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Ollivier-Ricci curvature in cycle overlap mode
Announce Type: replace Abstract: Ollivier-Ricci curvature of an edge (x,y) is defined by comparing the distance taken to transport from neighbors of x to neighbors of y. It is a structural measure that has been studied in many fields such as community detection and deep neural networks. However, high computational complexity or error limits its application in large scale-free graphs.
Ollivier-Ricci curvature in cycle overlap mode
Announce Type: new Abstract: Ollivier-Ricci curvature of an edge (x,y) is defined by comparing the distance taken to transport from neighbors of x to neighbors of y. It is a structural measure that has been studied in many fields such as community detection and deep neural networks. However, high computational complexity or error limits its application in large scale-free graphs.
Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation
Announce Type: replace Abstract: The pointwise determinant ratio \[ R_\psi(z)\equiv \log\!\left(\frac{\det g_{\mathrm{RF}}(z;\psi)}{\det g_{\mathrm{FS}}(z)}\right) \] measures how the Ricci-flat metric on the Dwork quintic departs from the Fubini--Study baseline. We ask whether this scalar observable can be described compactly in terms of a small number of projective invariants, and whether the same scaffold remains usable across complex-structure moduli. Using Donaldson's $k=10$ balanced...
Exponential thermalisation of viscous fluids on negatively curved manifolds
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Post-Training Neural Network Pruning using Graph Curvature
arXiv:2601.16366v2 Announce Type: replace Abstract: This paper provides a fresh view of the neural network (NN) pruning problem through the lens of graph theory. To achieve effective pruning, we aim to identify the main NN data flows and the corresponding NN connections that are most and least important for the performance of the full model. Unlike the standard approach to NN data flow analysis, which is based on information theory, we employ the notion of graph curvature, specifically...
Resolving the viscosity operator ambiguity on Riemannian manifolds via a kinematic selection principle
arXiv:2605.17502v2 Announce Type: replace-cross Abstract: On a general Riemannian manifold the Navier-Stokes equations admit several inequivalent formulations, differing in the choice of viscous operator: the Hodge Laplacian, the Bochner Laplacian, or the deformation Laplacian. We show that a Lagrangian kinematic construction, in which the strain rate is built from the rate of change of inner products of Lie-dragged connecting vectors, uniquely selects the deformation Laplacian for fluids...
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