Understanding Simplicity Bias towards Compositional Mappings via Learning Dynamics

TL;DR

This paper investigates why neural networks tend to learn simple, compositional mappings, revealing that such mappings are the simplest bijections and that the bias towards simplicity is intrinsic to gradient descent training, aiding generalization.

Contribution

The study demonstrates that compositional mappings are the simplest bijections and that neural network training inherently favors learning these simple mappings, explaining their generalization capabilities.

Findings

Compositional mappings are the simplest bijections based on coding length.

Simplicity bias is an intrinsic property of neural network training via gradient descent.

Models trained properly tend to spontaneously generalize well due to this bias.

Abstract

Obtaining compositional mappings is important for the model to generalize well compositionally. To better understand when and how to encourage the model to learn such mappings, we study their uniqueness through different perspectives. Specifically, we first show that the compositional mappings are the simplest bijections through the lens of coding length (i.e., an upper bound of their Kolmogorov complexity). This property explains why models having such mappings can generalize well. We further show that the simplicity bias is usually an intrinsic property of neural network training via gradient descent. That partially explains why some models spontaneously generalize well when they are trained appropriately.