Scaling can lead to compositional generalization

TL;DR

This paper demonstrates that scaling data and model size enables neural networks to achieve compositional generalization across tasks, with theoretical proofs and practical decoding methods linking internal representations to task success.

Contribution

It shows that standard neural networks can generalize compositionally when sufficiently scaled and trained on comprehensive data, supported by theoretical and empirical evidence.

Findings

Scaling data and model size improves compositional generalization.

Standard multilayer perceptrons can approximate compositional tasks with linear neurons.

Linearly decodable task constituents correlate with successful generalization.

Abstract

Can neural networks systematically capture discrete, compositional task structure despite their continuous, distributed nature? The impressive capabilities of large-scale neural networks suggest that the answer to this question is yes. However, even for the most capable models, there are still frequent failure cases that raise doubts about their compositionality. Here, we seek to understand what it takes for a standard neural network to generalize over tasks that share compositional structure. We find that simply scaling data and model size leads to compositional generalization. We show that this holds across different task encodings as long as the training distribution sufficiently covers the task space. In line with this finding, we prove that standard multilayer perceptrons can approximate a general class of compositional task families to arbitrary precision using only a linear number of neurons with respect to the number of task modules. Finally, we uncover that if networks successfully compositionally generalize, the constituents of a task can be linearly decoded from their hidden activations. We show that this metric correlates with failures of text-to-image generation models to compose known concepts.