← Back to all news
arXiv Machine Learning By Luis Contreras, Marco Nahas, Tejas Kotwal

On the Entropy Formula for Real, Complex, and Quaternionic Deep Linear Networks

Read the original on arXiv Machine Learning →

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 $\mathbb{H}$.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Oct 28

Proofs of strong forms of the Bovdi--Geche universality conjecture and a complex analogue

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.

By Victor Bovdi, Ambrus Pal
More like this →
arXiv Machine Learning
Aug 3

A Hamiltonian driven Geometric Construction of Neural Networks via the Lognormal family, Application to Financial Fraud Detection and to Network Security

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
More like this →