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.
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.
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.
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.
## Backward Network Building
grad_op_builder(fengjiayi)
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.
### Implement : Backward network
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`.
