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).
13 of 371 QUESTION documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| QUESTION-069 | Is the connectedness of trained solutions a property of the solutions, or of the path family searched, the shared history that produced them and the regime they were trained in? | Filed in the fourth synthesis pass to give readings no question asked for a place in the argument. It bears on CLAIM-187 and CLAIM-142. THEORY-105, THEORY-107, THEORY-108, THEORY-109, THEORY-110 and THEORY-114 answer it in part; the body gives each one’s limit. | Open |
| QUESTION-080 | When a trained network’s parameters keep moving after its loss has converged, what about the network stays fixed, and is the last-layer geometry of neural collapse among the things that do? | The record holds two pictures of the end of training. In one, the last layer converges to a fixed geometry through the terminal phase (THEORY-083, neural collapse). In the other, the parameters never stop: they sample a stationary distribution at constant speed (THEORY-209). The two may describe different regimes. The terminal phase of neural collapse is cross-entropy training past zero error, with no finite minimum, while the limiting dynamics assume a quadratic minimum. Nothing in the record relates them. Drawn by the assistant from the reading of Kunin et al., and filed at the owner’s request. | Open |
| QUESTION-081 | When the relative scale of a network’s layers sets its learning regime under gradient flow, does that regime survive SGD, whose minibatch noise drives the relative scale toward balance, and on what timescale compared with learning? | Two readings meet here. Under gradient flow, the relative scale of adjacent layers is conserved and sets whether learning is rich or lazy (THEORY-212, Dominé et al.). Under SGD, that scale is not conserved: minibatch noise drives it toward the point where the layers’ gradient noise balances, at a rate set by η/S (THEORY-211, Ziyin et al.). If the drift is fast compared with learning, an unbalanced start chosen to be lazy would drift toward balance and richness. If it is slow, the regime set at initialization stands. Neither paper addresses the other. Drawn by the assistant from reading both, and filed at the owner’s request. | Open |
| QUESTION-124 | When do endorsement dynamics turn a transient conflict among an organization’s demands into a persistent regime of frustration, and can the condition be stated in an architecture-sensitive update geometry such as modular duality’s? | A33’s proposed next result, U33 of the exchange of 2026-10-17, after the owner asked whether “the modular duality program might be useful to us here”: “characterize frustration in a modular update geometry, then ask when the dynamics of endorsement convert a temporary optimization conflict into a persistent organizational regime.” The record has the static parts, the residual and its certificate (CLAIM-365) and the structural/governance split (CLAIM-357), and a linear capture threshold (CLAIM-330). It has no dynamics joining them. An answer gives a condition on the coupling of endorsement to demands under which governance-induced frustration persists after the conflict that started it is gone, and says whether the update geometry enters 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-164 | Does the law of balance hold in a deep network trained on real data during its limiting dynamics: for parameter groups related by a rescaling symmetry, does the difference of squared norms move toward the value where the groups’ gradient-noise traces are equal, at a rate that scales with learning rate over batch size? | The promotion condition formerly on THEORY-211, moved here unchanged when THEORY-211 was narrowed and promoted on 2026-10-19 to the SDE model in which the law of balance is proved. Whether the law holds for a deep network trained on real data is not shown; the tests are small synthetic networks. | Open |
| QUESTION-206 | Does stochastic gradient noise drive training into a mirror-symmetric subspace where it is a saddle, beyond the second-order, diagonal-Hessian argument, and does a trained network’s distance to that subspace fall to zero past a threshold set by noise and curvature? | The promotion condition formerly on THEORY-213. THEORY-213 was narrowed and promoted on 2026-10-20 (ADR-047 v2) to the exact half of Ziyin’s Theorem 1: a mirror symmetry’s subspace is invariant under gradient training, and weight decay above half the lower bound on the Hessian puts every minimum in it. The SGD half, attraction to the subspace even at a saddle, rests on a diagonal approximation and is open. | Open |
| QUESTION-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-312 | Does linear mode connectivity emerge during training rather than at initialization outside image classification and beyond MLPs: in a language model or transformer, for copies spawned from a shared state and for independent runs aligned under the architecture’s symmetry group, and for standard-width convnets or ResNets after alignment? | The promotion condition formerly on THEORY-114, moved here when the tenth status review narrowed it to the image-classification networks and MLPs its two sources measured and promoted it, as THEORY-285’s moved to QUESTION-303. | Open |
| QUESTION-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-363 | When does the order in which stochastic gradient descent comes to occupy a network’s organizations over training time follow the order in which they come to dominate the Bayesian posterior as the sample grows, and what fixes the correspondence where it holds: an effective temperature set by learning rate and batch size, the accessibility of regions and the barriers between them, or the time allowed to equilibrate? | The owner’s challenge at U4 of the exchange “Analyze nucleation concepts” (2026-10-31). A3 had said that “Bayesian posterior dominance as sample size n changes is not the same process as gradient-based optimization as training time advances”. The owner: “Isn’t it? I think there’s a David M Blei paper that discusses this.” The paper is Mandt, Hoffman and Blei 2017 (LIT-1898). A4 conceded the separation was “too strong” and kept a narrower one, which is this question. It refines QUESTION-039, which asks what sets the order and moment of acquisition. | Open |