## Operator/expression 's Backward### MotivationIn 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 networkgiven 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.
