net design with NetBuilder (#2598)

* move net_design to framework

* change CreateNet result to unique_ptr

* rename "ScratchNet" -> "PlainNet"

* add three methods to NetBase

* add NetBuilder

* add InferShape to NetBuilder.Run

* rename ApplyGradient, ApplyOptimizer -> AddGradientOps, AddOptimiz

* rename PlainNet::CreateNet -> BuildNet

* add Error and other rename actions

paddle/framework/net_design.md

+# Network Design
+
+`Network` is the container and controller of a set of operators,
+user can build a real network from a `NetDesc` which is a protobuf message 
+and use `Network.Run()` to run all the operators in the network.
+
+A network object knows all Operators belonging to this network. Variables, 
+which are inputs and outputs of these operators, 
+are created and managed by a hierarchy of Scope objects.
+
+# API
+
+## Net
+To make the `Network` extendable, a base class is defined like this
+
+```c++
+// operator's index stored in a network.
+typedef int OpIndex;
+
+// The minimum a network should be implemented.
+class Net {
+ public:
+  // run all the operators and return success(true) or not, with all the
+  // variables are located in `scope`. `context` describes the detail execution
+  // environment for ops. `begin` and `end` specify the scope of `ops_` to run,
+  // If no positive indexes are provided, all operators in `ops_` will run.
+  virtual Error Run(Scope *scope, OpContext *context, OpIndex begin = -1,
+                   OpIndex end = -1) const = 0;
+
+  // Add an Operator according to `def`.
+  virtual OpIndex AddOp(const proto::OpDef &def) = 0;
+
+  // Add optimizer operators acctording to `attrs`.
+  virtual Error AddOptimizerOps(const OptAttrs &attrs) = 0;
+
+  // Add backward operators.
+  virtual Error AddBackwardOps() = 0;
+
+  // Infer the shapes of variables required by operators in the network. The
+  // `scope` will be mutated according to the inferred shapes.
+
+  static std::unique_ptr<Net> Create(const NetDesc &def = NetDesc());
+};
+```
+
+All network implementations should build networks from a protobuf message which 
+describes the structure of a real network; `Run` method should be implemented by 
+all implementations to offer a universal method to forward or backward compute a network.
+
+`Net::Create` is a method of factory pattern and can be implemented like
+
+```c++
+std::unique<Net> Net::Create(const NetDesc& def) {
+  switch (def.model_type()) {
+    case NN:
+      return new Network(def);
+    case Recursive:
+      return new RecursiveNet(def);
+    case Recurrent:
+      return new RecurrentNet(def);
+  }
+  return nullptr;
+}
+```
+
+Network is designed as the container of operators. to make it more extendable,
+we decouple it from the related variable resources. 
+
+`Run(Scope* scope)` takes the scope as a argument so that it can run in different scopes.
+
+Finally, `Net` can be used as followed
+
+```c++
+Scope default_scope;
+OpContext default_context;
+auto net = Net::CreateNet(def);
+
+if (net) {
+  net.Run(&default_scope, &default_context);
+}
+```
+
+## `PlainNet` as a simple implementation of `BaseNet`
+
+A very basic implementation is as follows. All it does is simply to run every operators in sequence.
+
+```c++
+class PlainNet : public Net {
+ public:
+  // Create a network describe by `def`.  NetDesc is the definition of a network.
+  PlainNet(const NetDesc &def);
+
+  // Infer all the operators' input and output varialbes' shapes, will be called before every mini-batch
+  training.
+  virtual Error InferShape(Scope *scope) override;
+
+  // Run all the operators with the `scope`, if no scope is provided, default
+  // scope will be used instead. If no OpContext is provicded, default context will be used.
+  virtual Error Run(Scope *scope = nullptr, OpContext *context=nullptr, OpIndex begin = -1,
+                   OpIndex end = -1) const override;
+
+  virtual OpIndex AddOp(const proto::OpDef &def) override;
+
+  virtual Error AddOptimizerOps(const OptAttrs &attrs) override;
+
+  virtual Error AddBackwardOps() override;
+
+ protected:
+  // Create operators accordding to `def`, will be called by the constructor.
+  Error BuildNet(const NetDesc &def);
+
+  // Add a operator which is identified as `type` and has attributes described
