// 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 =
      new std::unordered_map<string, std::unordered_set<int>>({
          {"SoftmaxCrossEntropyWithLogits", {1}},
          {"SparseSoftmaxCrossEntropyWithLogits", {1}},

    /// Wait on cond_var if state is FETCHING.
    absl::CondVar cond_var;
  };

  /// \brief The block map type for the file block cache.
  ///
  /// The block map is an ordered map from Key to Block.
  typedef std::map<Key, std::shared_ptr<Block>> BlockMap;

  /// Prune the cache by removing files with expired blocks.
  void Prune() ABSL_LOCKS_EXCLUDED(mu_);