Communication Dynamics Neural Networks: FFT-Diagonalized Layers for Improved Hessian Conditioning at Reduced Parameter Count

ArXi:2605.08171v1 Announce Type: cross Background and motivation. The Communication Dynamics (CD) framework, Layer construction. CDLinear is a block-circulant linear layer with block size B = 2l+1 and 1/B the parameter count of a dense layer of equal input/output dimensions. Three properties follow from the construction. (i) The Hessian of mean-squared loss with respect to the weights is diagonalized by the discrete Fourier transform, with eigenvalues |F[Xj](k)|^2 read directly from the input statistics (Theorem 1.