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.
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 graph, the operator/expression's backward pass will be generated respect to forward pass.
## Backward Operator Registry
### Implement : gradient 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.
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.
In most cases, there is a one-to-one correspondence between forward and backward operators. These correspondences are recorded by a global hash map(`OpInfoMap`). To follow the philosophy of minimum core and make operators pluggable, the registry mechanism is introduced.
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.
For example, we have got a `mul_op`, and we can register it's information and corresponding backward operator by the following macro:
The function `BuildGradOp` will sequentially execute following processes:
1. Get the `type_` of given forward operator, and then get the corresponding backward operator's type by looking up the `OpInfoMap`.
2. Build two maps named `inputs` and `outputs` to temporary storage backward operator's inputs and outputs. Copy forward operator's `inputs_` and `outputs_` to map `inputs`, except these are not necessary for gradient computing.
3. Add forward inputs' gradient variables into map `output`, adding forward outputs' gradient variables into map `input`.
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.
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`.
