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On neural network kernels and the storage capacity problem

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arxiv 2201.04669 v1 pith:KSULIU2K submitted 2022-01-12 cond-mat.dis-nn cs.LG

classification cond-mat.dis-nncs.LG
keywords neuralnetworkswidecapacitykernelliteraturenetworkproblem
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In this short note, we reify the connection between work on the storage capacity problem in wide two-layer treelike neural networks and the rapidly-growing body of literature on kernel limits of wide neural networks. Concretely, we observe that the "effective order parameter" studied in the statistical mechanics literature is exactly equivalent to the infinite-width Neural Network Gaussian Process Kernel. This correspondence connects the expressivity and trainability of wide two-layer neural networks.

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Cited by 1 Pith paper

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  1. Summary statistics of learning link changing neural representations to behavior

    q-bio.NC 2025-04 accept novelty 4.0 of 10

    A small set of population-level summary statistics can, in several solvable model classes, predict learning performance, and the authors argue these same statistics should guide analysis of neural recordings of learning.

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