# Design Doc: Gradient Operators Registration

## The Problem Posed

Currently, for each C++ operator class definition, a gradient operator creator function is registered, which takes as input a C++ operator instance and returns the corresponding gradient operator instance.

However, we noticed two problems with the current design:

1. As we decided to separate the compilation and the execution phases, we need to change the creator to take an OpDesc protobuf message in a ProgramDesc and inserts corresponding OpDesc messages into the ProgramDesc message.

2. For some operators, the gradient computation can be written in terms of existing operators. For example, the gradient of minus operator consists of two operators -- an identity operator followed by a scale operator. Hence the registration mechanism needs to support mapping from an operator to a set of operators for the gradient computation.

## The Current Implementation

Instances of the C++ class OpInfo are stored an associative map whose key is the operator type. The grad_op_type indicates the associated gradient operator type. An operator can create the gradient operator by invoking OpInfo::creator_ of the gradient operator. The pseudo code is as follows

struct OpInfo {
std::function<OperatorBase*(...)> creator_;
...
};

map<string, OpInfo> OpInfoMap;

OperatorBase* CreateGradientOperator(const OperatorBase& op) {
return OpInfoMap.at(op.Type()).creator_(...);
}


## Proposed Solution

The mapping relationship between an operator and its gradient operators is a function. The interface of this function is:

// (OpDesc) --> vector<OpDesc>
std::function<std::vector<OpDescBind>(const OpDescBind&)>;


The function takes an OpDescBind of the forward operator and returns one or many gradient operator descriptions. OpDescBind is a C++ wrapper for the protobuf message OpDesc for rapid manipulation of OpDesc.

The GradOpDescMaker will be registered in OpInfo and will replace the grad_op_type_ field. The OpInfo should look like

struct OpInfo {
...
};


The grad_op_maker_ is a nullptr if the operator does not have any associated gradient operators.

We propose a base class called GradOpDescMakerBase to let operator developers generate Gradient Operators easily. The public interface of that class is

class GradOpDescMakerBase {
public:
virtual std::vector<std::unique_ptr<OpDescBind>> operator()()const = 0;
};


We can convert GradOpDescMakerBase to std::function<std::vector<std::unique_ptr<OpDescBind>>(const OpDescBind&)> by

using GradOpMaker = ...;
std::function<std::vector<OpDescBind>(const OpDescBind&)> func;
func = [] (const OpDescBind& fwd_op) {
return maker();
};


We can write many helper functions since the GradOpDescMakerBase is a class now. The basic helper functions get the variables of Input, Output, InputGradient and OutputGradient in the forwarding operator.

We should change register macros at the same time. In the current solution, there is no difference between forwarding operators and backward operators. So REGISTER_OP just register one operator. If the REGISTER_OPERATOR contains OpProtoAndCheckerMaker and GradOpDescMaker, we just list them in the same macro. It can be done by a macro contains __VA_ARGS__.

The user interface should be

vector<OpDesc> MinusOpGradMaker(OpDesc) {...}
REGISTER_OPERATOR(minus, MinusOp, MinusOpProtoAndCheckerMaker, SumOpGradMaker);
// Developers can still manually implement gradient operator.

The interface of current REGISTER_OP macro could not be changed. In REGISTER_OP, it will invoke REGISTER_OPERATOR two times and generate GradOpDescMaker inside.
REGISTER_OP(minus, MinusOp, MinusOpProtoAndCheckerMaker, minus_grad, MinusGradOp);