Just How Flexible are Neural Networks in Practice?

TL;DR

This paper investigates the practical flexibility of neural networks, revealing that standard training methods limit their ability to fit data compared to theoretical capacity, with implications for model efficiency and generalization.

Contribution

It provides empirical insights into how optimization and architecture influence the data fitting capacity of neural networks in practice.

Findings

Optimizers find minima fitting fewer samples than parameters suggest

Convolutional networks are more parameter-efficient than MLPs and ViTs

SGD fits more data than full-batch gradient descent

Abstract

It is widely believed that a neural network can fit a training set containing at least as many samples as it has parameters, underpinning notions of overparameterized and underparameterized models. In practice, however, we only find solutions accessible via our training procedure, including the optimizer and regularizers, limiting flexibility. Moreover, the exact parameterization of the function class, built into an architecture, shapes its loss surface and impacts the minima we find. In this work, we examine the ability of neural networks to fit data in practice. Our findings indicate that: (1) standard optimizers find minima where the model can only fit training sets with significantly fewer samples than it has parameters; (2) convolutional networks are more parameter-efficient than MLPs and ViTs, even on randomly labeled data; (3) while stochastic training is thought to have a regularizing effect, SGD actually finds minima that fit more training data than full-batch gradient descent; (4) the difference in capacity to fit correctly labeled and incorrectly labeled samples can be predictive of generalization; (5) ReLU activation functions result in finding minima that fit more data despite being designed to avoid vanishing and exploding gradients in deep architectures.