A primary goal of the refactorization of PaddlePaddle is a more flexible representation of deep learning computation, in particular, a graph of operators and variables, instead of sequences of layers as before.
This document explains that the construction of a graph as three steps:
- construct the forward part
- construct the backward part
- construct the optimization part
Let us take the problem of image classification as a simple example. The application program that trains the model looks like:
```python
x=layer.data("images")
l=layer.data("label")
y=layer.fc(x)
cost=layer.mse(y,l)
optimize(cost)
train(cost,reader=mnist.train())
```
### Forward Part
The first four lines of above program build the forward part of the graph.
In particular, the first line `x = layer.data("images")` creates variable x and a Feed operator that copies a column from the minibatch to x. `y = layer.fc(x)` creates not only the FC operator and output variable y, but also two parameters, W and b.
In this example, all operators are created as `OpDesc` protobuf messages, and all variables are `VarDesc`. These protobuf messages are saved in a `BlockDesc` protobuf message.
### Backward Part
The fifth line `optimize(cost)` calls two functions, `ConstructBackwardGraph` and `ConstructOptimizationGraph`.
`ConstructBackwardGraph` traverses the forward graph in the `BlockDesc` protobuf message and builds the backward part.
According to the chain rule of gradient computation, `ConstructBackwardGraph` would
1. create a gradient operator G for each operator F,
1. make all inputs, outputs, and outputs' gradient of F as inputs of G,
1. create gradients for all inputs of F, except for those who don't have gradients, like x and l, and
1. make all these gradients as outputs of G.
### Optimization Part
For each parameter, like W and b created by `layer.fc`, marked as double circles in above graphs, `ConstructOptimizationGraph` creates an optimization operator to apply its gradient. Here results in the complete graph:
