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.
Representation learning — how learned systems come to represent their data — self-supervised and contrastive objectives, spectral embeddings, information bottlenecks, knowledge-graph embeddings, and whether representations converge.
59 of 371 QUESTION documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| QUESTION-024 | Can a pragmatic frame be induced from examples of communicative behaviour, and does the induced frame transfer across different wordings? | Opened at A44 §3C from Min et al.: a prompt can establish a convention without stating accurate propositions, which “resembles what we’ve been calling a delivery frame”. Kept as “convention induction” in outlines v3 and v4; absent from the manuscript. | Open |
| QUESTION-025 | Do correlated or hierarchical attributes in co-occurrence statistics still give linear attribute directions in an embedding, and with them a concept lattice that is not Boolean? | THEORY-185 derives linear directions for binary attributes from co-occurrence, but only for independent attributes, which make every combination possible and the concept lattice Boolean. The Lattice Representation Hypothesis (LIT-267) and CLAIM-119 need the opposite: attributes that imply or exclude each other. Whether the linear directions survive that structure is not answered by anything the record holds. | Open |
| 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-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-052 v2 | Beyond linear decisions at the population level, if a kind’s admissible transformations are given as a distribution over pairs of its realizations, is the top eigenspace of the pair operator, or the top left singular space when the transformations are directed, its stable, decision-sufficient signature, and what makes one span the signature when other spans tie? | Filed in the fourth synthesis pass to give readings no question asked for a place in the argument. It bears on QUESTION-027, CLAIM-098, CLAIM-193, CLAIM-164 and CLAIM-043. For linear decisions at the population level it is answered, for symmetric and directed pairs, and that part is QUESTION-245. Open here: nonlinear decisions, and what makes one span the signature when other spans tie. The body gives each reading’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-060 v2 | When a network is trained on data from a structured system, are the variables it comes to represent fixed by its training objective or by what its architecture can represent cheaply, and since an architecture that can represent the system’s coarse-graining need not learn it, when do they coincide with the system’s own relevant variables? | Filed in the fourth synthesis pass to give readings no question asked for a place in the argument. It bears on CLAIM-152 and QUESTION-025. THEORY-197 and THEORY-206 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-106 | Can a textual instruction, a retrieved structured record and an activation intervention preserve the same pragmatic obligations across context shifts, judged on the decisions that matter and not on outputs or embeddings? | A3’s question C. It asks CLAIM-050’s question of three conditioning mechanisms instead of two renderings. Its example obligation is the record’s own: describing a rejected claim without endorsing it. | Open |
| QUESTION-127 v2 | Which diagnoses of frustration among a learner’s demands survive quotienting by function-preserving symmetries, which belong only to an update geometry, and which only to a particular training organization with its optimizer? | A34 §6G of the exchange of 2026-10-17: “When do two functionally equivalent parameterizations yield equivalent frustration diagnoses?” The owner, at U35: “interesting question, double click on this.” A35 answered the first-order coordinate case, filed as CLAIM-366: the common-descent test is chart-invariant, gradient cosines are not, and a budgeted test needs the metric pulled back. The rest is open: function- preserving symmetries, which are not charts of one space, and training trajectories, where “same current function ≠ same learning dynamics”. An answer sorts each diagnosis by what it is a property of. | Open |
| QUESTION-135 v2 | When does spectral differentiation among learned features correspond to stabilizing coexistence among the processes that implement them, and what besides the feature geometry decides it? | From the synthesis the owner relayed on 2026-10-18. In symmetric resource-mediated competition the interaction matrix is the Gram matrix of the components’ feature vectors, A = UᵀU, so representational redundancy and competitive overlap are one object (CLAIM-369). In the two-component case invasion growth equals λ_min(A) (CASE-118). But the same A supports coexistence or exclusion depending on the growth rates. An answer says when the Gram spectrum of a learned representation predicts that the processes carrying its features will coexist, and what else, such as supply, task distribution or evaluation opportunities, has to be fixed for it to. | Open |
