.. _sphx_glr_beginner_examples_tensor_two_layer_net_numpy.py:


Warm-up: numpy
--------------

A fully-connected ReLU network with one hidden layer and no biases, trained to
predict y from x using Euclidean error.

This implementation uses numpy to manually compute the forward pass, loss, and
backward pass.

A numpy array is a generic n-dimensional array; it does not know anything about
deep learning or gradients or computational graphs, and is just a way to perform
generic numeric computations.



.. code-block:: python

    import numpy as np

    # 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 input and output data
    x = np.random.randn(N, D_in)
    y = np.random.randn(N, D_out)

    # Randomly initialize weights
    w1 = np.random.randn(D_in, H)
    w2 = np.random.randn(H, D_out)

    learning_rate = 1e-6
    for t in range(500):
        # Forward pass: compute predicted y
        h = x.dot(w1)
        h_relu = np.maximum(h, 0)
        y_pred = h_relu.dot(w2)

        # Compute and print loss
        loss = np.square(y_pred - y).sum()
        print(t, loss)

        # Backprop to compute gradients of w1 and w2 with respect to loss
        grad_y_pred = 2.0 * (y_pred - y)
        grad_w2 = h_relu.T.dot(grad_y_pred)
        grad_h_relu = grad_y_pred.dot(w2.T)
        grad_h = grad_h_relu.copy()
        grad_h[h < 0] = 0
        grad_w1 = x.T.dot(grad_h)

        # Update weights
        w1 -= learning_rate * grad_w1
        w2 -= learning_rate * grad_w2

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



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     :download:`Download Python source code: two_layer_net_numpy.py <two_layer_net_numpy.py>`



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