A self consistent theory of Gaussian Processes captures feature learning effects in finite CNNs

• URL: http://arxiv.org/abs/2106.04110v1
• Date: Tue, 8 Jun 2021 05:20:00 GMT
• Title: A self consistent theory of Gaussian Processes captures feature learning effects in finite CNNs
• Authors: Gadi Naveh and Zohar Ringel
• Abstract summary: Deep neural networks (DNNs) in the infinite width/channel limit have received much attention recently. Despite their theoretical appeal, this viewpoint lacks a crucial ingredient of deep learning in finite DNNs, laying at the heart of their success -- feature learning. Here we consider DNNs trained with noisy gradient descent on a large training set and derive a self consistent Gaussian Process theory accounting for strong finite-DNN and feature learning effects.
• Score: 2.28438857884398
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep neural networks (DNNs) in the infinite width/channel limit have received much attention recently, as they provide a clear analytical window to deep learning via mappings to Gaussian Processes (GPs). Despite its theoretical appeal, this viewpoint lacks a crucial ingredient of deep learning in finite DNNs, laying at the heart of their success -- feature learning. Here we consider DNNs trained with noisy gradient descent on a large training set and derive a self consistent Gaussian Process theory accounting for strong finite-DNN and feature learning effects. Applying this to a toy model of a two-layer linear convolutional neural network (CNN) shows good agreement with experiments. We further identify, both analytical and numerically, a sharp transition between a feature learning regime and a lazy learning regime in this model. Strong finite-DNN effects are also derived for a non-linear two-layer fully connected network. Our self consistent theory provides a rich and versatile analytical framework for studying feature learning and other non-lazy effects in finite DNNs.

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