arXiv:2606. 16579v1 Announce Type: new Abstract: We extend the entropy formula of Menon and Yu for the real Deep Linear Network (DLN) to its complex and quaternionic analogues, obtaining a unified formula for DLNs over $\mathbb{R}$, $\mathbb{C}$, and $\mathbb{H}$.
arXiv:2608.29279v1 Announce Type: new Abstract: Deep learning is often criticized for its theoretical research lagging behind practice. To make deep learning easier to understand, the entropy space t...
The paper proves two universality theorems for single‑neuron neural networks. First, it establishes a strong form of the Bovdi–Geche universality conjecture for neurons over finite fields, employing a modified discrete logarithm activation function and the Weil bound on multiplicative character sums. Second, it generalises Aizenberg’s universality theorem to complex binary neurons with a weight vector independent of the target function, using an equidistribution theorem for dilates of maps into tori.
arXiv:2509. 25778v3 Announce Type: replace Abstract: We presents a method for constructing neural networks intrinsically on statistical manifolds via the lognormal distribution.
arXiv:2609.07184v1 Announce Type: cross Abstract: We present tensor network representations for discrete maximum entropy distributions under expectation constraints. To this end, we introduce Computa...
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.
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.
arXiv:2609.05572v1 Announce Type: new Abstract: We prove that every strictly positive probability distribution on \(\{-1,1\}^n\) is represented exactly by a sigmoid belief network with finite paramet...
arXiv:2608. 01357v1 Announce Type: new Abstract: Traditional approximation theory measures convergence rates in terms of the number of parameters or degrees of freedom.
arXiv:2608. 19584v1 Announce Type: new Abstract: We study landscapes for complex-parameterized networks.
arXiv:2410. 00722v3 Announce Type: replace Abstract: We study convolutional neural networks with monomial activation functions.
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.
arXiv:2607. 19305v2 Announce Type: replace-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.