Since the input is an image it is convenient to represent it as a mtrix of its pixels which are black () or white (). The basic shape of identifies a set of these pixels which are black.
(a) Show that feature can be computed by the neural network node
Set if the pixel is black in the basic shape and otherwise. is the threshold that we want to decide how many correct black pixel needed for the input image to be considered to have that basic shape, for example.
However, what if the input image has only black color? Then maybe we want to set if the pixel is white in the basic shape, so that if the pixel in the input image is black then its total score will be penalized by point. But our input image may contain several basic shapes so it might not be smart to blindly penalize “incorrect” pixels like that, the weights should be adjusted in some ways to achieve the best performance and I believe that’s what Neural Network does (actually, through some Neural Network algorithms, the basic shapes may look pretty different).
(b) What are the inputs to the neural network node?
After the dicussion in (a), I think we all know what the inputs are.
(c) What do you choose as values for the weights? [Hint: consider separately the weights of the pixels for those and those ]
Dicussed in (a).
(d) How would you choose ? (Not all digits are written identically, and so a basic shape may not always be exactly represented in the image.)
Dicussed in (a).
(e) Draw the final network, filling in as many details as you can.
As implicitly mentioned in the e-chapter, the units and should be two implementations and by that their weights are defined, the output unit should output when the digit is and when the digit is and when the digit is neither nor (I feel like we are no longer in binary classification problem).