+  // in `attrs`, the `inputs` are the keys of readonly input variables,
+  // `outputs` are keys of mutable output variables. An `OpIndex` will be
+  // returned to indicate the offset of the new operator in `ops_`.
+  OpIndex AddOp(const std::string &type, const std::vector<string> &inputs,
+                const std::vector<string> &outputs,
+                const OprAttr &attrs = OprAttr());
+
+ private:
+  // the operators owned by `Network`.
+  std::vector<Operator> ops_;
+};
+```
+
+`PlainNet` will create operators so that a private member `ops_` is defined,
+the operators are created by `CreateNet`, and each operator is created by `AddOp`.
+
+
+## PlainNet Usage
+`PlainNet` can be used to define and run a network as follows
+
+```c++
+// create an empty scope located on CPU device.
+Scope scope(CPUPlace());
+
+// create and init variables described in `net_desc`.
+scope.CreateVariables(net_desc);
+scope.InitVariables(net_desc);
+
+// create a network according to `net_desc`
+auto net = Net::CreateNet(net_desc);
+// Add more operators if needed.
+net->AddOp(add...);
+net->AddOp(fc...);
+
+net->AddBackwardOps();
+net->AddOptimizerOps();
+
+// run the network providing the `scope`.
+net.Run(&scope);
+```
+
+## `NetBuilder` as a C++ syntax wrapper
+This is a detailed description of the user-related C++ network API, and may not needed in the prototype development stage.
+
+The `NetBuilder` will give users a much simpler syntax as follows to create a network, and demonstrates how to use the `BaseNet`'s raw interfaces.
+
+```c++
+Variable* fc_out = builder.AddOp("fc", input=image, size=100, activation="Sigmoid");
+Variable* prediction = builder.AddOp("fc", input=fc_out, size=10, activation="Sigmoid");
+Variable* loss = builder.AddOp("cross_entropy", input=prediction, label=label);
+Variable* avg_loss = builder.AddOp("mean", loss);
+
+builder.BackwardFrom(avg_loss)
+builder.AddOptimization(1e-4, "adam");
+builder.Run();
+```
+
+`NetBuilder` will call `Net` 's virtual functions to change the real network structure, here is a sample definition
+
+```c++
+class NetBuilder final {
+ public:
+  NetBuilder(Net* net) : net_(net) {}
+
+  Variable* AddOp(const string& type, const vector<Variable>& inputs,
+                  size_t size, Activation act) {
+    // much code here.
+    // ...
+    net_->AddOp(def);
+    need_rebuild_net_ = true;
+    net_->InferShape();
+    // ...
+  }
+
+  Error BackwardFrom(const Variable& cost);
+
+  Error Run(Scope* scope, OpContext* context, bool need_backward = true) {
+    // backward.
+    if (need_backward) {
+      if (need_rebuild_net_) {
+        AddBackwardOps();
+        AddOptimizerOps();
+      }
+      net_->Run(scope, context);
+      return;
+    }
+    // just forward.
+    net_->Run(scope, context, 0, last_forward_op_);
+  }
+
+ protected:
+  Error AddBackwardOps();
+  Error AddOptimizerOps();
+
+ private:
+  Net* net_;
+  OpIndex last_forward_op_{-1};
+  bool need_rebuild_net_{true};
+}
+```
+
+## Compatibility with RNN
+
+Benefitting from the decoupling of `PlainNet.Run` and `Scope`, `PlainNet` is compatible with future RNN design, 
+for example we can implement a simple recurrent neural network as follows
+
+```c++
+// copy some `vars` form `source` to `target`
+void Copy(const Scope &source, Scope &target,
+          const std::vector<std::string> &vars);
+
+Scope default_scope;
+// some initial mutations on `default_scope` here.
+
+auto rnn_step_net = PlainNet(rnn_step_net_def);
+
+// Create rnn's states, the last scope is used to store rnn outputs.
+Scope *rnn_states = new Scope[num_states + 1];
+
+for (int i = 0; i < num_states + 1; i++) {
+  // Initialize all rnn state scopes, copy parameters and so on.
+  rnn_states[i].CreateVars(rnn_step_net_def);
+  Copy(default_scope, rnn_states[i], rnn_related_vars);
+  // Prepare rnn's inlinks, just copy inlink variables to each state.
+  Copy(default_scope, rnn_states[i], inlink_vars);
+}
+
+// Run the rnn.
+for (int i = 0; i < num_states; i++) {
+  rnn_step_net.Run(rnn_states[i]);
+  // Copy current state's state variables to next state, the related variables
+  // are named like "previous_state_xxx".
+  Copy(rnn_states[i], rnn_states[i + 1], pre_state_vars)
+}
+
+// Copy rnn's final outputs to `default_scope`.
+Copy(rnn_states[num_states], default_scope, outlink_vars);
+```