.. _sphx_glr_beginner_examples_autograd_two_layer_net_autograd.py:


PyTorch: Variables and autograd
-------------------------------

A fully-connected ReLU network with one hidden layer and no biases, trained to
predict y from x by minimizing squared Euclidean distance.

This implementation computes the forward pass using operations on PyTorch
Variables, and uses PyTorch autograd to compute gradients.

A PyTorch Variable is a wrapper around a PyTorch Tensor, and represents a node
in a computational graph. If x is a Variable then x.data is a Tensor giving its
value, and x.grad is another Variable holding the gradient of x with respect to
some scalar value.

PyTorch Variables have the same API as PyTorch tensors: (almost) any operation
you can do on a Tensor you can also do on a Variable; the difference is that
autograd allows you to automatically compute gradients.



.. code-block:: python

    import torch
    from torch.autograd import Variable

    dtype = torch.FloatTensor
    # dtype = torch.cuda.FloatTensor # Uncomment this to run on GPU

    # N is batch size; D_in is input dimension;
    # H is hidden dimension; D_out is output dimension.
    N, D_in, H, D_out = 64, 1000, 100, 10

    # Create random Tensors to hold input and outputs, and wrap them in Variables.
    # Setting requires_grad=False indicates that we do not need to compute gradients
    # with respect to these Variables during the backward pass.
    x = Variable(torch.randn(N, D_in).type(dtype), requires_grad=False)
    y = Variable(torch.randn(N, D_out).type(dtype), requires_grad=False)

    # Create random Tensors for weights, and wrap them in Variables.
    # Setting requires_grad=True indicates that we want to compute gradients with
    # respect to these Variables during the backward pass.
    w1 = Variable(torch.randn(D_in, H).type(dtype), requires_grad=True)
    w2 = Variable(torch.randn(H, D_out).type(dtype), requires_grad=True)

    learning_rate = 1e-6
    for t in range(500):
        # Forward pass: compute predicted y using operations on Variables; these
        # are exactly the same operations we used to compute the forward pass using
        # Tensors, but we do not need to keep references to intermediate values since
        # we are not implementing the backward pass by hand.
        y_pred = x.mm(w1).clamp(min=0).mm(w2)

        # Compute and print loss using operations on Variables.
        # Now loss is a Variable of shape (1,) and loss.data is a Tensor of shape
        # (1,); loss.data[0] is a scalar value holding the loss.
        loss = (y_pred - y).pow(2).sum()
        print(t, loss.data[0])

        # Use autograd to compute the backward pass. This call will compute the
        # gradient of loss with respect to all Variables with requires_grad=True.
        # After this call w1.grad and w2.grad will be Variables holding the gradient
        # of the loss with respect to w1 and w2 respectively.
        loss.backward()

        # Update weights using gradient descent; w1.data and w2.data are Tensors,
        # w1.grad and w2.grad are Variables and w1.grad.data and w2.grad.data are
        # Tensors.
        w1.data -= learning_rate * w1.grad.data
        w2.data -= learning_rate * w2.grad.data

        # Manually zero the gradients after updating weights
        w1.grad.data.zero_()
        w2.grad.data.zero_()

**Total running time of the script:** ( 0 minutes  0.000 seconds)



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