Merge pull request #4026 from dzhwinter/backward_graph

rewrite the document

Author: dzhwinter

paddle/framework/backward.md

@@ -2,11 +2,22 @@
 
 ## Motivation
 
-In Neural Network, the backpropagation algorithm follows the chain rule, so we need to compound the gradient operators/expressions together with the chain rule. Every forward network needs a backward network to construct the full computation graph, the operator/expression's backward pass will be generated respect to forward pass.
+In Neural Network, many model is solved by the the backpropagation algorithm(known as BP) at present. Technically it caculates the gradient of the loss function, then distributed back through the networks. Follows the chain rule, so we need a module chains the gradient operators/expressions together with to construct the backward pass. Every forward network needs a backward network to construct the full computation graph, the operator/expression's backward pass will be generated respect to forward pass. 
 
-## Backward Operator Registry
+## Implementation
 
-A backward network is built up with several backward operators. Backward operators take forward operators' inputs outputs, and output gradients and then calculate its input gradients.
+In this design doc, we exported only one API for generating the backward pass.
+
+```c++
+std::unique_ptr<OperatorBase> Backward(const OperatorBase& forwardOp,
+    const std::unordered_set<std::string>& no_grad_vars);
+```
+
+The implementation behind it can be divided into two parts, **Backward Operator Creating** and **Backward Operator Building**.
+
+### Backward Operator Registry
+
+A backward network is built up with several backward operators. Backward operators take forward operators' inputs, outputs, and output gradients and then calculate its input gradients.
 
 |                        | forward operator | backward operator 
 | ---------------------- | ---------------- |------------------------- |		
@@ -25,7 +36,7 @@ REGISTER_OP(mul, MulOp, MulOpMaker, mul_grad, MulOpGrad);
 
 `mul_grad` is the type of backward operator, and `MulOpGrad` is its class name.
 
-## Backward Opeartor Creating
+### Backward Opeartor Creating
 
 Given a certain forward operator, we can get its corresponding backward operator by calling:
 
@@ -43,40 +54,47 @@ The function `BuildGradOp` will sequentially execute following processes:
 
 4. Building backward operator with `inputs`, `outputs` and forward operator's attributes.
 
-## Backward Network Building
-
-A backward network is a series of backward operators. The main idea of building a backward network is creating backward operators in the inverted sequence and put them together.
+### Backward Network Building
 
-In our design, the network itself is also a kind of operator. So the operators contained by a big network may be some small network. 
-
-given a forward network, it generates the backward network. We only care about the Gradients—`OutputGradients`, `InputGradients`.
+A backward network is a series of backward operators. The main idea of building a backward network is creating backward operators in the inverted sequence and append them together one by one. There is some corner case need to process specially.
 
 1. Op 
 
-   when the input forward network is an Op, return its gradient Operator Immediately.
+   When the input forward network is an Op, return its gradient Operator Immediately. If all of its outputs are in no gradient set, then return a special `NOP`.
 
 2. NetOp 
 
-   when the input forward network is a NetOp, it needs to call the sub NetOp/Operators backward function recursively. During the process, we need to collect the `OutputGradients` name according to the forward NetOp.
+   In our design, the network itself is also a kind of operator(**NetOp**). So the operators contained by a big network may be some small network. When the input forward network is a NetOp, it needs to call the sub NetOp/Operators backward function recursively. During the process, we need to collect the `OutputGradients` name according to the forward NetOp.
+
+3. RnnOp
+
+   RnnOp is a nested stepnet operator.  Backward module need to recusively call `Backward` for every stepnet.
+
+4. Sharing Variables
+
+   **sharing variables**. As illustrated in the pictures, two operator's share the same variable name of W@GRAD, which will overwrite their sharing input variable. 
+
+<p align="center">
+<img src="./images/duplicate_op.png" width="50%" ><br/>
 
-   **shared variable**. As illustrated in the pictures, two operator's `Output` `Gradient` will overwrite their shared input variable.  
+​	pic 1. Sharing variables in operators. 
 
-   <p align="center">
-   <img src="./images/duplicate_op.png" width="50%" ><br/>
+</p>
 
-   1. Shared variable in operators. 
+​	Sharing variable between operators or same input variable used in multiple operators leads to a duplicate gradient variable. As demo show above, we need to rename gradient name recursively and add a generic add operator to replace the overwrite links. 
 
-   </p>
+<p align="center">
+<img src="images/duplicate_op2.png" width="40%" ><br/>
 
-   Share variable between operators or same input variable used in multiple operators leads to a duplicate gradient variable. As demo show above, we need to rename gradient name recursively and add a generic add operator replace the overwrite links. 
+​	pic 2. Replace sharing variable's gradient with `Add` operator.
 
-   <p align="center">
-   <img src="images/duplicate_op2.png" width="50%" ><br/>
+</p>
 
-   2. Replace shared variable's gradient with `Add` operator.
+​	Because our framework finds variables accord to their names, we need to rename the output links. We add a suffix of number to represent its position in clockwise. 
 
-   </p>
+5. Part of Gradient is Zero.
 
+   In the whole graph, there is some case of that one operator's gradient is not needed, but its input's gradient is a dependency link of other operator,  we need to fill a same shape gradient matrix in the position. In our implement, we insert a special `fillZeroLike` operator.
 
 
-​	Then collect the sub graph `OutputGradients`/`InputGradients` as the NetOp's and return it.
+Follow these rules above, then collect the sub graph `OutputGradients`/`InputGradients` as the NetOp's and return it.