// The entry, "FusedBatchNorm": [1, 2, 3, 4], indicates that only the gradient
// corresponding to index 0 is used, and the gradient values at indices 1-4 are
// ignored (and hence can be None). The backprop algorithm can then leverage
// this by not constructing zeros to pass for those indices.
std::unordered_map<string, std::unordered_set<int>>*
FunctionsAcceptingNoneForIndicesMap() {
  static auto* const m =