| QUESTION-136 | As the number of stimuli grows, do the task-averaged readout identities with white-noise tasks have a non-degenerate population form, with (1/M²)Tr(K̂_X K̂_Y) converging to the Hilbert–Schmidt inner product of the kernel operators, and at what rate when the regularizer is estimated? | The population clause of THEORY-008’s former promote_when. On 2026-10-19 THEORY-008 was confined to a finite stimulus set, where Harvey, Lipshutz & Williams prove its identities, and promoted. Their App. A.3 sketch does not reach the K_z = I case, where its limit is zero (NOTE-834). GULP’s population analysis may answer it, and the record does not hold it. | Open |
| QUESTION-140 | In trained networks, how far do CKA and normalized Bures similarity disagree in ranking pairs of representations, and does the rank-dependent envelope between them matter in practice? | The empirical clause of THEORY-233’s former promote_when. On 2026-10-19 THEORY-233 was promoted: its envelope between CKA and NBS was checked by a direct derivation. Harvey, Larsen & Williams (LIT-250) illustrate the gap only on random Wishart matrices. Whether it matters for real representations needs a measurement on trained networks, and the record holds none. | Open |
| QUESTION-141 | For an asymmetric self-supervised objective, such as BYOL or SimSiam with a predictor and stop-gradient, does the eigenfunction characterization of spectral methods fail, or is it replaced by the singular functions of a non-self-adjoint operator? | The open clause of THEORY-009’s former promote_when. On 2026-10-19 THEORY-009 was narrowed to its reading of the positive-pair papers, where self-adjointness comes from the symmetry of the positive-pair distribution, and promoted. What replaces eigenfunctions when the objective is asymmetric was never part of that reading. No published analysis held by the record answers it. The near misses are LIT-228, LIT-242 and LIT-975. | Open |
| QUESTION-145 | In trained models, do the features’ dimensionality-weighted projectors sum to the identity on their span, as they do in the exact polytope and tegum configurations of uniform superposition? | The promotion condition formerly on THEORY-021, moved here unchanged when THEORY-021 was narrowed to the exact configurations and promoted on 2026-10-19. The algebra is settled for those configurations. Whether trained weights reach them is a measurement no one has made. | Open |
| QUESTION-148 | Do bilinear knowledge-graph scores (RESCAL, ComplEx, HolE, the Neural Tensor Network, QuatE) admit a representation as a coboundary of a sheaf of vector spaces, or is there a proof that they do not? | The open half of THEORY-299’s former promote_when. On 2026-10-19 THEORY-299 was narrowed and promoted: structured and translational embeddings are 0-cochains of a pulled-back sheaf scored by a norm of the coboundary. Gebhart, Hansen and Schrater (LIT-232) state that bilinear models fall outside the framework as given (App. A.1) and do not prove it. Whether any sheaf of vector spaces takes them in is open. | Open |
| QUESTION-149 | In released language models, do the relational linear properties reported so far lie in the subspaces that enter the logits, with Γ ⊆ N and Γ_q ⊆ M, so that they are properties of the distribution and not of one fitted model? | The trained-model half of the promotion condition formerly on THEORY-234, moved here unchanged when THEORY-234 was narrowed and promoted on 2026-10-19. Theorem 14 of Marconato et al. says a relational linear property is shared by every model inducing the same distribution when it lies in N with Γ_q ⊆ M. Whether the linearities reported in trained models meet that condition has not been measured. | Open |
| QUESTION-150 | In the Poincaré ball H^r for r > 2, does embedding a tree with worst-case distortion 1 + ε need Ω((ℓ/(εr)) log deg_max) bits per coordinate for r up to about log deg_max, and Ω(ℓ/ε) beyond, matching the code-based upper bound? | The higher-dimensional half of the promotion condition formerly on THEORY-196, moved here when THEORY-196’s planar lower bound was split off as THEORY-734 on 2026-10-19. LIT-874’s Proposition 3.1 gives the upper bound in H^r. No lower bound in H^r is held, so whether dimension helps exactly as much as the construction uses is open. | Open |
| QUESTION-157 | Do networks trained on factored sequence processes other than Mess3 and Bloch Walk factors, or under an objective other than next-token prediction, also settle near the factored dimension in per-factor subspaces, and what loss gap does the factored representation pay when noise makes it lossy? | The promotion condition formerly on THEORY-256, moved here unchanged when THEORY-256 was narrowed to the transformers and processes tested and promoted on 2026-10-19 (ADR-047 v3). The embedding theorem is settled. Whether the training behaviour holds beyond one synthetic family and one objective, and what the lossy case costs, has not been measured. | 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-160 | Does the heat kernel of a metric tree satisfy the Hellinger Hölder and separation bounds of the multiscale hyperbolic diffusion theorem, with which Hölder exponent, and when does the diffusion operator of sampled data approximate a latent tree’s heat kernel? | The promotion condition formerly on THEORY-478, moved here unchanged when THEORY-478 was narrowed on 2026-10-19 to the conditional equivalence under two Hellinger bounds, with the admissible range α < θ/β. Whether a metric tree’s heat kernel meets those bounds, with which θ, and whether sampled data yield such a kernel, is not settled by anything the record holds. | Open |
