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id: version-3.0.0-graph title: Computational Graph original_id: graph

The forward and backward propagation in a neural network can be represented using a set of operations such as convolution and pooling. Each operation takes some input tensors and applies an operator to generate output tensors. By representing each operator as a node and each tensor as an edge, all operations form a computational graph. With the computational graph, speed and memory optimization can be conducted by scheduling the execution of the operations and memory allocation/release intelligently. In SINGA, users only need to define the neural network model using the Module API. The graph is constructed and optimized at the C++ backend automatically.

Example

The following code illustrates the usage of the Module API.

1. Implement the new model as a subclass the Module class.

class CNN(module.Module):

    def __init__(self, optimizer):
        super(CNN, self).__init__()
        # define layers
        self.conv1 = autograd.Conv2d(1, 20, 5, padding=0)
        self.conv2 = autograd.Conv2d(20, 50, 5, padding=0)
        self.linear1 = autograd.Linear(4 * 4 * 50, 500)
        self.linear2 = autograd.Linear(500, 10)
        self.pooling1 = autograd.MaxPool2d(2, 2, padding=0)
        self.pooling2 = autograd.MaxPool2d(2, 2, padding=0)

        self.optimizer = optimizer

    def forward(self, x):
        # define the forward operations
        y = self.conv1(x)
        y = autograd.relu(y)
        y = self.pooling1(y)
        y = self.conv2(y)
        y = autograd.relu(y)
        y = self.pooling2(y)
        y = autograd.flatten(y)
        y = self.linear1(y)
        y = autograd.relu(y)
        y = self.linear2(y)
        return y

    def loss(self, x, ty):
        # define the training loss
        return autograd.softmax_cross_entropy(x, ty)

    def optim(self, loss):
        # update the parameters using SGD algorithms
        self.optimizer.backward_and_update(loss)

2. Create an instance of the model, and do some configurations

model = CNN(sgd)
# set the mode of running the operations:
# True for training; False for evaluation
model.train(mode=True)
# set the device for running the operations
model.on_device(dev)
# whether to create the graph or run the operations imperatively
model.graph(mode=True)

3. Train the model iteratively

for b in range(num_train_batch):
    # generate the next mini-batch
    x, y = ...

    # Copy the data into input tensors
    tx.copy_from_numpy(x)
    ty.copy_from_numpy(y)

    # run forward propagation
    out = model(tx)
    loss = model.loss(out, ty)
    # run backward propagation
    model.optim(loss)

A Google Colab notebook of this example is available here.

More examples:

• MLP
• CNN
• ResNet

Implementation

Graph Construction

SINGA constructs the computational graph in three steps:

1. buffer the operations
2. analyze the dependencies operations
3. create the nodes and edges based on the dependencies

Take the matrix multiplication operation from the dense layer of a MLP model as an example. The operation is called in the forward function of the MLP class

class MLP(module.Module):

    def forward(self, inputs):
        x = autograd.matmul(inputs, self.w0)
        ...

autograd implements the matmul operator by calling the function Mult exposed from CPP via SWIG.

# implementation of matmul()
singa.Mult(inputs, w)

At the backend, the Mult function is implemented by calling GEMV a CBLAS function. Instead of calling GEMV directly, Mult submits GEMV and the arguments to the device as follows,

// implementation of Mult()
C->device()->Exec(
    [a, A, b, B, CRef](Context *ctx) mutable {
        GEMV<DType, Lang>(a, A, B, b, &CRef, ctx);
    },
    read_blocks, {C->block()});

The Exec function of Device buffers the function and its arguments. In addition, it also has the information about the blocks (a block is a chunk of memory for a tensor) to be read and written by this function.

Once Module.forward() has been executed once, all operations are buffered by Device. Next, the read/write information of all operations are analyzed to create the computational graph. For example, if a block b is written by one operation O1 and is later read by another operation O2, we would know O2 depends on O1 and there is a directed edge from A to B, which represents block b (or its tensor). After that a directed acyclic graph is constructed as shown below. The graph is constructed once.

Figure 1 - The computational graph of the MLP example.

Optimization

Currently, the following optimizations are done based on the computational graph.

Lazy allocation When tensor/blocks are created, devices do not allocate memory for them immediately. Instead, when the block is accessed for the first time, the memory is allocated.

Automatic recycling The reference count of each tensor/block is calculated based on the graph. Before executing the operations, the reference count is the number of operations that read this block. During the execution, once an operation is executed, the reference count of the every input block is decreased by 1. If one block's reference count reaches 0, it means that this block will not be read again in the remaining operations. Therefore, its memory can be released safely. In addition, SINGA tracks the usage of the block outside of the graph. If a block is used by Python code (not by autograd operators), it will not be recycled.

Memory sharing SINGA uses memory pool, e.g., CnMem to manage CUDA memory. With Automatic recycling and memory pool, SINGA can share the memory among tensors. Consider two operations c = a + b and d=2xc. Before executing the second operation, according to Lazy allocation, the memory of d should be allocated. Suppose a is not used in the rest operations. According to Automatic recycling, the block of a will be released after the first operation. Therefore, SINGA would submit four operations to the CUDA stream: addition, free a, malloc b, and multiplication. The memory pool is then able to share the memory released by a with b instead of ask the GPU to do real malloc for b.

