text: The paper is clear and well written. It is an incremental modification of prior work (ResNeXt) that performs better on several experiments selected by the author;  comparisons are only included relative to ResNeXt. This paper is not about gating (c.f., gates in LSTMs, mixture of experts, etc) but rather about masking or perhaps a kind of block sparsity,  as the "gates" of the paper do not depend upon the input:  they are just fixed masking matrices (see eq (2)). The main contribution appears to be the optimisation procedure for the binary masking tensor g.  But this procedure is not justified:  does each step minimise the loss?  This seems unlikely due to the sampling.  Can the authors show that the procedure will always converge?  It would be good to contrast this with other attempts to learn discrete random variables  (for example, The Concrete Distribution: Continuous Relaxation of Continuous Random Variables, Maddison et al, ICLR 2017).