A convolutional Ising classifier has two convolutional layers with periodic padding
PHYSICS · Multi-part · Fermi University Physics · Computational Physics · High-performance and data-driven computational physics · High-performance and data-driven computational physics
Scientific Computing for Physicists, Ch Neural networks on physical data: backpropagation, convolution and symmetry
Problem
A convolutional Ising classifier has two 3×3 convolutional layers with periodic padding, the first taking the single spin channel to 8 channels and the second taking those 8 channels to 16, each with one bias per output channel. A global average over sites turns the 16 channel maps into 16 numbers, which feed one sigmoid output unit with its own weights and bias.
((a)) Count the parameters of each convolutional layer and of the output unit, and give the total.
((b)) Give the total for lattices of side L=16 and L=128.
((c)) For comparison, count the parameters of a dense layer taking all L2 spins to 8 hidden units, at L=16 and at L=128.