A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.
arXiv preprint arXiv:1810.04374 , year=
4 Pith papers cite this work. Polarity classification is still indexing.
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An extension of the finite expression method using TranNet-initialized shallow neural operators is proposed as an effective solver for high-dimensional partial differential equations.
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Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model
A solvable hierarchical model with power-law feature strengths yields explicit power-law scaling of prediction error through sequential recovery of latent directions by a layer-wise spectral algorithm.
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A unified data reconstruction attack achieves provable finite-width recovery in random feature networks and efficient subspace-based reconstruction for general models using weight changes.
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Random Neural Network Expressivity for Non-Linear Partial Differential Equations
Random neural networks achieve a dimension-free approximation rate of 1/2 for sufficiently regular time-dependent Sobolev functions and can efficiently approximate solutions to Porous Medium Equations and Compressible Navier-Stokes Equations.
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Finite Expression Method with TranNet-based Function Learning for High-Dimensional Partial Differential Equations
An extension of the finite expression method using TranNet-initialized shallow neural operators is proposed as an effective solver for high-dimensional partial differential equations.