Double-descent curves in neural networks: a new perspective using Gaussian processes

Conference item

Double-descent curves in neural networks describe the phenomenon that the generalisation error initially descends with increasing parameters, then grows after reaching an optimal number of parameters which is less than the number of data points, but then descends again in the overparameterized regime. In this paper, we use techniques from random matrix theory to characterize the spectral distribution of the empirical feature covariance matrix as a width-dependent perturbation of the spectrum of the neural network Gaussian process (NNGP) kernel, thus establishing a novel connection between the NNGP literature and the random matrix theory literature in the context of neural networks. Our analytical expressions allow us to explore the generalisation behavior of the corresponding kernel and GP regression. Furthermore, they offer a new interpretation of double-descent in terms of the discrepancy between the width-dependent empirical kernel and the width-independent NNGP kernel.

Authors: El Harzli, O; Cuenca Grau, B; Valle-Pérez, G; Louis, AA

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Association for the Advancement of Artificial Intelligence
• Journal: Proceedings of the AAAI Conference on Artificial Intelligence
• Volume: 38
• Issue: 10
• Pages: 11856-11864
• Publication date: 2024-03-24
• Acceptance date: 2023-12-09
• Event title: Thirty-Eighth AAAI Conference on Artificial Intelligence
• Event location: Vancouver, Canada
• Event website: https://aaai.org/aaai-conference/
• Event start date: 2024-02-20
• Event end date: 2024-02-27
• DOI: 10.1609/aaai.v38i10.29071
• EISSN: 2374-3468
• ISSN: 2159-5399
• Commissioning body: Association for the Advancement of Artificial Intelligence
• ISBN-10: 1-57735-887-2
• ISBN-13: 978-1-57735-887-9
• Language: English
• Keywords: ML: deep learning theory; ML: kernel methods