arXiv:2509. 25778v3 Announce Type: replace Abstract: We presents a method for constructing neural networks intrinsically on statistical manifolds via the lognormal distribution.
By Prosper Rosaire Mama Assandje, Landry Foka Marius, Arnaud Gires Fobasso Tchinda, Fr\'ed\'eric Barbaresco, St\'ephane R. Gael Ekodeck, Serge Alain Ebele
arXiv:2606. 04390v1 Announce Type: new Abstract: We find the asymptotic ratio between the storage capacities when enforcing real pre-activations in a complex hypothesis class as opposed to complex ones in the same class.
By Andrew Gracyk
arXiv:2512. 19819v2 Announce Type: replace-cross Abstract: One of the primary applications of classical Boltzmann machines is generative modeling, wherein the goal is to tune the parameters of a model distribution so that it closely approximates a target distribution.
By Mark M. Wilde
arXiv:2608. 01357v1 Announce Type: new Abstract: Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom.
By Tong Mao, Jinchao Xu
arXiv:2410. 00722v3 Announce Type: replace Abstract: We study convolutional neural networks with monomial activation functions.
By Vahid Shahverdi, Giovanni Luca Marchetti, Kathl\'en Kohn
arXiv:2607. 19305v1 Announce Type: cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
By Chen Ziheng