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.
34 of 547 CLAIM documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| CLAIM-008 | The abstract similarity between renderings is similarity of higher-order latents, which can survive large differences in lower-order ones | The owner’s U27 request and A73’s answer: a hierarchy of latents up to a relational configuration, with D_prag, D_dyn and local versus global distances. Superseded at U28 when the owner made the levels levels of observables. | Superseded — by CLAIM-042 |
| CLAIM-029 v3 | A language model’s response to a context is functionally a parameterized pragmatic frame | The owner at U17, offered as a motivating example “maybe even just for notational purposes”. The assistant made it the primary formal example (A43), then one running case of three (A52). Its formal statement, frame as a parameterized family of contexts, did not survive outline v4. | Proposed |
| CLAIM-049 v2 | An adaptive interpreter’s state includes its message, context knowledge and learned parameters, and learning can make some relational invariants more stable and others less | A110 §22, recovered, with its case: a translator familiar with an underworld genre conserves its affiliative humour, a naive one turns it into a moral statement. The manuscript keeps one sentence (§11) on adapted receivers. | Active |
| CLAIM-058 v2 | Context-conditioned language models give a controlled computational setting in which the theory’s frame, order and transport effects can be tested before human studies | A45 §8: “Put the three LLM experiments before the human-participant studies, positioning the former as controlled computational tests and the latter as external validation.” The conclusion of the U17 analogy, limited by the circularity objection. | Proposed |
| CLAIM-065 | Pragmatic fidelity is approximate preservation of the ways an utterance conditions, transforms and constrains later interpretation and interaction, across transient framing and learned interpretive dispositions | The thesis of the U17 replies and outline v3 (A45 §10, A48), adding learned dispositions and language models to A40’s observation-relative thesis. Superseded at A50–A52 by the transport thesis. | Superseded — by CLAIM-101 |
| CLAIM-074 v4 | Fidelity is relative to the interpreter’s learning history: what the current context supplies and what earlier experience has left in the interpreter are separate histories, told apart by what they carry and not by whether the change sits in activations or in weights, so fidelity under a fixed interpreter, across interpreters and across states of adaptation are different quantities | A44 §4 and A48 §5.5, recovered. Kept to outline v4 (§9.5); absent from the manuscript, which keeps the context/interpreter split but not its consequence for fidelity. Apparently dropped by inadvertence. | Active |
| CLAIM-085 v2 | A framing effect in a language model is a property of that model under those prompts, and what a translation ought to preserve is a normative question that model response distributions, being descriptive, cannot settle | A45 §8–9 and A48 §8.5, recovered. Both limbs went in the de-hedging after U19, though neither is a hedge: one is a design constraint, the other a distinction between normative and descriptive fidelity. The manuscript keeps part of the remedy and neither argument. | Active |
| CLAIM-111 | A text supports a distribution over possible communicative situations, and a translation can be faithful by preserving that distribution and its response to further evidence | A45 §6, recovered: fidelity as P_o(z | c_o, u_o) ≈ P_t(τ_z(z) | c_t, u_t), “an interesting middle position between our original relativistic account and the later dynamical account”. Dropped at outline v3 without critique. | Proposed |
| CLAIM-118 v5 | Context and interpreter are separate sources of interpretive change, told apart by what each carries and not by mechanism: what the current context supplies, whether held in activations or in weights updated on it and discarded after, is the signal; what earlier contexts have left in the interpreter and it carries into new ones is the interpreter; and improving the signal differs from improving the interpreter | A43’s first point about the U17 proposal, developed at A44–A45 into three sources of change (evidence, transient computation, parameters). The manuscript §5 keeps it in two sentences. | Active |
| CLAIM-126 v3 | Model stitching tests whether a transport preserves decision-relevant information only in its reconstruction form: a map fitted to reproduce the target representation certifies one direction of Blackwell sufficiency, while task-loss stitching compares one decision problem through a fixed head, and a failure to stitch is no evidence against sufficiency | Proposed by the record on 2026-10-09 as an operational handle on the decision-relevant half of CLAIM-125, and qualified by the reading of Bansal, Nakkiran & Barak before it was filed: only reconstruction-fitted stitching certifies sufficiency, and only within the map class. | Active |
