DeepAI AI Chat
Log In Sign Up

Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent

by   Jaehoon Lee, et al.

A longstanding goal in deep learning research has been to precisely characterize training and generalization. However, the often complex loss landscapes of neural networks have made a theory of learning dynamics elusive. In this work, we show that for wide neural networks the learning dynamics simplify considerably and that, in the infinite width limit, they are governed by a linear model obtained from the first-order Taylor expansion of the network around its initial parameters. Furthermore, mirroring the correspondence between wide Bayesian neural networks and Gaussian processes, gradient-based training of wide neural networks with a squared loss produces test set predictions drawn from a Gaussian process with a particular compositional kernel. While these theoretical results are only exact in the infinite width limit, we nevertheless find excellent empirical agreement between the predictions of the original network and those of the linearized version even for finite practically-sized networks. This agreement is robust across different architectures, optimization methods, and loss functions.


Disentangling trainability and generalization in deep learning

A fundamental goal in deep learning is the characterization of trainabil...

Infinite-width limit of deep linear neural networks

This paper studies the infinite-width limit of deep linear neural networ...

On the Optimization Dynamics of Wide Hypernetworks

Recent results in the theoretical study of deep learning have shown that...

Asymptotics of Wide Networks from Feynman Diagrams

Understanding the asymptotic behavior of wide networks is of considerabl...

Implicit Acceleration and Feature Learning in Infinitely Wide Neural Networks with Bottlenecks

We analyze the learning dynamics of infinitely wide neural networks with...

A Bayesian Perspective on Training Speed and Model Selection

We take a Bayesian perspective to illustrate a connection between traini...