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.
Compositionality — how the structure and meaning of a whole come from its parts and how they are combined — the principle of compositionality and compositional semantics, the emergence of compositional structure in languages under transmission, and composition and binding in learned models (generalization to unseen combinations, attribute binding, composing distributions or concepts). A work on making a model generalize compositionally is ML practice and goes to the anthology (ADR-031).
34 of 1352 THEORY documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| THEORY-117 v3 | In Uselis, Dittadi and Oh’s two-concept grids, ResNet-50s trained from scratch, with checkpoints chosen on the unseen pairs, reach unseen combinations as the share of combinations seen grows and not as up to four times more data of the same combinations is added; and when embeddings are exactly linearly factored, seen pairs that connect every value of both concepts, as two per value arranged in one cycle do, determine the embedding of every unseen pair | Uselis, Dittadi & Oh (2025), LIT-667. In an n × n grid of two concepts with k combinations seen per value, ResNet-50s trained from scratch fit seen pairs and fail on unseen ones; four times the data of the same combinations leaves 60–80% drops, while more values and more combinations help. Features pass from spurious, to decodable but entangled, to linearly factored as coverage grows. Model selection was on the test set, by design, so the results bound what is possible. The record re-derived that exactly factored embeddings of every unseen pair are fixed by seen pairs connecting every value, as the paper’s k = 2 cycle does. Honest selection, other architectures and more concepts are QUESTION-207. | Active |
| THEORY-164 v3 | As Raviv, Meyer and Lev-Ari report it, in a laboratory game where 12 fully connected groups of eight and 12 of four built a new communication system with total interaction held fixed, the larger groups’ languages grew more systematic faster, ended more systematic and differed less from one another, while communicative success and convergence did not differ by size; input variability, higher in the larger groups, predicted the next round’s gain in structure, an association measured and not manipulated | Raviv, Meyer & Lev-Ari (2019), LIT-825, read in NOTE-628: fully connected groups of eight built more systematic languages than groups of four, faster and more uniformly, with total interaction and network structure fixed; input variability, larger in bigger groups, predicted the gains. One laboratory study, two group sizes, and a mechanism supported by lagged association, not manipulation. It says nothing yet about natural communities, where size travels with network density and second-language learners. | Active |
| THEORY-167 v3 | The Russian wondertale is built from a small fixed set of character functions in a fixed order, so that all wondertales share one composition and differ in who performs the functions and how | Propp (1928), LIT-828, read in NOTE-615: in Afanasyev’s tales 50–151 the constant elements are 31 functions of characters, defined by their consequence for the action, occurring in one order and falling to seven roles. One analyst, one corpus of a hundred tales, and a class of “wondertales” redefined in the end as the tales that follow the scheme. It does not say all folktales, or all narratives, share the structure, and the claims of a single source tale and of mythic origin are conjectures the book does not support. | Proposed |
| THEORY-185 v4 | When each binary attribute of a word affects its co-occurrence independently and multiplicatively, the PMI is affine in the attributes with rank at most d + 1, so a spectral PMI embedding is a linear image of the attribute hypercube and parallelogram analogies hold exactly; over the full hypercube of words, each attribute’s two values equally frequent, the raw co-occurrence ratio mixes in products of attributes, and keeps exact analogies only when the strengths are alike enough that every attribute mode outranks every product mode | Korchinski, Karkada, Bahri and Wyart (2025), LIT-863: proved for a generative model of co-occurrence in which words are bundles of independent binary attributes, with robustness to noise, pruning and deleted pairs argued from eigenvalue bounds and simulated. The embeddings are eigendecompositions, not trained models; that real co-occurrence is close to this form is inferred from spectral and accuracy-curve shapes, not measured. | Active |
