  We present a novel approach which is able to explore the configuration of
grouped convolutions within neural networks. Group-size Series (GroSS)
decomposition is a mathematical formulation of tensor factorisation into a
series of approximations of increasing rank terms. GroSS allows for dynamic and
differentiable selection of factorisation rank, which is analogous to a grouped
convolution. Therefore, to the best of our knowledge, GroSS is the first method
to enable simultaneous training of differing numbers of groups within a single
layer, as well as all possible combinations between layers. In doing so, GroSS
is able to train an entire grouped convolution architecture search-space
concurrently. We demonstrate this through architecture searches with
performance objectives on multiple datasets and networks. GroSS enables more
effective and efficient search for grouped convolutional architectures.
