Merge branch 'develop' of https://github.com/PaddlePaddle/Paddle into executor-design
Yang Yang
8 years ago
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## Optimizer Design
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### The Problem
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A PaddlePaddle program, or a block, is a sequence of operators operating variables. A training program needs to do three kinds of works:
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1. the forward pass, which computes intermediate results and the cost(s),
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1. the backward pass, which derives gradients from intermediate results and costs, and
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1. the optimization pass, which update model parameters to optimize the cost(s).
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These works rely on three kinds of operators:
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1. forward operators,
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1. gradient operators, and
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1. optimization operators.
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It's true that users should be able to create all these operators manually by calling some low-level API, but it would be much more convenient if they could only describe the forward pass and let PaddlePaddle create the backward and optimization operators automatically.
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In this design, we propose a high-level API that automatically derives the optimisation pass and operators from the forward pass.
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### High-level Python API to describe the training process
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1. User write code to describe the network:
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```python
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images = layer.data("images")
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labels = layer.data("labels")
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w1 = pd.var("w1")
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b1 = pd.var("b1")
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hidden = layer.fc(images, w=w1, b=b1)
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cost = layer.mse(hidden, labels)
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```
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The above code snippet will create forward operators in [Block](https://github.com/PaddlePaddle/Paddle/blob/develop/doc/design/block.md).
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2. Users create a certain kind of Optimizer with some argument.
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```python
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optimizer = AdagradOptimizer(learing_rate=0.001)
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```
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3. Users use the optimizer to `minimize` a certain `cost` through updating parameters in parameter_list.
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```python
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opt_op_list = optimizer.minimize(cost, parameter_list=[w1, b1])
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```
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The above code snippet will create gradient and optimization operators in Block. The return value of `minimize()` is list of optimization operators that will be run by session.
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4. Users use Session/Executor to run this opt_op_list as target to do training.
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```python
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sess.run(target= opt_op_list, ...)
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```
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#### Optimizer Python interface:
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```python
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class Optimizer(object):
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"""Optimizer Base class.
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"""
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def __init__(self):
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pass
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def create_backward_pass(self, loss, parameter_list=None):
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"""
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create and add gradient Operators in BlockDesc to Compute gradients of `loss`
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for parameters in parameter_list
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Args:
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loss: an variable generated by cost function.
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parameter_list: parameters that need to compute gradient and update to optimize the lost.
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Returns:
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list of (parameters, gradients) pair.
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"""
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return None
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def create_optimization_pass(self, parameters_and_grads):
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"""Add optimization operators to update gradients to variables.
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Args:
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parameters_and_grads: a list of (variable, gradient) pair to update.
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Returns:
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optmization_op_list: a list of optimization operator that will update parameter using gradient.
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"""
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return None
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def minimize(self, loss, parameter_list):
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"""Add operations to minimize `loss` by updating `parameter_list`.
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This method combines interface `create_backward_pass()` and
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`create_optimization_pass()` into one.
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"""
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params_grads = self.create_backward_pass(loss, parameter_list)
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update_ops = self.create_optimization_pass(params_grads)
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return update_ops
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```
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Users can inherit the Optimizer above to create their own Optimizer with some special logic, such as AdagradOptimizer.
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# Design Doc: Selected Rows
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`SelectedRows` is a kind of sparse tensor data type, which is designed to support `embedding` operators. The gradient of embedding table is a sparse tensor. Only a few rows are non-zero values in that tensor. It is straightforward to represent the sparse tensor by the following sparse tensor data structure:
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```cpp
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class SelectedRows {
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private:
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vector<int> rows_;
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Tensor value_;
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int height_;
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};
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```
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The field `height_` shows the first dimension of `SelectedRows`. The `rows` are the indices of which rows of `SelectedRows` are non-zeros. The `value_` field is an N-dim tensor and shape is `[rows.size() /* NUM_ROWS */, ...]`, which supplies values for each row. The dimension of `SelectedRows` satisfies `[height_] + value_.shape[1:]`.
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Suppose that a SelectedRows-typed variable `x` has many rows, but only two of them have values -- row 73 is `[1, 2]` and row 84 is `[3, 4]`, the `SelectedRows` representation would be:
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```
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x = SelectedRow {
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rows = [73, 84],
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value = [[1, 2], [3,4]]
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}
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```
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## SelectedRows in Protobuf
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`SelectedRows` is a kind of `Variable`. `VarDesc` in protobuf should describe the `SelectedRows` information. Only the tensor dimension of a `SelectedRows` will be described in compile-time since the `rows_` and `value_` are related to training data.
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So we use `TensorDesc` to unify `data_type` and `dims`. A LodTensorDesc contains a `TensorDesc` and `lod_level`. The description of `SelectedRows` is a Tensor description.
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```proto
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message TensorDesc {
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required DataType data_type = 1;
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repeated int64 dims = 2; // [UNK, 640, 480] is saved as [-1, 640, 480]
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}
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message LodTensorDesc {
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required TensorDesc tensor = 1;
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optional int lod_level = 2;
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}
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message VarDesc {
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required string name = 1;
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enum VarType {
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LOD_TENSOR = 0;
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SELECTED_ROWS = 1;
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}
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required VarType type = 2;
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optional LodTensorDesc lod_desc = 3;
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optional TensorDesc selected_rows_desc = 4;
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optional bool persistable = 5 [ default = false ];
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}
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```
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## InferShape for Selected Rows
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Just like `LoD` information, `InferShape` method will inference output tensor type as well. The operator should decide whether its output is a `SelectedRows` or `Dense` tensor.
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For example, the gradient operator of `TableLookup` will always generate `SelectedRows`. Its `InferShape` method should be like following
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```cpp
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void TableLookupGrad::InferShape(context) {
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...
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context.SetDataType("Embedding.Grad", kSelectedRows);
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}
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```
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## Sparse Operators
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There are several operators should be written to support `SelectedRows`. They are:
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1. Operators which generates `SelectedRows` gradient. e.g. Gradient of `TableLookupOp`.
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2. Optimize operators which support `SelectedRows` gradient. e.g. `SGD` or `AdaGrad` for `SelectedRows`. However, there should be only one `SGD` operator. `OpWithKernel::Run` should select a suitable kernel for both `dense` tensor or `SelectedRows`.
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