Neural networks trained with SGD learn distributions of increasing complexity
This work addresses the problem of understanding how neural networks generalize by revealing a simplicity bias related to data structure, which is incremental as it builds on existing theories of simplicity biases.
The paper demonstrates that neural networks trained with stochastic gradient descent initially rely on lower-order input statistics (e.g., mean and covariance) and only later exploit higher-order statistics, a phenomenon termed distributional simplicity bias (DSB). This was shown in a solvable model with synthetic data and empirically validated in deep convolutional networks and visual transformers on CIFAR10, even extending to ImageNet pre-trained networks.
The ability of deep neural networks to generalise well even when they interpolate their training data has been explained using various "simplicity biases". These theories postulate that neural networks avoid overfitting by first learning simple functions, say a linear classifier, before learning more complex, non-linear functions. Meanwhile, data structure is also recognised as a key ingredient for good generalisation, yet its role in simplicity biases is not yet understood. Here, we show that neural networks trained using stochastic gradient descent initially classify their inputs using lower-order input statistics, like mean and covariance, and exploit higher-order statistics only later during training. We first demonstrate this distributional simplicity bias (DSB) in a solvable model of a neural network trained on synthetic data. We empirically demonstrate DSB in a range of deep convolutional networks and visual transformers trained on CIFAR10, and show that it even holds in networks pre-trained on ImageNet. We discuss the relation of DSB to other simplicity biases and consider its implications for the principle of Gaussian universality in learning.