There are two typical ways to implement autograd, via symbolic differentiation like Theano or reverse differentiation like Pytorch. SINGA follows Pytorch way, which records the computation graph and apply the backward propagation automatically after forward propagation. The autograd algorithm is explained in details here. We explain the relevant modules in Singa and give an example to illustrate the usage.
There are three classes involved in autograd, namely singa.tensor.Tensor, singa.autograd.Operation, and singa.autograd.Layer. In the rest of this article, we use tensor, operation and layer to refer to an instance of the respective class.
Three attributes of Tensor are used by autograd,
.creator is an Operation instance. It records the operation that generates the Tensor instance..requires_grad is a boolean variable. It is used to indicate that the autograd algorithm needs to compute the gradient of the tensor (i.e., the owner). For example, during backpropagation, the gradients of the tensors for the weight matrix of a linear layer and the feature maps of a convolution layer (not the bottom layer) should be computed..stores_grad is a boolean variable. It is used to indicate that the gradient of the owner tensor should be stored and output by the backward function. For example, the gradient of the feature maps is computed during backpropagation, but is not included in the output of the backward function.Programmers can change requires_grad and stores_grad of a Tensor instance. For example, if later is set to True, the corresponding gradient is included in the output of the backward function. It should be noted that if stores_grad is True, then requires_grad must be true, not vice versa.
It takes one or more Tensor instances as input, and then outputs one or more Tensor instances. For example, ReLU can be implemented as a specific Operation subclass. When an Operation instance is called (after instantiation), the following two steps are executed:
creators of the input tensors..forward()There are two member functions for forwarding and backwarding, i.e., .forward() and .backward(). They take Tensor.data as inputs (the type is CTensor), and output Ctensors. To add a specific operation, subclass operation should implement their own .forward() and .backward(). The backward() function is called by the backward() function of autograd automatically during backward propogation to compute the gradients of inputs (according to the require_grad field).
For those operations that require parameters, we package them into a new class, Layer. For example, convolution operation is wrapped into a convolution layer. Layer manages (stores) the parameters and calls the corresponding Operations to implement the transformation.
Multiple examples are provided in the example folder. We explain two representative examples here.
The following codes implement a MLP model using only Operation instances (no Layer instances).
from singa.tensor import Tensor from singa import autograd from singa import opt
The parameter tensors are created with both requires_grad and stores_grad set to True.
w0 = Tensor(shape=(2, 3), requires_grad=True, stores_grad=True) w0.gaussian(0.0, 0.1) b0 = Tensor(shape=(1, 3), requires_grad=True, stores_grad=True) b0.set_value(0.0) w1 = Tensor(shape=(3, 2), requires_grad=True, stores_grad=True) w1.gaussian(0.0, 0.1) b1 = Tensor(shape=(1, 2), requires_grad=True, stores_grad=True) b1.set_value(0.0)
inputs = Tensor(data=data) # data matrix target = Tensor(data=label) # label vector autograd.training = True # for training sgd = opt.SGD(0.05) # optimizer for i in range(10): x = autograd.matmul(inputs, w0) # matrix multiplication x = autograd.add_bias(x, b0) # add the bias vector x = autograd.relu(x) # ReLU activation operation x = autograd.matmul(x, w1) x = autograd.add_bias(x, b1) loss = autograd.softmax_cross_entropy(x, target) for p, g in autograd.backward(loss): sgd.update(p, g)
The following example implements a CNN model using layers provided by the autograd module.
conv1 = autograd.Conv2d(1, 32, 3, padding=1, bias=False) bn1 = autograd.BatchNorm2d(32) pooling1 = autograd.MaxPool2d(3, 1, padding=1) conv21 = autograd.Conv2d(32, 16, 3, padding=1) conv22 = autograd.Conv2d(32, 16, 3, padding=1) bn2 = autograd.BatchNorm2d(32) linear = autograd.Linear(32 * 28 * 28, 10) pooling2 = autograd.AvgPool2d(3, 1, padding=1)
The operations in the forward pass will be recorded automatically for backward propagation.
def forward(x, t): # x is the input data (a batch of images) # t is the label vector (a batch of integers) y = conv1(x) # Conv layer y = autograd.relu(y) # ReLU operation y = bn1(y) # BN layer y = pooling1(y) # Pooling Layer # two parallel convolution layers y1 = conv21(y) y2 = conv22(y) y = autograd.cat((y1, y2), 1) # cat operation y = autograd.relu(y) # ReLU operation y = bn2(y) y = pooling2(y) y = autograd.flatten(y) # flatten operation y = linear(y) # Linear layer loss = autograd.softmax_cross_entropy(y, t) # operation return loss, y
autograd.training = True for epoch in range(epochs): for i in range(batch_number): inputs = tensor.Tensor(device=dev, data=x_train[ i * batch_sz:(1 + i) * batch_sz], stores_grad=False) targets = tensor.Tensor(device=dev, data=y_train[ i * batch_sz:(1 + i) * batch_sz], requires_grad=False, stores_grad=False) loss, y = forward(inputs, targets) # forward the net for p, gp in autograd.backward(loss): # auto backward sgd.update(p, gp)
The following <<<<<<< HEAD example implements a CNN model using the Model API.
Define the model class, it should be the subclass of Model. In this way, all operations used during the training phase will form a computational graph and will be analyzed. The operations in the graph will be scheduled and executed efficiently. Layers can also be included in the model class.
class MLP(model.Model): # the model is a subclass of Model def __init__(self, data_size=10, perceptron_size=100, num_classes=10): super(MLP, self).__init__() # init the operators, layers and other objects self.relu = layer.ReLU() self.linear1 = layer.Linear(perceptron_size) self.linear2 = layer.Linear(num_classes) self.softmax_cross_entropy = layer.SoftMaxCrossEntropy() def forward(self, inputs): # define the forward function y = self.linear1(inputs) y = self.relu(y) y = self.linear2(y) return y def train_one_batch(self, x, y): out = self.forward(x) loss = self.softmax_cross_entropy(out, y) self.optimizer(loss) return out, loss def set_optimizer(self, optimizer): # attach an optimizer self.optimizer = optimizer
# create a model instance model = MLP() # initialize optimizer and attach it to the model sgd = opt.SGD(lr=0.005, momentum=0.9, weight_decay=1e-5) model.set_optimizer(sgd) # input and target placeholders for the model tx = tensor.Tensor((batch_size, 1, IMG_SIZE, IMG_SIZE), dev, tensor.float32) ty = tensor.Tensor((batch_size, num_classes), dev, tensor.int32) # compile the model before training model.compile([tx], is_train=True, use_graph=True, sequential=False) # 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) # Training with one batch out, loss = model(tx, ty)
# define the path to save the checkpoint checkpointpath="checkpoint.zip" # save a checkpoint model.save_states(fpath=checkpointpath)
# define the path to load the checkpoint checkpointpath="checkpoint.zip" # load a checkpoint import os if os.path.exists(checkpointpath): model.load_states(fpath=checkpointpath)
Refer here for more details of Python API.