On Lazy Training in Differentiable Programming

TL;DR

This paper investigates the 'lazy training' phenomenon in neural networks, revealing it as a consequence of model scaling that makes training akin to linearized kernel methods, and shows its limitations in practical deep learning tasks.

Contribution

The work demonstrates that lazy training is not exclusive to over-parameterized networks and provides theoretical bounds and analysis for its occurrence in non-convex optimization.

Findings

Lazy training arises from model scaling, making neural networks behave like linear models.

Theoretical bounds are established for the difference between lazy and linearized training paths.

Lazy training degrades performance in practical deep convolutional neural networks.

Abstract

In a series of recent theoretical works, it was shown that strongly over-parameterized neural networks trained with gradient-based methods could converge exponentially fast to zero training loss, with their parameters hardly varying. In this work, we show that this "lazy training" phenomenon is not specific to over-parameterized neural networks, and is due to a choice of scaling, often implicit, that makes the model behave as its linearization around the initialization, thus yielding a model equivalent to learning with positive-definite kernels. Through a theoretical analysis, we exhibit various situations where this phenomenon arises in non-convex optimization and we provide bounds on the distance between the lazy and linearized optimization paths. Our numerical experiments bring a critical note, as we observe that the performance of commonly used non-linear deep convolutional neural networks in computer vision degrades when trained in the lazy regime. This makes it unlikely that "lazy training" is behind the many successes of neural networks in difficult high dimensional tasks.