Sampling weights of deep neural networks

Erik Lien Bolager, Iryna Burak, Chinmay Datar, Qing Sun, Felix Dietrich

Research output: Contribution to journalConference articlepeer-review

Abstract

We introduce a probability distribution, combined with an efficient sampling algorithm, for weights and biases of fully-connected neural networks. In a supervised learning context, no iterative optimization or gradient computations of internal network parameters are needed to obtain a trained network. The sampling is based on the idea of random feature models. However, instead of a data-agnostic distribution, e.g., a normal distribution, we use both the input and the output training data to sample shallow and deep networks. We prove that sampled networks are universal approximators. For Barron functions, we show that the L2-approximation error of sampled shallow networks decreases with the square root of the number of neurons. Our sampling scheme is invariant to rigid body transformations and scaling of the input data, which implies many popular pre-processing techniques are not required. In numerical experiments, we demonstrate that sampled networks achieve accuracy comparable to iteratively trained ones, but can be constructed orders of magnitude faster. Our test cases involve a classification benchmark from OpenML, sampling of neural operators to represent maps in function spaces, and transfer learning using well-known architectures.

Original languageEnglish
JournalAdvances in Neural Information Processing Systems
Volume36
StatePublished - 2023
Event37th Conference on Neural Information Processing Systems, NeurIPS 2023 - New Orleans, United States
Duration: 10 Dec 202316 Dec 2023

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