| QUESTION-162 | In hyperbolic neural networks on tree-like data, does the advantage over Euclidean networks go with the Möbius bias translations and the distance-based output layer, the only operations through which curvature acts, or do networks without them keep it? | The promotion condition formerly on THEORY-566, moved here unchanged when THEORY-566 was promoted on 2026-10-19 on its structural claim. That the curvature of Ganea et al.’s networks acts only through two operations is settled; whether their gains on tree-like data come from those two operations is untested, since no ablation removes either. | 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-171 | Do volume-maximizing joint-embedding objectives prefer equal-sized clusters as they are actually trained, and does the preference cost semantic transfer on naturally long-tailed data? | The promotion condition formerly on THEORY-306, moved here when THEORY-306 was narrowed to MSN’s and SwAV’s explicit prior and one study’s imbalanced-batch measurement, and promoted on 2026-10-19 (ADR-047 v3). LIT-231 reaches the same prior for VICReg only through an informal reduction of a simplified loss to K-means, and for SimCLR only through a cited equivalence. Its imbalance experiment uses two to eight ImageNet classes per batch, not a natural long tail. | 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-178 | Is word co-occurrence close to independent, multiplicative binary attributes in the analogy families where spectral embeddings complete parallelograms, and does adding an interaction between two attributes break their parallelogram? | Filed when the promotion audit (batch 037, ADR-047 v2) narrowed and promoted THEORY-185, Korchinski et al.’s conditional theorem: under independent, multiplicative binary attributes the PMI is affine in the attributes and its spectral embedding gives exact parallelograms. The theorem is conditional on that premise. Its former promote_when asked for the premise to be measured on real text, and this question holds that request. | 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-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-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-200 | Is the subspace-patching effect measured in GPT-2 Small’s layer-8 MLP an instance of the dormant-direction construction, rather than two cancelling subspaces in that component, and does its dependence on the disconnected component replicate in a second model family? | The promotion condition formerly on THEORY-282. THEORY-282 was promoted on 2026-10-20 (ADR-047 v2) for what its construction proves: a subspace patch can reproduce a variable’s output effect without localizing it. Whether the measured cases are such patches, rather than two cancelling subspaces in the patched component, is open. | 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-205 | Inside Kadanoff’s kernel families, where each hidden spin couples to a block through a kernel of fixed form, does the exact trace condition force the coarse Hamiltonian to keep the relevant operators, or does some further stated condition still have to choose them? | The promotion condition formerly on THEORY-202. THEORY-202 was narrowed and promoted on 2026-10-20 (ADR-047 v2): over general Boltzmann machines, neither a matched partition function nor Kadanoff’s exact trace condition fixes which variables a coarse-graining keeps. Its second counterexample needs visible–visible couplings, so it lies outside Kadanoff’s kernel families. Whether the trace condition suffices inside those families is open. | Open |
| QUESTION-207 | Without choosing checkpoints on the unseen pairs, does coverage of combinations still beat volume for compositional generalization, in a second architecture or with more than two concepts? | The promotion condition formerly on THEORY-117. THEORY-117 was narrowed to what Uselis, Dittadi and Oh measured and promoted on 2026-10-20 (ADR-047 v3), with a determination result the record re-derived: from-scratch ResNet-50s on two-concept grids, with checkpoints chosen on the unseen pairs, reach unseen combinations as coverage grows and not under up to four times more data of the same combinations. Whether that survives honest model selection, another architecture or more concepts is open. | Open |
| QUESTION-211 | How far are independently trained latent spaces from a cosine-preserving map: is the held-out residual of the best orthogonal-times-scalar map close to that of the best linear map where anchor-based stitching works, and does the gap grow where it fails? | The promotion condition formerly on THEORY-175. THEORY-175 was promoted on 2026-10-20 (ADR-047 v3) on its invariance, re-derived, and on what Moschella et al. measured: independently trained encoders agree in their cosine profiles to matched anchors only approximately, enough for untrained decoder transfer with loss, while their nearest neighbours mostly differ. The source never fits a map between two spaces. | Open |
