The Selective G-Bispectrum and its Inversion: Applications to G-Invariant Networks
(2024) NeurIPS 2024: The Thirty-Eighth Annual Conference on Neural Information Processing Systems — Location: Vancouver (10.December.2024)
Files
Invariant_NN_2024.pdf
Preprint
Open Access - Adobe PDF
- 1.91 MB
Details
- Authors
- Abstract
- 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—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.
- Affiliations
Citations
Mataigne, S., Johan Mathe, Sophia Sanborn, Christopher Hillar, & Nina Miolane. (2024). The Selective G-Bispectrum and its Inversion: Applications to G-Invariant Networks. Advances in Neural Information Processing Systems 37 (NeurIPS 2024), p. 115682--115711. https://hdl.handle.net/2078.5/252410