Convolutional networks trained on a random hierarchical grammar improve twice as fast with data as transformers, because weight sharing reuses the statistical signal across all positions.
These correlations are given by the fol- lowing (vm)×v C(X−t,X−1)µ,ν :=P{X−t =µ,X−1 =ν} − P{X−t =µ} P{X−1 =ν}
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Scaling Laws and Representation Learning in Simple Hierarchical Languages: Transformers vs. Convolutional Architectures
Convolutional networks trained on a random hierarchical grammar improve twice as fast with data as transformers, because weight sharing reuses the statistical signal across all positions.