In extensive-width networks, features are recovered sequentially through sharp phase transitions, yielding an effective width k_c that unifies Bayes-optimal generalization error scaling as Θ(k_c d / n).
Learning curves theory for hierarchi- cally compositional data with power-law distributed features
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Critical percolation clusters embedded in high dimensions, combined with taxonomic latent variables, form an analytically tractable synthetic data model whose ground-truth hierarchy can be linearly decoded from network activations.
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Sharp feature-learning transitions and Bayes-optimal neural scaling laws in extensive-width networks
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Critical percolation clusters embedded in high dimensions, combined with taxonomic latent variables, form an analytically tractable synthetic data model whose ground-truth hierarchy can be linearly decoded from network activations.
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