Scaling Laws and Representation Learning in Simple Hierarchical Languages: Transformers vs. Convolutional Architectures

TL;DR

This paper develops theoretical scaling laws for neural language models trained on synthetic hierarchical data, showing that convolutional architectures outperform transformers in learning efficiency due to architectural biases.

Contribution

It extends existing theory to compare how convolutional and transformer models learn hierarchical structures, revealing the impact of architectural biases on scaling behavior.

Findings

Convolutional networks scale faster than transformers on hierarchical data.

Architectural biases influence the efficiency of representation learning.

Theoretical predictions are empirically validated with synthetic datasets.

Abstract

How do neural language models acquire a language's structure when trained for next-token prediction? We address this question by deriving theoretical scaling laws for neural network performance on synthetic datasets generated by the Random Hierarchy Model (RHM) -- an ensemble of probabilistic context-free grammars designed to capture the hierarchical structure of natural language while remaining analytically tractable. Previously, we developed a theory of representation learning based on data correlations that explains how deep learning models capture the hierarchical structure of the data sequentially, one layer at a time. Here, we extend our theoretical framework to account for architectural differences. In particular, we predict and empirically validate that convolutional networks, whose structure aligns with that of the generative process through locality and weight sharing, enjoy a faster scaling of performance compared to transformer models, which rely on global self-attention mechanisms. This finding clarifies the architectural biases underlying neural scaling laws and highlights how representation learning is shaped by the interaction between model architecture and the statistical properties of data.