| QUESTION-216 | Does the output Fisher–Rao geometry agreement across language models replicate with released code, and does it fall when models are fitted to different laws while their activation geometry stays as it was, with only a small part of the shared eigenvector structure exceeding a fair law-matched null? | The promotion condition formerly on THEORY-230. THEORY-230 was narrowed and promoted on 2026-10-20 (ADR-047 v2 and v3). Its identification is re-derived: the Fisher–Rao geometry of next-token laws is a function of the laws. Its measurement is one study read in full: mean rank agreement 0.88 against 0.62 in Picozzi’s ten models, and about 9% of the top eigenvector overlap beyond a displacement-matched null. Replication, and a test that varies the law, are open. | 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-232 | Does the coarse-graining that maximizes mutual information with the system beyond a buffer find the renormalization-group variables of a system where they were not known beforehand, and does it give short-ranged effective Hamiltonians in two or more dimensions? | The promotion condition formerly on THEORY-194, moved here when THEORY-194 was narrowed to what Koch-Janusz and Ringel measured on the 2D Ising and dimer models and promoted on 2026-10-20 (ADR-047 v3). Every 2D case in that study had a known answer, and the link to a short-ranged effective Hamiltonian is proved only for 1D and quasi-1D chains. | Open |
| QUESTION-234 v3 | Do interchange interventions leave the mediating direction underdetermined in trained networks: do two basis-related alignments in a trained model tie on every interchange drawn from the data, and for which networks are alignments that agree on all such interventions unique up to a stated symmetry? | Filed when the promotion audit (batch 062, ADR-047 v2) narrowed and promoted THEORY-243 to what the constructed three-unit network proves: two basis-related alignments tie on every interchange intervention on the input. Whether such ties occur in trained networks, or are ruled out for some class up to a symmetry, 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-245 | For linear decisions at the population level, if a kind’s admissible transformations are given as a distribution over pairs of its realizations, is the top eigenspace of the pair operator a stable, decision-sufficient span, and what span takes that role when the pairs are directed? | The linear part of QUESTION-052, split off under ADR-049. For symmetric pairs, yes: the top eigenfunctions are the most view-invariant directions, and their span is minimax-optimal for linear prediction of approximately view-invariant targets (THEORY-007) and bounds linear-probe error by leakage over conductance (THEORY-228). For directed pairs, the top left singular functions of the conditional-expectation operator take that role (THEORY-239), and a linear readout of the full density ratio suffices for redundant labels (THEORY-319). Other spans can tie. Nonlinear decisions, and what picks one signature out, stay with QUESTION-052. | Answered |
| QUESTION-274 v2 | Do two dictionaries of equal fidelity, trained on the same model with different seeds or widths, give the same validated circuit for the same prompt and behaviour, or is a feature circuit fixed only relative to the dictionary that supplies its units? | Feature circuits (sparse feature circuits, transcoder circuits, attribution graphs) are stated over the units of a learned dictionary. The dictionaries are not unique: features split and merge as the dictionary grows, and which concepts get a feature depends on their frequency relative to its size. Whether the circuit found for a behaviour survives a change of dictionary at equal fidelity is the question THEORY-802 asks of alignments, asked of dictionaries. No work the record holds has run the comparison. | 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-286 | Under smooth invertible changes of the parameter coordinates, which first-order frustration diagnoses among a learner’s demands are invariant: pairwise Euclidean gradient angles, common strict first-order descent, or budgeted feasibility with the update geometry transported? | The coordinate part of QUESTION-127, split off by the status review of 2026-10-27 under ADR-049, because CLAIM-366 (Active) settles it in full. Common strict descent, 0 ∉ conv{g_i}, is invariant under smooth invertible reparameterization. The sign of a Euclidean gradient inner product is not, and a negative inner product does not exclude common descent. A budgeted test is invariant when the metric is pulled back. These are the first three rows of A35 §2’s table. | Answered |