| THEORY-195 v3 | On the Random Hierarchy Model, in the experiments reported (s = 2, L ≤ 4, small v), deep CNNs matched to the tree and trained in a feature-learning regime reach a tenth of chance error from about n_c m^L examples, polynomial in the input dimension, at the training-set size at which their hidden layers become invariant to swapping synonymous tuples; two-layer networks and the same CNNs as fixed kernels need a number proportional to the whole input space, exponential in the input dimension, and deep CNNs stay near chance when every tuple is made equally likely in every class | Cagnetta, Petrini, Tomasini, Favero and Wyart (2023), LIT-877: measured for depth-(L + 1) CNNs and deep fully connected networks on the Random Hierarchy Model with s = 2 and L ≤ 4, with a large-v scaling argument for the correlation threshold and an exact one-step-gradient model of a two-layer network on one patch. The law n_c m^L is fitted, not proved for trained deep networks, and in this model the correlation threshold and the grammar’s size are the same expression, so the data cannot say which of the two sets it. | Active |
| THEORY-199 | In data generated by a random hierarchical grammar, the Bayes-optimal denoiser recovers the top-level class only below a threshold noise, which becomes sharp as the tree deepens and exists only when the grammar uses a small enough fraction of possible tuples (branching times that fraction below one), while low-level features degrade smoothly with noise and so survive past the threshold | Sclocchi, Favero and Wyart (2024), LIT-884: an annealed mean-field map of belief propagation on the Random Hierarchy Model, with its fixed points, checked against exact BP on single rule draws at s = 2, v = 32, L = 10. Not proved for quenched rules, a statement about an ideal denoiser that knows the grammar, not about a trained diffusion model. | Proposed |
| THEORY-200 v2 | On sparse hierarchical data, deep networks become insensitive to swapping synonymous parts and to small displacements of informative features at the training-set size at which they learn the task | Tomasini and Wyart (2024), LIT-880: measured for locally connected, convolutional and fully connected networks on the Sparse Random Hierarchy Model with s ≤ 3 and L ≤ 3, with thresholds for the two sensitivities tuned per setting; the sample size is about (s0 + 1)^L n_c m^L times s^(L/2) without weight sharing, with a one-step argument for the (s0 + 1)^L, and about (s0 + 1)^2 n_c m^L with it, unexplained. Both invariances keep the parent’s label statistics by construction, so the model shows that trained networks do the grouping, not that the invariances could not separate, and the extension to images is an analogy. | Proposed |
| THEORY-201 v2 | In next-token prediction on hierarchically generated sequences, the correlation between two tokens falls by about a factor m per level of their common ancestor, so a training set of P sequences resolves correlations only out to a distance t*(P) at which they meet sampling noise; learners come to represent the hidden symbols up to that depth, giving loss steps at about v m^(2ℓ−1) examples, and on character-level text the context at which the loss saturates grows as P^(1/(2β)) with β the measured correlation decay | Cagnetta and Wyart (2024), LIT-883, extending LIT-877 from labels to masked tokens: the correlation plateaus and the noise floor are derived for the Random Hierarchy Model in the large-v, large-m limit; the loss steps and the representation probes are measured in small transformers and CNNs; the link between them is argued, not proved; and the real-text evidence, from two character-level corpora, tests the effective context window, not the hierarchy. | Proposed |
| THEORY-203 | In data generated by a random hierarchical grammar, the tokens that Bayes-optimal noising and denoising changes do so in blocks set by the depth of the latent that changed, and the block size, measured as the correlation length of the changes, diverges at the noise threshold where the top-level class is lost, as a power of the distance to it whose exponent is log(branching) over log(slope of the level-to-level belief map at its unstable fixed point); a Gaussian field with power-law spectrum has instead a correlation length of changes that grows with noise to the end of the process | Sclocchi, Favero, Levi and Wyart (2024; ICLR 2025), LIT-886: an annealed mean-field computation of the pair statistics of token changes in the Random Hierarchy Model, a scaling argument for the exponent, and one data collapse against exact BP at v = 32, m = 8, s = 2. It builds on the threshold of THEORY-199 and inherits its limits. Not about trained diffusion models, and not evidence that text or images are hierarchical. | Proposed |
