Combinational-convolution for flow-based sampling algorithm

We propose a new class of efficient layer called {\it CombiConv} (Combinational-convolution) that improves the acceptance rate for the flow-based sampling algorithm for quantum field theory on the lattice. CombiConv is made from a $d$-dimensional convolution out of lower $k$-dimensional $\mycomb{d}{k}$ convolutions and combining their outputs, and CombiConv has fewer parameters than the standard convolutions.We apply CombiConv to the flow-based sampling algorithm,Furthermore, we find that for every $d=2,3,4$-dimensional scalar $\phi^4$ theory CombiConv for $k=1$ achieves a higher acceptance rate than others.