Work

Interplay between depth and width for interpolation in neural ODEs

Year: 2024

Type: article

Abstract: for measures. In the high-dimensional and wide setting where d,p>N, our result can be refined to achieve L=0. This naturally raises the problem of data interpolation in the autonomous regime, characterized by L=0. We adopt two alternative approaches: either controlling in a probabilistic sense, or by relaxing the target condition. In the first case, when p=N we develop an inductive control strategy based on a separability assumption whose probability increases with d. In the second one, we establish an explicit error decay rate with respect to p which results from applying a universal approximation theorem to a custom-built Lipschitz vector field interpolating D.

Source: Neural Networks

DOI: 10.1016/j.neunet.2024.106640

Authors: Antonio Álvarez-López, Arselane Hadj Slimane, Enrique Zuazua

Institutions: Friedrich-Alexander-Universität Erlangen-Nürnberg, Universidad Autónoma de Madrid, École Normale Supérieure - PSL

Language: English

Topic: Neural Networks and Applications

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,350