A general system of ordinary differential equations describing geodesics in the DLN is derived and an investigation into using an entropic log-volume form related to the geometry on the full-rank manifold as an explicit regularizer for a simple class of energies is investigated.
If a dataset locally looks like a low-dimensional linear space – a condition testable directly from data and derivable from the empirically supported manifold hypothesis under well-behaved conditions – then an approximating manifold M can be constructed and neural networks can approximate C1 functions uniformly on M, w...
Jakob Konstantin Hecker· Mitteilungen der Deutschen M...· 0 citations
This work studies the LLC of a graph attention model by exploiting symmetries in both the graph structure and the attention parameters, and develops an analytic framework through a teacher--student setting and explicit LLC estimates after considering the symmetry--induced degeneracies.
Vishnu Varadarajan, Mihir More, Aritra Das et al.· 0 citations
This work develops a bootstrap algorithm on Riemannian manifolds that is both computationally efficient and accurate for hypothesis testing and confidence region construction, and establishes high-order asymptotics under an appropriate coordinate representation induced by a second-order retraction.
Cheng-Zhu Huang, An-Ru R. Zhang· Annals of Statistics· 0 citations
It is shown that a symmetry fixes what variables are: a network layer is a sum over interchangeable units, so relabeling the units leaves it unchanged; given smoothness and the condition that a unit's gradient vanish at the origin, symmetry then enforces a universal leading form for the expansion about the near-zero we...
Zi-Yin Liu, Yi-Zhou Xu, Tomaso A. Poggio et al.· 0 citations
This work expresses the known accessibility transition in an equivalent conic form, centered for compact convex targets at the statistical dimension of the polar cone, and introduces Random Mapping Networks (RaMaN), which instantiate the predicted latent dimension using structured Hadamard or seed-regenerated Gaussian...
Andrew Cheng, Ali Eslamian, Jie Cheng et al.· 0 citations
This thesis develops a unified framework for Riemannian deep learning from three complementary perspectives: reusable neural modules, manifold-specific network architectures, and the design of underlying geometries.
Zi-Heng Chen· arXiv.org· 0 citations
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