// watched and not the result of any operation in the tape.
using TensorTape = std::unordered_map<int64_t, int64_t>;

// Map from operation-id to tape entry.
template <typename BackwardFunction, typename TapeTensor>
using OpTape =
    std::unordered_map<int64_t, OpTapeEntry<BackwardFunction, TapeTensor>>;

// Operations the tape needs to perform on tensors to do backpropagation. Named

// the op that produced it (or -1 if this tensor was watched using
// `GradientTape::Watch`.) The op_id is simply a unique index assigned to each
// op executed under the tape. A separate map (`tensorflow::eager::OpTape`)
// maintains the map from `op_id` to a `OpTapeEntry` which stores the `op_type`,
// inputs and outputs and the gradient function These data structures combined