A unified Fourier slice method to derive ridgelet transform for a variety of depth-2 neural networks

arXiv:2402.15984v1 Announce Type: new
Abstract: To investigate neural network parameters, it is easier to study the distribution of parameters than to study the parameters in each neuron. The ridgelet transform is a pseudo-inverse operator that maps a given function $f$ to the parameter distribution $\gamma$ so that a network $\mathtt{NN}[\gamma]$ reproduces $f$, i.e. $\mathtt{NN}[\gamma]=f$. For depth-2 fully-connected networks on a Euclidean space, the ridgelet transform has been discovered up to the closed-form expression, thus we could describe how the parameters …

abstract arxiv cs.lg distribution fourier function maps math.fa network networks neural network neural networks neuron parameters stat.ml study type