| THEORY-250 | DALL-E 3 renders single familiar relations well but is not robustly compositional: human-judged agreement falls when subject and object of an asymmetric relation are reversed and when two relations are combined, and its failures on reversed prompts are mostly wrong or role-swapped relations, not missing objects | Fu et al. (2025), LIT-938, read in full in NOTE-813. Three human-rating experiments on one model: the reversal drop is significant (t(29) = 3.67), the compositional result is descriptive, and the error analysis covers only images below 0.2 agreement. The authors’ explanation by training-data likelihood rests on a Spearman r of 0.09 against a GPT-3 proxy. The finding is about one generator, and the “>5 objects” failure often quoted with it comes from the vision-language models, not from DALL-E 3. | Proposed |
| THEORY-405 v2 | Adding one classifier-free guidance term per concept to a diffusion model’s unconditional noise prediction samples images that satisfy several concepts at once without retraining, and on synthetic scenes it composes object positions far better than compositional energy-based models but relations no better; the reading of the summed score as the score of a product of experts holds only for concepts conditionally independent given the image, unit weights, a conservative field and the noise-free distribution | Liu, Li, Du, Torralba & Tenenbaum (2022), LIT-770, read in NOTE-597. CLEVR object positions, 1/2/3 components: 86.42/59.20/31.36% against an EBM’s 70.54/28.22/7.34%. Relations: 60.40/21.84/2.80% against 78.14/24.16/4.26%. FFHQ attributes are comparable to LACE. Text-model composition (GLIDE, Stable Diffusion) is shown only in figures, with attribute confusion and hybrid objects among its listed failures. The product is derived at the data distribution and applied at every noise level, which NOTE-597 notes is in general not the score of the noised product. | Active |
| THEORY-519 | Supervised learners compose only once each carries a request function that passes a corrected input upstream; with it they form a symmetric monoidal category, and for a fixed step size and an error whose derivative in its first argument is invertible, gradient descent with backpropagation is a faithful strong symmetric monoidal functor into it from differentiable parametrised functions | Fong, Spivak & Tuyéras (2017; LICS 2019), LIT-827, read in full in NOTE-625, which followed the chain-rule proof of Theorem A.1 line by line. Learners (P, I, U, r) form Learn (Prop. II.4); Theorem III.2 makes gradient descent with backpropagation a functor Para → Learn. Covered: fixed step size, one datum per update, deterministic updates, and errors with invertible ∂e/∂x, which excludes cross-entropy at 0 and 1. That learners cannot compose without a request is argued, not proved. Learn says how learners compose, not whether they learn. | Active |
| THEORY-522 | Open text-to-image diffusion models of 2022–2023 render a single named object almost always but fail most on relative position and next on attribute binding, by human rating and by detector checks alike; scaling the image model or continuing pretraining does not fix position, and interactions are rated near ceiling only by rubrics that ask whether an action is depicted | GenEval (Ghosh, Hajishirzi & Schmidt 2023, LIT-782, NOTE-593) and T2I-CompBench with its journal extension (Huang et al. 2023 and 2025, LIT-783 and LIT-798, NOTE-592 and NOTE-610), two independent benchmarks that do not cite each other. GenEval: single object 0.97–0.98 for every diffusion model, position at most 0.15, binding at most 0.35. Human ratings in T2I-CompBench: 2D spatial 0.31–0.46, shape binding 0.51–0.70, interactions 0.81–0.99. Human ratings cover only six 2023-era models; the 2024–25 generation is ranked by automatic judges validated on the older ones, so the ordering is not established for it. | Active |
| THEORY-611 v2 | Classifier-free guidance extrapolates between a conditional and an unconditional score learned by one network; with exact scores this equals classifier guidance by the classifier the generative model defines through Bayes’ rule, but learned scores need not be conservative, so the guided field is in general the gradient of no density and the tilted distribution that motivates guidance is not shown to be what is sampled | Ho & Salimans (2022), LIT-839, read in full in NOTE-603, with the derivations of Section 3 checked line by line. The non-conservativeness argument is credited to Salimans & Ho (2021). The FID–IS trade-off is shown on class-conditional ImageNet only. NOTE-603 declined a THEORY because the anthology holds the account of what the guidance weight does to metrics; this one states only the probabilistic point, which the record’s CLAIM-123 uses. | Active |
