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

作者：Sho Sonoda, Isao Ishikawa, Masahiro Ikeda · 发表于：Journal of Statistical Planning and Inference · 年份：2024 · DOI：10.1016/j.jspi.2024.106184 · 被引用次数：4 · 研究领域：Neural Networks and Applications、Image Processing and 3D Reconstruction、Advanced Image Fusion Techniques

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 γ so that a network NN[γ] reproduces f, i.e. NN[γ]=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 are distributed. However, for a variety of modern neural network architectures, the closed-form expression has not been known. In this paper, we explain a systematic method using Fourier expressions to derive ridgelet transforms for a variety of modern networks such as networks on finite fields Fp, group convolutional networks on abstract Hilbert space H, fully-connected networks on noncompact symmetric spaces G/K, and pooling layers, or the d-plane ridgelet transform.