| CLAIM-129 v3 | A factorization recovers only the structure visible in the relations it is fitted to, so a topic can survive a transformation that changes the communicative act, and a kind must be tested against probe families chosen for their bearing on the act | The assistant’s, at A210 §5 after the owner’s U58, and again at A214 §3–§4. It recurs from U56 (A203 §37) to U60 (A218 H3), so it gets a code. It is CLAIM-004’s distinction between changing the frame and changing the act, in a factorization, and TERM-014’s relativity to a family of measurements, stated for factorizations. It does not say lexical structure is irrelevant to the act, or that a richer factorization cannot capture acts. | Proposed |
| CLAIM-146 | Recovering latent relational structure from an interaction matrix, with no privileged latent coordinates, is decades-old prior art, so the manuscript’s contribution cannot be that recovery | The owner’s prior-art objection at U58 to A207’s closing framing, conceded by A210 in its first sentence and extended by A214 to identifiability and cross-lingual alignment. It is the line’s third in-band prior-art retraction, after CLAIM-019 and CLAIM-100 → CLAIM-125. The concession holds for structure. It does not hold for individual topics, which are recovered only by privileging the nonnegative representation, and uniquely only under separability or anchor-word conditions. | Active |
| CLAIM-148 v4 | A matrix factorization is identified only up to an invertible change of latent coordinates, which weight decay narrows to rotations and nonnegativity to rescalings and permutations plus a data-dependent remainder; such a gauge is not a symmetry of the relational system, and automorphisms of the data act on the factors only when the factorization is identifiable | Drawn by the assistant at A207 §3, made explicit at A214 §6 and kept in A218 (§4.2, Ch5.4–5.9). Granted, because it is elementary, and the record already held its mathematics. The record adds the full list of invariants, the data-dependent freedom of nonnegative factorization, and why identifiability must come before automorphisms and characters. It does not say latent axes are meaningless, or that observed data have non-trivial automorphisms. | Active |
| CLAIM-149 v2 | A probe family that supplies a transformation’s training signal cannot also certify what the transformation preserves: preservation must be shown under probes that were not used to train it | The owner set the frame at U51 (“a useful case study … the projected GAN work”); A184 §§3–4 argued it, with its Experiment C and closing maxim, and A203 §30 and A218 Study 6 keep it. It carries CLAIM-011’s remedy from correspondences to training objectives. Kynkäänniemi et al. (CASE-041) is a documented instance, which the exchange did not know of. The documented support is one training case, in image generation, and one selection case, in translation (CASE-071). | Active |
| CLAIM-187 v2 | Whether two systems compute the same way can be tested by quotienting the full admissible symmetry group and measuring what remains: a residual barrier marks a different mechanism, and a feature with no counterpart blocks the comparison | The record’s one fully measured case of “factor out the admissible symmetries, then test what survives”, which the pragmatic-transport line’s questions about invariants under admissible transformation (QUESTION-027, QUESTION-029, QUESTION-036) ask for in the abstract. From five mode-connectivity THEORYs held without links to the line. The carry-over from trained networks to communicative kinds is the filer’s, and is the claim’s weak point. | Proposed |
| CLAIM-193 v4 | A linear probe family can tell apart only realizations whose representations differ in normalized kernel, and kernels fix a representation only up to the symmetry of what is observed: any distinction beyond that is supplied by the analyst | A partial answer to QUESTION-031 for the linear case, from THEORYs the record held without linking them to the line. What a regularized linear readout decodes is a function of the normalized kernel (THEORY-008); kernels fix a representation only up to the symmetry of what is observed (THEORY-004, THEORY-723); an inner product beyond that is a stipulation (THEORY-018); and spectral degeneracy does not identify the symmetry (THEORY-019). Proved results for learned representations; the carry-over to communicative realizations is the filer’s. | Proposed |
| CLAIM-203 v4 | The only design for the October thesis builds its outcome in: the act is fixed by whoever writes the items, and the topic-only baseline is built to fail on the critical cells | Found in the record’s audit of the line on 2026-10-10 (empirical lens); no turn of the exchange raises it. CASE-040 “makes the act a manipulated factor rather than an outcome”, so recovering the act recovers the item writer’s intent, close to a manipulation check. Its held-out items are built to “break the familiar correlation”, so a lexical topic model fails on them by construction. And its baseline is topic-only NMF, not the embedding or surface similarity of CLAIM-139’s own defeat condition. Through CLAIM-135 it reaches CLAIM-139’s epistemic clause. CASE-040’s “What it cannot show” covers neither point. It does not say the design is useless as a first pilot. | Superseded — by ARG-011 |