| THEORY-678 v2 | In Stable Diffusion, a subject named in a two-subject prompt is left out of the image when its token governs no region of the cross-attention map early in sampling, and raising that token’s smoothed peak attention during the first half of sampling, by gradient steps on the latent with no retraining, brings the subject back; that this also fixes attribute binding is argued, not measured by the paper | Chefer, Alaluf, Vinker, Wolf & Cohen-Or (2023), LIT-806, read in NOTE-639, with T2I-CompBench++ (LIT-798, NOTE-610) for the binding measurement the paper lacks. Evidence is on 276 templated two-subject prompts by CLIP image–text similarity, BLIP-caption similarity and a 65-person preference study (77–91% preferred it); no neglect rate is reported, before or after. NOTE-639 filed no THEORY, because the paper’s method is machine-learning practice; the account of why subjects go missing is a finding about the model and is filed here as Proposed. | Proposed |
| THEORY-686 v2 | An observation modelled as a monotone map between preorders can show of a joined system more than the join of its observations of the parts, and out of a preorder with all joins the observations that preserve all joins, the empty join and infinite joins included, are exactly the left adjoints | Fong & Spivak (2018), LIT-803, Chapter 1, read closely in a Skimmed NOTE (NOTE-601) whose other chapters were seen only at their openings. Def. 1.93, after Adam, defines a generative effect as Φ(a) ∨ Φ(b) < Φ(a ∨ b). Prop. 1.111 and Thm 1.115 give that left adjoints preserve all joins and, from a source with all joins, only they do. The results are standard order theory, re-derived by the record because NOTE-601 is a skim. The absence of generative effects is weaker than preserving all joins, and does not characterise the left adjoints. | Active |
| THEORY-778 | In the Random Hierarchy Model with v symbols per level, m rules per symbol and s-tuples, the covariance between two tokens whose lowest common ancestor is ℓ levels up has zero mean over grammars and root-mean-square size about ((1 − m/v^(s−1))/(v³ m^(2ℓ−1)))^(1/2), falling by a factor m per level, while its estimate from P sequences carries noise of about (v²P)^(−1/2), so the two meet at P_ℓ ≈ v m^(2ℓ−1)/(1 − m/v^(s−1)); all to leading order in large v and m | Cagnetta and Wyart (2024), LIT-883, App. D–F, read in NOTE-687; re-derived to leading order by the promotion audit and checked against exact covariances of sampled grammars. A statement about the statistics of the generative model only: it says nothing about what a trained network learns, or when, and nothing about natural language. | Active |
| THEORY-786 | Deep networks learn hierarchically generated data from a number of examples set by when the correlations between input patches and the class rise above sampling noise, so detecting those correlations is how they learn the grammar, as Cagnetta and coauthors propose | Cagnetta, Petrini, Tomasini, Favero and Wyart (2023), LIT-877, propose that deep networks learn compositional data by detecting the correlations between input patches and the class, and that the sample complexity is where those correlations emerge from sampling noise. The record holds as shown, in THEORY-195, the measured law and the synonym-invariance it coincides with. This is the mechanism, filed under ADR-047 v4 when the narrowing dropped it. | Proposed |
| THEORY-794 | In vision models, compositional generalization to unseen combinations of concepts is driven by the diversity of the combinations seen in training rather than by data volume, and arrives with representations that are linearly factored by concept, as Uselis, Dittadi and Oh propose | Uselis, Dittadi & Oh (2025), LIT-667, read in NOTE-525. Their title and abstract present diversity of combinations, not data volume, as what drives compositional generalization in vision models. Their evidence is ResNet-50s trained from scratch on two-concept grids, with checkpoints chosen on the unseen pairs, and that measured part, with the factorization theorem, is the Active THEORY-117. This THEORY holds the general causal claim. | Proposed |
| THEORY-948 | On Stable Diffusion 2, MultiDiffusion’s 512 × 4608 panoramas had crops closer in FID to the reference model’s own samples than two outpainting baselines (10.3 against 18.4 and 45.5, fresh reference samples scoring 6.05) at equal CLIP score, over 8 prompts; and on 1,000 COCO layouts of two to four objects, the overlap of a segmenter’s output with the target layout was 0.26 IoU against 0.16–0.17 for the baselines and 0.43 for the real images, of which region fusion alone gave 0.18 and an early phase showing each region’s denoiser only its own region gave the rest | Bar-Tal, Yariv, Lipman and Dekel (2023), LIT-1522, read in NOTE-1158. Panorama quality is measured against the reference model’s own crops, not against real panoramas, and the baselines extrapolate from a centre image. The layout result rests on one segmenter and one overlap score, with spreads whose basis is not stated. Comparison with models trained for region-to-image generation is qualitative only. | Active |
