2024/07/10 by Simon Mataigne, Mataigne, Simon, Johan Mathe +7 · 2 citations
Computer Science · Engineering · Mathematics · #20K01 #68R01 #68T01 #68T07 #Blind Source Separation Techniques #Control Systems and Identification #FOS: Computer and information sciences #Machine Learning (cs.LG) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2407.07655
openalex publication_date 2024/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An important problem in signal processing and deep learning is to achieve invariance to nuisance factors not relevant for the task. Since many of these factors are describable as the action of a group G (e.g. rotations, translations, scalings), we want methods to be G-invariant. The G-Bispectrum extracts every characteristic of a given signal up to group action: for example, the shape of an object in an image, but not its orientation. Consequently, the G-Bispectrum has been incorporated into deep neural network architectures as a computational primitive for G-invariance\textemdash akin to a pooling mechanism, but with greater selectivity and robustness. However, the computational cost of the G-Bispectrum (O(|G|2), with |G| the size of the group) has limited its widespread adoption. Here, we show that the G-Bispectrum computation contains redundancies that can be reduced into a selective G-Bispectrum with O(|G|) complexity. We prove desirable mathematical properties of the selective G-Bispectrum and demonstrate how its integration in neural networks enhances accuracy and robustness compared to traditional approaches, while enjoying considerable speeds-up compared to the full G-Bispectrum.