| CLAIM-248 v4 | The founding stimuli (Villon, Henley’s Villon, Hofstadter’s Marot) and commentary on them are likely in language models’ training data, and what a context does to one model need not be what it does to another, so a model’s reading of their footing may be recall, and a directional match in one model may not hold in the next | Found in the record’s audit of the line on 2026-10-10 (empirical lens); no turn of the exchange raises it. Agreement in direction is what a model trained on human descriptions of teasing and reproach would show anyway, and Villon, Henley and Hofstadter’s Marot are likely in training data, so a model’s “interpretation” of them may be recall. ARG-008 and CLAIM-085 already bound what model results show about human pragmatics. What is new is that CLAIM-058’s validity bar is too low, and the contamination point. Minor. | Active |
| CLAIM-263 v3 | Whether two trained networks compute the same way can be tested by quotienting the architecture’s full symmetry group and measuring what remains: a barrier that survives alignment marks a different mechanism, connection after alignment means shared feature structure, and the test cannot run where features have no counterpart | The general content of CLAIM-187, filed alone in learned-structure under ADR-040: a measured protocol for asking whether two trained solutions are the same solution. Quotient the full symmetry group, including the orthogonal map on a transformer’s residual stream (THEORY-112). Read a barrier that survives as a difference of mechanism (THEORY-116). Between linearly connected image classifiers, nearly every layer’s features interpolate (THEORY-111). The test cannot run where features have no counterpart (THEORY-113) or the objectives share no structure (THEORY-115). It is the first claim in the learned-structure line. | Proposed |
| CLAIM-266 v2 | A family of probes that supplies an optimized system’s training signal cannot also certify what the system preserves: optimization pushes toward whatever the probes reward, including what they cannot see, so preservation must be shown under probes not used to train it | The general content of CLAIM-149, filed alone under ADR-040 so that it does not rest on CLAIM-011’s account of correspondences in translation. Training against a probe family pushes a system toward whatever the family rewards, including differences it cannot see, so the family is not a certificate of what was preserved. CASE-041 is a documented instance: a Projected FastGAN trained against ImageNet features matches StyleGAN2’s FID, also computed in ImageNet features, while doing worse in CLIP space and with human judges. | Active |
| CLAIM-268 v2 | Model stitching certifies an order of information only in its reconstruction form: a map fitted to reproduce the target layers shows the source representation is at least as informative for every decision on the label, task-loss stitching compares one decision problem through a fixed head, and a failure to stitch is no evidence against sufficiency | The general content of CLAIM-126, filed alone under ADR-040 so that the result about stitching does not rest on CLAIM-050’s account of fidelity. Reconstruction-fitted stitching makes the target a garbling of the source given the label, which certifies one direction of Blackwell sufficiency (THEORY-176). Task-loss stitching (LIT-850) compares one decision problem through a fixed head, orders neither representation, and is not invariant under reparametrisation. In both forms a failure says only that no map in the class works. | Active |
| CLAIM-269 v5 | A regularized linear readout can tell apart only representations that differ in normalized kernel, and kernels fix a representation only up to the symmetry of what is observed, so no such readout supplies a distinction beyond that symmetry | The general content of CLAIM-193, filed alone under ADR-040 so that the linear result does not rest on CLAIM-142, whose realist reading is about communicative identity. What a regularized linear readout decodes is a function of the normalized kernel (THEORY-008). Kernels fix a representation only up to the symmetry of what is observed (THEORY-004, THEORY-723). An inner product beyond that is a stipulation (THEORY-018). And spectral degeneracy does not identify the symmetry (THEORY-019). These are proved results for learned representations. | Active |
| CLAIM-290 | A positive-definite kernel’s minimal realizations are unique up to a unitary, and two finite representation matrices with the same centred Gram matrix differ by a translation and an orthogonal map | The record’s own proofs of two steps that THEORY-004 rests on and that its sources state without proof. (a) Jorgensen & Tian’s Cor. 1.35: minimal realizations of a positive-definite kernel are unique up to a unitary. The book leaves this “as an exercise”, and NOTE-829 supplied the book’s own proof of Thm 4.35, transferred. (b) The finite case that LIT-250 §5.3 states as known: XXᵀ = YYᵀ implies Y = XQ with Q orthogonal, with no assumption that the rows span R^d. With centring this becomes a translation and an orthogonal map. It does not say Q is unique, which fails when the rank is below d. | Active |
