Scaling Laws and Representation Learning in Simple Hierarchical Languages: Transformers vs. Convolutional Architectures
This work clarifies architectural biases in neural scaling laws, addressing how model architecture interacts with data statistics for representation learning, though it is incremental as it extends a prior theoretical framework.
The authors investigated how neural language models learn hierarchical structure from next-token prediction by deriving theoretical scaling laws for performance on synthetic datasets from the Random Hierarchy Model. They found that convolutional networks, due to their local and weight-sharing structure aligning with the generative process, scale faster in performance compared to transformers, which rely on global self-attention.
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.