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.
Loss landscapes — the geometry of trained solutions in weight space — mode connectivity, linear and along curves, barriers between minima and the permutation symmetries that hide or remove them, re-basin alignment, star domains and connecting simplexes, local versus global landscape structure, and model merging as its use (ADR-027).
8 of 547 CLAIM documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| 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-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-351 | A zero aggregate gradient does not show that the demands it aggregates are reconciled: with positive weights it holds both when every demand’s own gradient vanishes and when nonzero gradients cancel, and in the second case no update improves them all to first order; even the first is only joint first-order stationarity, which a demand’s maximum or saddle also has | A33 §5 of the exchange of 2026-10-17: “Zero aggregate gradient does not imply absence of frustrated demands.” With L₁ = (θ − 1)² and L₂ = (θ + 1)² at θ = 0 (CASE-115), the equal-weight gradient is zero and the aggregate is at its global minimum, while each loss is 1 and wants the opposite move. In general a vanishing positive combination of gradients is either every gradient zero or a certificate that no update improves them all, and the scalar cannot tell which. The sharp edge: it is a fact about a weighted sum, not about what a monitor reading it represents. A29’s “the unity of the distress signal need not arise from the unity of the underlying causes” is the interpretive reading, kept apart in the body. | Active |
| CLAIM-365 v2 | On a norm-ball update set the local frustration residual Φ_r = min over ‖d‖ ≤ r of max_i(ε_i + g_iᵀd) equals the maximum over the simplex of Σλ_iε_i − r‖Σλ_ig_i‖_*, so infeasibility of the declared improvements has a certificate, and any admissible actual update exceeds Φ_r by a nonnegative governance regret | A34 §4 and A35 §3 of the exchange of 2026-10-17, checked. The residual is the smallest worst-case shortfall of the declared local improvements ε_i over updates of size at most r. Minimax for the bilinear problem on two compact convex sets gives the dual over the simplex, so Φ_r > 0 exactly when some λ certifies that no update meets all demands (A34’s form). Governance regret Γ is the gap between an actual admissible update’s shortfall and Φ_r, and is never negative. For L₁ = (θ − 1)², L₂ = (θ + 1)² at θ = 0, Φ_r = ε for every r. The sharp edge: per A37 it is a cardinal refinement of the ordinal fact (CLAIM-347), and its magnitude depends on units (A36 §2D). | Active |
| CLAIM-366 v3 | Whether several objectives share a strict first-order descent direction, 0 ∉ conv{g_i}, is invariant under smooth invertible reparameterization, while the sign of a Euclidean gradient inner product is not, and a negative inner product does not exclude common descent; a budgeted version is invariant only with the metric pulled back | A35 §2 of the exchange of 2026-10-17, at the owner’s U35 “double click” on whether functionally equivalent parameterizations give equivalent frustration diagnoses. Gradients transform as g′ = Jᵀg and directions as v′ = J⁻¹v, so directional derivatives, and with them the common-descent test 0 ∉ conv{g_i}, do not depend on coordinates. A Euclidean inner product does: g₁ = (1, 1), g₂ = (1, −½) have product ½, and under θ = diag(½, 2)ψ their transforms have −7/4, while d = (−1, 0) lowers both throughout. The sharp edge: it covers coordinate changes of one parameter space at first order, not function-preserving symmetries or training trajectories (QUESTION-127). The practice corollary, not to diagnose task conflict by gradient cosine, is the anthology’s. | 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-499 | The linear barrier left after aligning independently trained networks over the architecture’s symmetries rises with depth | The depth clause of THEORY-112’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 measures or states it for barriers after alignment: it is the record’s composition of Entezari et al.’s unaligned depth curves with Ferbach et al.’s compounding width bound. Its defeater is the depth paragraph of the old promote_when. | Proposed |
| CLAIM-524 | Whether functionally equivalent realizations are connected depends on which paths are admissible: for f = u₁v₁ + u₂v₂ with nonnegative weights, (1, 1, 0, 0) and (0, 0, 1, 1) are joined by a curve along which f stays 1 though the straight line between them falls to ½, and under any resource budget below √2 times the endpoints’ cost no path with f = 1 joins them | From the owner’s remark at U17 of the exchange “Analyze nucleation concepts” (2026-10-31), that the reconstruction fibres “reminds me of loss landscape connected mode stuff (which might just be a consequence of high dimensional geometry? … probably already discussed on the nucleation record)”. It is: see below. A17 §9 gave the curve and A18 §7 the budget for a tied-weight family; the general bound here is the reader’s, rechecked. “Viable mode connectivity” is A18’s name and is not filed as a term. | Active |