| CLAIM-291 | The adjoint of a square-integrable integral operator is the integral operator with the conjugate-transposed kernel | The record’s own step, written down in THEORY-009 and marked there as not the Riesz article’s, which covers matrices and bounded operators only. For a kernel k in L²(μ⊗ν), the operator (Tf)(x) = ∫ k(x,y) f(y) dν(y) from L²(ν) to L²(μ) has adjoint (T*g)(y) = ∫ k̄(x,y) g(x) dμ(x), by Cauchy–Schwarz and Fubini. So T is self-adjoint, when μ = ν, exactly when k(x,y) = k̄(y,x) almost everywhere. It does not say where the symmetry of k comes from, which is THEORY-009’s question, and it is not claimed for kernels that are not square-integrable. | Active |
| CLAIM-356 v4 | An objective that originates outside a learning system can become a goal of the training organization, through its causal role in selecting, stabilizing and reproducing the learned structure it rewards; exogenous origin does not disqualify a goal, but it does not show that the network governs or endorses the objective, and what is selected is performance on the updating distribution, not generalization | The owner’s, U35 of the exchange of 2026-10-17, against A34’s guardrail that “Loss minimization does not automatically mean the model has its own goals”: the externally assigned objective “can motivate identification and persistence of learned features”, so the training process can be described as “having endogenous goals”. A35 granted it: “Yes, in a qualified but important sense”, and weakened the generalization half, since selection is for performance on “the encounters and feedback distribution actually used for updating”. It objects in part to CLAIM-288: it grants that a modeller-fixed objective does not show self-constitution, and denies that exogenous origin bars a goal from becoming the training organization’s own regulation. The sharp edge: the goal belongs to the training organization (CLAIM-367), not to the network, and nothing here says the network endorses or governs it. | Active |
| CLAIM-360 v2 | The deep-versus-shallow learning results separate three effects that aggregate loss conflates: a larger realizable function class, a larger set reachable within a fixed data and compute budget, and a different internal organization with the same attainable outcomes; the deep linear results show the third, the random-hierarchy results the second, and the depth-separation result for products of inputs the first, at fixed size | The owner’s, U38 of the exchange of 2026-10-17, on A37’s proposed experiment: “I think we may already have an empirical demonstration that would be useful here in the wide vs deep literature.” A38 refined it into three effects, (A) enlarged realizable function class, (B) enlarged budgeted reachable set, (C) new internal organization without better attainable outcomes, filed Saxe et al. under C and the random hierarchy model under B, and said A “needs a separately established expressivity restriction”. The record has one: Rolnick and Tegmark (THEORY-206), a separation at fixed neuron count. The sharp edge: which effect a result shows depends on the budget, and A38 warned against “depth produces individuation while width merely provides redundant capacity”. | Active |
| CLAIM-370 | For a symmetric positive-pair distribution with marginal p, the conditional-expectation operator on L²(p) has the density ratio K⁺ as its kernel, and it is Hilbert–Schmidt exactly when the χ²-divergence of the pair from the product of its marginals is finite, in which case it is compact and self-adjoint with an orthonormal eigenbasis | THEORY-005’s derivation, stated as the record’s own and with its proof. Johnson et al. (LIT-258) write the operator on a finite space without an integrability condition. HaoChen et al. (LIT-249) reach the Hilbert– Schmidt property from a uniform bound, which is stronger. Here the condition is exact: Hilbert–Schmidt if and only if finite χ². It says nothing about what trained features span. | Active |
| CLAIM-378 | A representational similarity index invariant to every invertible linear map depends on a representation only through its column space, so it takes one value on all column-centred representations of rank n − 1, as it does on all representations of rank n | The generalization of THEORY-236’s theorem. If col(X) = col(Y), write X = BC and Y = BD with B a basis of the common column space and C, D of full row rank, extend C and D to invertible matrices, and the quotient maps X onto Y. Since XA always has the column space of X, the GL(p) orbits are exactly the sets of n × p matrices sharing a column space. Theorem 1 is the case of column space ℝⁿ. Column-centred matrices of rank n − 1 all have column space 1^⊥, so an invariant index cannot tell them apart either. | Active |
