namespace {

template <typename BackwardFunction, typename TapeTensor>
struct BackpropInitialState {
  OpTape<BackwardFunction, TapeTensor> op_tape;

  // Map from tensor ID to how many references still exist for this tensor in
  // the tape.
  std::unordered_map<int64_t, int64_t> tensor_usage_counts;

  // Maps from op ID to how many output tensors of this op still need to have
  // their gradients computed.