| 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-294 | When a network’s architecture can represent a structured system’s renormalization step exactly, must training by distribution fitting make the variables it represents the system’s relevant ones? | The representability part of QUESTION-060, split off by the status review of 2026-10-27 under ADR-049, because THEORY-197 (Active) settles it, in the negative. Mehta and Schwab’s RBM–renormalization correspondence is an identity of parametrizations, and an exact RG step is a perfect fit of the data distribution. Away from that point a contrastive-divergence RBM spends its hidden units on noise, not on the relevant fields. The architecture’s match does not fix what training keeps. | 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-316 | Is it the difference in task, and not depth and initialisation alone, that leaves features with no counterpart in the other model and makes merging fail: at matched width, do models trained from different initialisations on disjoint tasks lose cross-model feature correlation faster with depth than models trained on the same task, with merging failing at that depth? | The promotion condition formerly on THEORY-113, moved here when the eleventh status review narrowed it to what Stoica et al. measured, with their explanation given as theirs, and promoted it, as THEORY-114’s moved to QUESTION-312. | Open |
| QUESTION-317 | Does aligning independently trained networks over the architecture’s full symmetry group remove most of the linear barrier at standard width, on ImageNet or a language corpus, with an alignment computed without data; is the barrier that remains a difference in what the endpoints compute; and does it rise with depth? | The promotion condition formerly on THEORY-112, with its dropped depth clause, moved here when the eleventh status review narrowed it to what alignment removed in the networks its sources measured and promoted it, as THEORY-114’s moved to QUESTION-312. | Open |
| QUESTION-318 | Does layerwise linear feature connectivity hold outside image classification, in transformers and language models connected by spawning, shared pretraining or alignment, and does it carry from pairs to the many-model averages practice uses, model soups and SWA? | The promotion condition formerly on THEORY-111, moved here when the eleventh status review narrowed it to the pairs of image classifiers its source measured and promoted it, as THEORY-114’s moved to QUESTION-312. | Open |
| QUESTION-344 | Does raising or holding below threshold one relation’s subject–object co-occurrences in pretraining, with the rest of the corpus unchanged, make its LRE causality cross 0.9 or fail to, and is the threshold, with its spread, recovered across more model sizes and families? | The promotion condition formerly on THEORY-269, moved here when the status review of 2026-10-30 promoted it under ADR-065. Merullo et al. measured a correlation in three models and say they can draw neither causal claims nor conclusions about scale from it. | Open |
| QUESTION-357 | Outside MNIST and CIFAR-10, or under a second probe family such as a regularized nonlinear readout, do encoders constrained to preserve their input’s information exactly still span a range of downstream quality that includes worse than the raw input? | The promotion condition formerly on THEORY-227, moved here when the status review of 2026-10-30 promoted it under ADR-065. Tschannen et al. (LIT-247, read in NOTE-749) showed the spread on MNIST halves, with CIFAR-10 for two experiments, under a linear probe only. | Open |
| QUESTION-360 | When does a learned distinction become a concept rather than a discriminator or a habit (by being reused systematically, transferring to counterfactual cases, integrating with other capacities, or being correctable), is the transition graded or categorical, and how is a concept told apart from the organization that realizes it and from the thing it is about? | From the owner’s questions at U4 to U6 of the exchange “Analyze nucleation concepts” (2026-10-31): “how does our current position characterize the notion of a ‘concept’?”, “can we distinguish between a ‘concept’ and a ‘thing’?” and “how about ‘entity’?”. The assistant defined “concept” three times in three turns, each a little differently, which is the record’s signal to give it a code. A candidate term is filed beside it, Proposed (TERM-098); this question asks what would settle it. | Open |
| QUESTION-370 | Do the concepts a language model’s workspace makes reportable across an Assistant episode share an episode-level mixture, so that an LDA-style admixture over J-lens readouts predicts their co-occurrence better than one persona selected per conversation and better than independent draws per position; does intervening on the inferred mixture change which concepts reach report while leaving the consumers that bypass the workspace unchanged; and if two models matched on persona distribution and mixture differ under such interventions, whose will-organization is that difference: the simulated Assistant’s, the network’s or the deployed system’s? | From the owner’s U10 and U12 of the exchange “Assess SDT Coverage” (2026-11-02): “the J-Space is basically this kind of LDA”, and H2, not H1, is the LDA because of the Dirichlet over each episode’s mixture (CLAIM-536). With U9’s question, how to read an LDA as will-organization under the Persona Selection Model. The paper is held and read (LIT-1347, NOTE-1069). At the level of a concept the analogy holds, as the owner put it at review: “J-space is a concept space. concepts are distributions over words. concepts are directions in a word space.” What keeps it a question: the paper fits no episode-level mixture, concepts combine additively in logits rather than as a mixture, and the workspace’s privilege is selective, where an LDA topic mediates every word. | Open |