Correcting some grammatical mistakes in register_grad_op.md (#4938)

doc/design/register_grad_op.md

@@ -3,17 +3,17 @@
 
 ## The Problem Posed
 
-Currently, for each C++ operator class definition, there registers a *gradient operator creator* function, which takes a C++ operator instance and returns the corresponding gradient operator instance.
+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 deisgn:
+However, we noticed two problems with the current design:
 
-1. As we decided to separate the *compilation* and *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.
+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.
 
-1. Some operator's gradient computation requires more than one gradient operators.  For example, the gradient of *minus* consists of two operators -- an identity operaotr and a scale operator.  So we need to make the registration mechanism to support the mapping from an operator to a set of operators for gradient computation.
+1. 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
 
-The C++ class `OpInfos` store in a association map which key is the operator type. The `grad_op_type` indicate associated gradient operator type. Operator can create gradient operator by `OpInfo::creator_` of gradient. The pseudo code is
+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
 
 ```cpp
 struct OpInfo {
@@ -31,16 +31,16 @@ OperatorBase* CreateGradientOperator(const OperatorBase& op) {
 
 ## Proposed Solution
 
-The mapping relationship between an operator and its gradient operators is a function. The interface of that function is:
+The mapping relationship between an operator and its gradient operators is a function. The interface of this function is:
 
 ```cpp
 // (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 protobuf message `OpDesc` to manipulate `OpDesc` fast.
+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`, to replace `grad_op_type_` field. The `OpInfo` should be
+The `GradOpDescMaker` will be registered in `OpInfo` and will replace the `grad_op_type_` field. The `OpInfo` should look like 
 
 ```cpp
 struct OpInfo {
@@ -49,7 +49,7 @@ struct OpInfo {
 };
 ```
 
-The `grad_op_maker_ ` is `nullptr` if the operator does not have associated gradient operators.
+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
 
@@ -74,7 +74,7 @@ func = [] (const OpDescBind& fwd_op) {
 
 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 chagne 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__`.
+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