| THEORY-949 | When several LoRAs take turns over one denoising trajectory, each given the same share of steps, the result depends on the schedule and not only on the shares: switching at every step scored worst (a composition win rate against weight merging near 38%, against about 59% when each LoRA kept five consecutive steps), shortening the turns late in sampling scored worse than keeping them fixed, and which LoRA acted first mattered more than the order of the rest, the character first scoring best and the style first slightly below a random order | Zhong et al. (2024), LIT-1529, read in NOTE-1160. An ablation of LoRA Switch judged by GPT-4V against weight merging. It says that equal shares of steps do not fix the outcome; it does not say how large the order effect is beyond noise, or how much each LoRA contributes to the image, which was not measured. The authors’ explanation, that core elements should come first, is theirs and untested. | Proposed |
| THEORY-955 | On 480 sets of two to five public LoRAs on two Stable Diffusion 1.5 checkpoints, GPT-4V’s paired judgements, averaged over both presentation orders and three seeds, scored giving each LoRA its own denoising steps in rotation (LoRA Switch) and averaging every LoRA’s guided noise prediction at every step (LoRA Composite) above merging the LoRAs’ weights at 0.8 each, at every number of LoRAs, the composition gap growing from 0.04–0.11 points of 10 at two LoRAs to 0.92–1.32 at five as merging fell from about 8.7 to 5.2; two annotators rating 120 images agreed in direction; the design does not separate composing at sampling time from the merged update’s scale growing with the number of LoRAs | Zhong et al. (2024), LIT-1529, read in NOTE-1160. The measurement is a GPT-4V comparison with a positional bias of about ten points, correlated 0.45 with two annotators, on LoRAs selected to be compatible. The two methods are compared with each other only through the baseline. It does not show that sampling-time composition is what helps: the baseline adds k updates at full scale, the two methods keep one adapter’s scale. | Active |
| THEORY-958 | When each view takes pixels directly (a crop of a larger canvas, or the whole image under a region mask), MultiDiffusion’s step, the least-squares reconciliation of several denoisers’ proposed next states, is their per-pixel average weighted by the weights of the views covering that pixel; this is exact for 0/1 weights, the only ones the paper uses, while for other weights the loss as printed weights by their squares; with a deterministic update affine in the noise prediction it is one step taken with the per-pixel weighted mean of the views’ noise predictions; and the guarantee that each view then follows the reference model’s diffusion path holds only if the loss is zero at every step, which overlapping proposals that disagree do not reach | Bar-Tal, Yariv, Lipman and Dekel (2023), LIT-1522, read in NOTE-1158. The fusion is an average, not a sum: where views overlap each takes a convex share of the pixel’s update. The paper’s closed form is the minimizer of its loss only for 0/1 weights. Its distributional guarantee is conditional on zero loss and, in the proceedings version, on strictly positive weights, so it covers neither the overlaps as they behave nor masked region generation. Nothing here says what distribution the fused sampler targets. | Active |
| THEORY-977 | In the two-layer attention-only transformer that Elhage et al. reverse-engineer, the second-layer heads that compose substantially with first-layer heads do so through their keys, mainly with a head that attends to the previous token and, after the published correction, also with one that attends over the last several tokens; these heads are induction heads, attending from a token to the one after its earlier occurrence, including on repeated random tokens, with positive-eigenvalue copying OV and same-matching QK circuits, and the second-order virtual-head terms add little to the loss reduction | Elhage et al. (2021), LIT-1534, read in NOTE-1189: Analyzing a Two-Layer Model, Induction Heads, Term Importance Analysis, and the Correction. Composition between heads was scored by a normalized Frobenius norm of matrix products, minus its value for random matrices. The heads it picked out attend to the token after the present token’s previous occurrence and copy it, which is the minimal induction circuit the framework predicts from K-composition with a previous-token head. It is one model, with no seeds or training details reported, and says nothing about models with MLPs or about when the heads form. | Active |