Other optimization techniques e.g., from compliers, such as common sub-expression elimination and parallelizing operations on different CUDA streams can also be applied.

New Operator

Each operator defined in autograd module implements two functions: forward and backward, which are implemented by calling the operators from the backend. To add a new operator in autograd, you need to add the multiple operators at the backend.

Take the Conv2d operator as an example, at the Python side, the forward and backward function are implemented by calling the operators from the backend depending on the device type.

class _Conv2d(Operation):

    def forward(self, x, W, b=None):
        ......
        if training:
            if self.handle.bias_term:
                self.inputs = (x, W, b) # record x, W, b
            else:
                self.inputs = (x, W)

        if (type(self.handle) != singa.ConvHandle):
            return singa.GpuConvForward(x, W, b, self.handle)
        else:
            return singa.CpuConvForward(x, W, b, self.handle)

    def backward(self, dy):
        if (type(self.handle) != singa.ConvHandle):
            dx = singa.GpuConvBackwardx(dy, self.inputs[1], self.inputs[0],
                                        self.handle)
            dW = singa.GpuConvBackwardW(dy, self.inputs[0], self.inputs[1],
                                        self.handle)
            db = singa.GpuConvBackwardb(
                dy, self.inputs[2],
                self.handle) if self.handle.bias_term else None
        else:
            dx = singa.CpuConvBackwardx(dy, self.inputs[1], self.inputs[0],
                                        self.handle)
            dW = singa.CpuConvBackwardW(dy, self.inputs[0], self.inputs[1],
                                        self.handle)
            db = singa.CpuConvBackwardb(
                dy, self.inputs[2],
                self.handle) if self.handle.bias_term else None
        if db:
            return dx, dW, db
        else:
            return dx, dW

For each operator at the backend, it should be implemented in the following way:

• Suppose the operator is foo(); its real implementation should be wrapped in another function e.g., _foo(). foo() passes _foo together with the arguments as a lambda function to Device's Exec function for buffering. The blocks to be read and written are also passed to Exec.

• All arguments used in the lambda expression need to be captured according to the following rules.

  • capture by value: If the argument variable is a local variable or will be immediately released (e.g. intermediate tensors). Otherwise, these variables will be destroyed once foo() exists.

  • capture by reference：If the variable is recorded on the python side or a persistent variable (e.g. parameter W and ConvHand in the Conv2d class).

  • mutable: The lambda expression should have the mutable tag if a variable captured by value is modified in _foo()

Here is one example operator implemented at the backend.

Tensor GpuConvBackwardx(const Tensor &dy, const Tensor &W, const Tensor &x,
                        const CudnnConvHandle &cch) {
  CHECK_EQ(dy.device()->lang(), kCuda);

  Tensor dx;
  dx.ResetLike(x);

  dy.device()->Exec(
      /*
       * dx is a local variable so it's captured by value
       * dy is an intermediate tensor and isn't recorded on the python side
       * W is an intermediate tensor but it's recorded on the python side
       * chh is a variable and it's recorded on the python side
       */
      [dx, dy, &W, &cch](Context *ctx) mutable {
        Block *wblock = W.block(), *dyblock = dy.block(), *dxblock = dx.block();
        float alpha = 1.f, beta = 0.f;
        cudnnConvolutionBackwardData(
            ctx->cudnn_handle, &alpha, cch.filter_desc, wblock->data(),
            cch.y_desc, dyblock->data(), cch.conv_desc, cch.bp_data_alg,
            cch.workspace.block()->mutable_data(),
            cch.workspace_count * sizeof(float), &beta, cch.x_desc,
            dxblock->mutable_data());
      },
      {dy.block(), W.block()}, {dx.block(), cch.workspace.block()});
      /* the lambda expression reads the blocks of tensor dy and w
       * and writes the blocks of tensor dx and chh.workspace
       */

  return dx;
}

Benchmark

Single node

• Experiment settings
  • Model
    • Using layer: ResNet50 in resnet.py
    • Using module: ResNet50 in resnet.py
  • GPU: NVIDIA RTX 2080Ti
• Notations
  • s ：second
  • it ： iteration
  • Mem：peak memory usage of single GPU
  • Throughout：number of images processed per second
  • Time：total time
  • Speed：iterations per second
  • Reduction：the memory usage reduction rate compared with that using layer
  • Speedup: speedup ratio compared with dev branch
• Result

Multi processes

• Experiment settings
  • Model
    • using Layer: ResNet50 in resnet_dist.py
    • using Module: ResNet50 in resnet.py
  • GPU: NVIDIA RTX 2080Ti * 2
  • MPI: two MPI processes on one node
• Notations: the same as above
• Result

Conclusion

• Training with the computational graph enabled can significantly reduce the memory footprint.
• Currently, there is a little improvement in terms of speed. More optimizations can be done towards the efficiency.