3 papers
cs.LG2025
Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures
Mathilde Papillon, Sophia Sanborn, Johan Mathe +8
The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern mach…
cs.LG2024
The Selective G-Bispectrum and its Inversion: Applications to G-Invariant Networks
Simon Mataigne, Johan Mathe, Sophia Sanborn +2
An important problem in signal processing and deep learning is to achieve \textit{invariance} to nuisance factors not relevant for the task. Since many of these factors are describ…
cs.LG2024
Harmonics of Learning: Universal Fourier Features Emerge in Invariant Networks
Giovanni Luca Marchetti, Christopher Hillar, Danica Kragic +1
In this work, we formally prove that, under certain conditions, if a neural network is invariant to a finite group then its weights recover the Fourier transform on that group. Thi…