"add part of design doc"

paddle/framework/backward.md

@@ -1 +1,38 @@
-## Backward Policy Design
+## Operator/expression 's Backward
+
+### Motivation
+
+In Neural Network, the backpropagation algorithm follows the chain rule, so we need to compound the fundmental gradient operators/expressions together with chain rule . Every forward network need a backward network to construct the full computation lineage, the operator/ expression's Backward feature will generate the backward pass respect to forward pass.
+
+### Implement : gradient operator registry
+
+|                        | forward operator | backward operator                |
+| ---------------------- | ---------------- | -------------------------------- |
+| **Operator::inputs_**  | Inputs           | Inputs, Outputs, OutputGradients |
+| **Operator::outputs_** | Outputs          | InputGradients                   |
+
+Inputs/Outputs means the input/output of the operator,  InputGradients/OutputGradients is the gradient respect to forward opeartor. Forward operator and Backward operator are isomorphic, save their corresponding needs into member attribute.
+
+We use a global hash map record the gradient operators available, follow the philosophy  of minimum core, make operator pluggable unit. Each gradient is an operator and it needs to regist itself. 
+
+grad_op_builder(fengjiayi)
+
+### Implement : Backward network
+
+given a forward network, it generates the backward network. We only care about the Gradients—`OutputGradients`,`InputGradients`.
+
+1. bla bla bla (yuyang)
+
+2. NetOp 
+
+   when the input forward network is a NetOp, it need to call the sub NetOp/Operators backward function recursively and ensure them done. During the process, we need to collect the `OutputGradients` name.
+
+   We share variable in the same scope, as a result, duplicate operator `OutputGradients` will overwirte then duplicate variable.  
+
+   ![./images/duplicate_op]()
+
+    Share variable between operators or same input variable used in multiple operators lead to a duplicate gradient variable. As demo show above, we need to rename gradient name recursively, and add a generic add operator instead. 
+
+![./images/duplicate_op2]()
+
+​	Then collect the sub graph OutputGradients/InputGradients as the NetOp's and return it.