information-bottleneck optimum nest under the β → ∞ optimum, what test on a pair of optimal encoders decides whether two finite budgets nest, and do the optima nest at every pair of budgets when Y is a function of X or when X and Y are both binary? | The settled part of QUESTION-220, split off by the status review of 2026-10-27 under ADR-049, because THEORY-743, THEORY-753 and THEORY-757 (Active) answer it. Every finite-β optimum is a stochastic coarsening of the causal partition. Two budgets nest iff some pair of optimal encoders forms X → T₂ → T₁, a convex-hull test on decoder points. The optima nest at every pair of budgets when Y is a function of X and when X and Y are both binary. | Answered |
| QUESTION-305 | From small random weights not aligned with the data’s eigenbasis, does a linear-attention layer trained on in-context regression come into alignment with that basis before or while its modes are learned, so that its learning is staged by the input spectrum without the alignment being assumed? | The promotion condition formerly on THEORY-481, moved here when the ninth status review narrowed it to the aligned case it derives and promoted it, as THEORY-285’s moved to QUESTION-303. THEORY-186 holds the same open claim for two-layer linear networks. | Open |
| QUESTION-312 | Does linear mode connectivity emerge during training rather than at initialization outside image classification and beyond MLPs: in a language model or transformer, for copies spawned from a shared state and for independent runs aligned under the architecture’s symmetry group, and for standard-width convnets or ResNets after alignment? | The promotion condition formerly on THEORY-114, moved here when the tenth status review narrowed it to the image-classification networks and MLPs its two sources measured and promoted it, as THEORY-285’s moved to QUESTION-303. | Open |
| QUESTION-338 | Measured on another game, or on Hex with a standard AlphaZero implementation or larger networks, is the iso-strength trade between training compute and tree-search compute again a straight line in log–log space ending at a one-node search, and is its slope, reported with its uncertainty and with test-time compute in a stated unit, within error of Jones’s −1.2? | The promotion condition formerly on THEORY-342, moved here when the status review of 2026-10-30 promoted it under ADR-065. Jones measured one game with one nonstandard implementation and gave no uncertainty on the slope, and he asks twice for the test on other games. | Open |
| QUESTION-349 | On tasks other than Jacobs and colleagues’ four-class vowel discrimination, do mixtures of experts trained on the error of a single expert chosen stochastically by the gate, or on the mixture’s negative log-likelihood, leave most experts with near-zero mixing proportions while matching the accuracy of a dense network of equal size? | The replication THEORY-937’s promotion condition asked for, moved here when the twenty-third status review promoted that reading of one study (ADR-065 §3: a request to replicate moves to a QUESTION). The vowel task needs two or three lines; whether the sparse division appears on tasks without so few natural subtasks is open. | Open |
| QUESTION-361 | Is an organization’s recursive production usefully understood as self-distillation, each realization generating a specification of its own effective organization that constrains how its successor is built, and if so, what makes the distillation the organization’s own rather than run by an outside optimizer, and what makes a successor a good teacher as well as a faithful student? | The owner’s proposal at U15 of the exchange “Analyze nucleation concepts” (2026-10-31): “maybe framing this recursive production as self-distillation could be helpful or at least interesting?”, with Teoh’s multi-token-prediction paper (LIT-1896). A15 and A16 developed it as “organizational inheritance”. It refines QUESTION-016, which asks when iterated reconstruction preserves task-relative sufficiency, by adding who runs the reconstruction and whether the successor can carry it on. | 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 |