| CLAIM-379 | On a finite set of stimuli, regularized linear readouts with ridge b > 0 cannot tell apart two centred representations of the same width exactly when one is an orthogonal transformation of the other, and the unregularized CCA member cannot tell apart representations with the same column space, which differ by an invertible linear map | The proved core of CLAIM-269. What a regularized linear readout decodes is a function of K_X = X G⁻¹ Xᵀ/M, with G = aC_X + bI (THEORY-008). For b > 0, K_X and the Gram matrix XXᵀ determine each other, by a monotone map on the shared eigenvalues; and equal Gram matrices mean an orthogonal transformation (CLAIM-290, THEORY-004). For b = 0, K_X is the projection onto the column space, which fixes X only up to an invertible linear map, as for a softmax layer (THEORY-723). | Active |
| CLAIM-382 | In an autoencoder initialised with i.i.d. Gaussian weights and zero biases and trained by SGD or momentum SGD on a loss of its output, the law of each hidden layer’s learned representation is invariant under every orthogonal map of that layer that commutes with its activation, so under a radial activation no basis is privileged in law, while elementwise tanh or Leaky-ReLU yields invariance only under the signed permutations or the permutations, which leaves the standard axes free to be privileged | THEORY-288’s symmetry argument, stated as the record’s own and proved. Transform the parameters by orthogonal maps Q_l of the hidden spaces that commute with the activation. The network then computes Q_l h_l and the same output, so the loss is invariant. Gradient steps commute with the transformation, and an i.i.d. Gaussian initialisation is invariant under it, so the law of the trained representations is too. For radial activations this is all of O(n), and no basis is privileged in law. For elementwise ones it is a finite group, so the axes may be privileged. Whether they are, and how strongly, is THEORY-288’s empirical content. The argument needs an orthogonally equivariant optimiser, and fails for Adam. | Active |
| CLAIM-385 v2 | If a symmetric operator on ℝⁿ commutes with an orthogonal representation of a compact group, each eigenspace is a sum of real irreducibles and each multiplicity a sum of multiples of their dimensions, so SO(2) and ℤ/n for n ≥ 3 force paired eigenvalues; conversely the spectrum fixes neither the group nor a basis inside an eigenspace | Active | |
| CLAIM-394 | In a stationary linear Gaussian VAR(1) that is time-reversible (AΠ = ΠAᵀ, Π the stationary covariance), every slow-feature direction is a left eigenvector of A, so any span of slow features is an exactly dynamically independent coarse-graining; off reversibility a slow feature is in general neither independent nor free of memory | Derived in the reading of Schüler and Wiskott (2025), NOTE-1015, and re-checked here. It says when slowness, the criterion of slow feature analysis (THEORY-746), picks out a closed coarse-graining in THEORY-733’s sense: always in the reversible linear Gaussian VAR(1), which is the class of noise-free square mixtures of independent AR(1) processes, and not in general otherwise. Linear features, linear Gaussian dynamics, lag one. | Active |
| CLAIM-498 | Averaging weights within a basin averages features: the network whose weights are the average of several networks in one low-loss basin has, in every layer, the average of their features | The averaging clause of THEORY-111’s old title, kept as a Proposed claim by the ADR-047 sweep of 2026-10-30 (kind 2) when the eleventh status review’s narrowing had dropped it. No source measured or asserts it: it is the record’s step from pairs to many-model averages, and its defeater is the averaging half of the old promote_when. | Proposed |
| CLAIM-543 | What separates a language model’s distribution over personas from a distribution over organizational perspectives is not whether the latent model is hierarchical, since a mixture or an LDA-style admixture already is, but whether some latent components condition which others are available or consequential: a model whose components are exchangeable given their weights is organizationally flat however many levels its prior has, and dependencies among components count as organization (organization as relational arrangement) only where interventions, not fit, support them | The owner’s U8 of the exchange “Assess SDT Coverage” (2026-11-02): “think of the relations as bayesian hierarchy, so H1 is a flat plate model and H2 has hierarchical/causal structure”, said of a language model read as a distribution over perspectives under the Persona Selection Model (U6). Stated here with A9’s correction: an LDA is itself a three-level hierarchical model drawn in plates, so “flat” has to mean organizationally flat, components exchangeable given their weights, not probabilistically flat. The precise form of the owner’s H1/H2 contrast is CLAIM-536. Proposed: the contrast is argued, and no study separates the two kinds of model on a language model. | Proposed |