  We introduce a generalization to the lottery ticket hypothesis in which the
notion of "sparsity" is relaxed by choosing an arbitrary basis in the space of
parameters. We present evidence that the original results reported for the
canonical basis continue to hold in this broader setting. We describe how
structured pruning methods, including pruning units or factorizing
fully-connected layers into products of low-rank matrices, can be cast as
particular instances of this "generalized" lottery ticket hypothesis. The
investigations reported here are preliminary and are provided to encourage
further research along this direction.