| THEORY-988 | In an attention-only transformer without layer norm or biases, once every attention pattern is held at its value on the input, the logits are exactly a sum of end-to-end path terms, a direct path from embedding to unembedding, one term per head and one per chain of heads composed through their values, and each head’s attention scores are a bilinear form in the tokens through which earlier heads can enter on the query side, the key side or both | Elhage et al. (2021), LIT-1534, read in NOTE-1189. For a two-layer model, T = Id ⊗ W_U W_E + Σ_h A^h ⊗ W_U W^h_OV W_E + Σ_{h₂,h₁} A^{h₂}A^{h₁} ⊗ W_U W^{h₂}_OV W^{h₁}_OV W_E, with each A^h computed from the model’s own run and then held fixed. It is an identity, not an approximation, and it is exact only under its conditions: no MLPs, no layer norm (which enters as a per-path rescaling), no biases, and attention frozen. It does not say the terms are small, interpretable or independent in what they compute. | Active |
| THEORY-1054 | One arrangement of harmonic particles on a finite graph, with the same wiring, potential and inverse-mass response, gives the discrete wave equation when the integrator stores position and momentum and the discrete heat equation when it stores position alone; both are governed by the symmetrized graph Laplacian, and the coupling data do not decide between them | Spivak (2026), LIT-1649, read in NOTE-1225 from arXiv v2. In the operad ArrSm, harmonic particles wired along a finite directed graph form one closed arrangement with potential Σ(κ_e/2)(q_tgt − q_src)². The phase semantics gives m_v q̈_v = −(L_G q)_v (Proposition 7.4.1) and a symplectic step; the configuration semantics gives m_v(q_v(t+1) − q_v(t)) = −(L_G q(t))_v (Remark 7.4.2). Active: both are short exact computations. It says nothing about time scales, and what differs between the two is a modelling choice, not the coupling. | Active |
| THEORY-1057 | Gradient descent with backpropagation, weight decay and Newton’s method are one discrete-time semantics of an operad of potential-carrying lenses, in which the state moves by subtracting the sharpened sum of three pulled-back covectors (from the output, from the input wiring and from the potential); the semantics is an operad functor, so a composite’s update is assembled from its parts’ updates, and backpropagation is that functoriality | Spivak (2026), LIT-1649, read in NOTE-1225 from arXiv v2. Lens internalization (Corollary 3.3.4) and an integrator give operad functors ArrSm → PC (Theorem 4.3.6, Corollary 6.4.1). Under the configuration integrator the state update is q ↦ q − ♯_q(ξ_Q), with ξ_Q the Q*-component of the sum in (58); a parameterized map wired to a loss gives gradient descent (76), a weight-only potential gives weight decay (Proposition 7.2.3), and an inverse-Hessian response gives Newton’s method (67). Active as mathematics. Per datum, deterministic, explicit-Euler; Adam and momentum are conjectures. | Active |
| THEORY-1063 | Black-boxing a passive linear circuit, which keeps only the Lagrangian relation its terminals’ potentials and currents can jointly satisfy, is a hypergraph functor from open circuits to Lagrangian relations: the external behaviour of a circuit glued from parts is the relational composite of the parts’ external behaviours, so circuits with the same behaviour are interchangeable in every composite, and the effective relation a composite presents at its boundary is fixed by its parts’ black boxes alone | Baez and Fong (arXiv 2015, TAC 2018), LIT-1644, read in NOTE-1223: Thm 1.1, proved as Thm 7.7, for circuits of passive, linear, two-terminal components over a field with positive elements, inductors and capacitors entering through the Laplace transform with zero initial conditions. The functor is not faithful, which is the point: circuits with one behaviour are identified. It says nothing about nonlinear or active components, and nothing in time-domain terms. | Active |
| THEORY-1089 | In a passive linear network, eliminating interior nodes by the principle of minimum power, which over a general field with positive elements is stationarity, takes a Dirichlet form to a Dirichlet form on the remaining nodes, linearly in their values; eliminating one node s adds c_is·c_js/Σ_k c_ks to each coupling c_ij, so two resistors in series act at their ends as one of resistance r_AB + r_BC; composing Dirichlet forms by this elimination is associative but lacks identities, because an ideal wire of zero impedance has no power functional | Baez and Fong (arXiv 2015, TAC 2018), LIT-1644, read in NOTE-1223: Thm 3.3, Lemma 3.4, Example 2.9 and Sec. 3.3. The elimination is what is usually called Kron reduction, a name the paper does not use. Over ℝ(s), with inductors and capacitors, the “minimum” is a formal stationarity condition, Kirchhoff’s current law at interior nodes. The absence of identities is computed for a one-element set and asserted as typical otherwise. | Active |
