The Birkhoff Geometry of Manifold-Constrained Hyper-Connections: Two Channels, Vertex Viscosity, and Sinkhorn as a Retraction 9D2N76AJAT
| URI | m2://res/9D2N76AJAT |
|---|---|
| Kind | preprint |
| Creators | Xiaoyu Li, Zhizhou Sha, Chiwun Yang |
| Date | 2026-10-05 |
| Subjects | arxiv cs.LG, arxiv math.OC, arxiv stat.ML |
| Scope | border |
Expressions
e1: version, preprint
| Date | 2026-10-05 |
|---|---|
| Ids | arXiv 2610.06653 |
Items in this resource
The mentions of the inventory that name this resource. Each name links to the card of its inventory row.
| Item | Kind | Where | Source |
|---|---|---|---|
| Induced dynamics | statement | theorem 4.3 | arxiv |
| Cayley transform | statement | lemma D.8 | arxiv |
| Rigidity | statement | proposition 3.4 | arxiv |
| Balancing equations are normal equations | statement | lemma E.2 | arxiv |
| Perron--Frobenius | statement | theorem D.3 | arxiv |
| Convergence on $\On$ | statement | proposition B.4 | arxiv |
| Two channels | statement | theorem 3.1 | arxiv |
| Sinkhorn | statement | theorem D.2 | arxiv |
| Vertex viscosity of the logit flow | statement | theorem 5.3 | arxiv |
| Operator-norm ball | statement | lemma D.6 | arxiv |
| Contraction | statement | theorem 3.2 | arxiv |
| Global chart | statement | lemma 4.1 | arxiv |
| Exponential rate of the Fisher--Rao flow | statement | theorem 5.4 | arxiv |
| Birkhoff--von Neumann | statement | theorem D.1 | arxiv |
| Width as a fading memory | statement | corollary 3.3 | arxiv |
| Small gradients near vertices | statement | lemma 5.2 | arxiv |
| Gauge complement | statement | lemma E.1 | arxiv |
| The price of a long horizon | statement | corollary 5.6 | arxiv |
| Local convergence factor | statement | proposition 6.1 | arxiv |
| Two streams | statement | proposition 5.5 | arxiv |
| Weighted additive fits | statement | lemma 5.1 | arxiv |
| Monotonicity of the vertex proximity | statement | lemma E.4 | arxiv |
| Differential of the chart | statement | lemma 4.2 | arxiv |
| Knight | statement | theorem D.10 | arxiv |
| A norm inequality | statement | lemma D.7 | arxiv |
| Drift of the backward gain | statement | proposition 6.2 | arxiv |
| Spanning trees and incidence matrices | statement | theorem D.5 | arxiv |
| Cauchy--Binet formula and Cramer's rule | statement | theorem D.4 | arxiv |
| Isometric mixers | statement | proposition 7.1 | arxiv |
| Block structure | statement | lemma E.3 | arxiv |
| Dini comparison | statement | lemma E.5 | arxiv |
| Hilbert's projective metric | statement | theorem D.9 | arxiv |
Catalogue records
- arxiv: 2610.06653 (work)