Daniel Voigt Godoy - Deep Learning with PyTorch Step-by-Step A Beginner’s Guide-leanpub

one matrix for each data point, each matrix containing a grid of errors.
The only step missing is to compute the mean squared error. First, we take the
square of all errors. Then, we average the squares over all data points. Since our
data points are in the first dimension, we use axis=0 to compute this average:
all_losses = (all_errors ** 2).mean(axis=0)
all_losses.shape
Output
(101, 101)
The result is a grid of losses, a matrix of shape (101, 101), each loss corresponding
to a different combination of the parameters b and w.
These losses are our loss surface, which can be visualized in a 3D plot, where the
vertical axis (z) represents the loss values. If we connect the combinations of b and
w that yield the same loss value, we’ll get an ellipse. Then, we can draw this ellipse
in the original b x w plane (in blue, for a loss value of 3). This is, in a nutshell, what a
contour plot does. From now on, we’ll always use the contour plot, instead of the
corresponding 3D version.
Figure 0.4 - Loss surface
In the center of the plot, where parameters (b, w) have values close to (1, 2), the loss
is at its minimum value. This is the point we’re trying to reach using gradient
Step 2 - Compute the Loss | 35