| THEORY-1140 | If every entity’s O(d) frame may change independently and relation transports change as Tᵢⱼ ↦ gᵢTᵢⱼgⱼ⁻¹, then functions of the transports alone carry no invariant information except around cycles, a triangle’s invariants are exactly the class functions of its holonomy H = TᵢⱼTⱼₖTₖᵢ, and an equivariant update of an edge from one cycle through it is Ψ(H)Tᵢⱼ with Ψ conjugation-equivariant; the symmetry fixes a family of updates, not one mechanism, and says nothing about whether a task has the symmetry | Sarkar, Mukherjee and Sato (2026), LIT-1820, §2 and App. B, read in NOTE-1331. The gauge-fixing argument is standard in lattice gauge theory and group synchronization, as the paper says, and its covariance was checked numerically here. Active: a conditional theorem. What it does not support is the paper’s framing: “unique” holds for a family, and the antecedent is an inductive bias by the companion paper’s own statement (LIT-1803). | Active |
| THEORY-1154 | People interpreting an analogy carry relations from base to target and drop the attributes of objects, and among the relations they prefer those bound into a system by higher-order relations, such as causal or mathematical constraints, over isolated ones (structure-mapping and its systematicity principle) | Gentner (1983), LIT-1810, read in NOTE-1349. Argued from worked examples (the Rutherford analogy, heat and water) with one study, summarized without statistics, showing relational content dominating interpretations of analogies but not descriptions of objects. The systematicity principle is stated as a likelihood on p. 163 and as determination in the abstract and summary. The rules work on a predicate structure the theory takes as given, which its footnote 4 concedes is a modelling choice. Proposed. | Proposed |
| THEORY-1158 v2 | On synchronization of S4 relations with outliers, an untrained mechanism that composes relations through third vertices gains 26–45 points over the single direct path, and weighting the candidate paths by the Wilson loops of squares that avoid the missing edge adds 0.6–7.8 points, most where clean two-hop paths become a minority; it stays below spectral synchronization with one reweighting pass on every setting and within 2.2 points of plain spectral synchronization either way; its 0.99 AUC for corrupted triangles is the ceiling that exactly flat clean data set, not a measure of detection power | Sarkar, Mukherjee and Sato (2026), LIT-1820, §3 and Table 1, read in NOTE-1331. The accuracies are the paper’s, on 1000 instances per cell, and were not rerun. The AUC ceiling was recomputed here: 1.42% of corrupted triangles at p = 0.3 have cancelling corruptions, so the ceiling is 0.9929. What the experiment does not show is anything about learned operators, language, or relations not given as group elements. | Active |
| THEORY-1164 | Propp proposes, from his analysis of Afanasyev’s tales 50–151, that the Russian wondertale is built from 31 character functions, each defined by its consequence for the action, occurring in one order and falling to seven roles, so that wondertales share one composition and differ in who performs the functions and how | What Propp’s Morphology proposes, split from THEORY-167 by the twelfth status review (ADR-058’s route, on THEORY-1110’s pattern) so that claims needing only the proposal can stand on it. The book was read in full in Russian (NOTE-615, with appendices II–III in a second text), so the reading of what it proposes is held. Whether the proposal is true of the class, which an independent coding would test, stays THEORY-167’s question, Proposed. The order is shown on 45 schemes Propp selected, partly for keeping it. | Active |
| THEORY-1171 | In groups that build a new communication system, larger groups make it more systematic, and the greater variety of input they face drives the effect | The wide form of Raviv, Meyer and Lev-Ari (2019), LIT-825, kept here when the fifteenth status review narrowed THEORY-164 to what their experiment showed and promoted it (ADR-047, kind 1). The paper asserts that larger groups make an emerging language more systematic and that the greater variety of input they face drives the effect. One laboratory study with two group sizes found the size effect, and the mechanism rests on lagged association within its data; whether the effect replicates, and whether variability causes it, is open. | Proposed |