update on week42

doc/src/week42/week42.do.txt

@@ -49,6 +49,41 @@ and the slides of "CS231":"http://cs231n.github.io/convolutional-networks/".
 
 Another good read is the article here URL:"https://arxiv.org/pdf/1603.07285.pdf". 
 
+
+
+
+!split
+===== Neural Networks vs CNNs =====
+
+Neural networks are defined as _affine transformations_, that is 
+a vector is received as input and is multiplied with a matrix of so-called weights (our unknown paramters) to produce an
+output (to which a bias vector is usually added before passing the result
+through a nonlinear activation function). This is applicable to any type of input, be it an
+image, a sound clip or an unordered collection of features: whatever their
+dimensionality, their representation can always be flattened into a vector
+before the transformation.
+
+However, when we consider images, sound clips and many other similar kinds of data, these data  have an intrinsic
+structure. More formally, they share these important properties:
+* They are stored as multi-dimensional arrays (think of the pixels of a figure) .
+* They feature one or more axes for which ordering matters (e.g., width and height axes for an image, time axis for a sound clip).
+* One axis, called the channel axis, is used to access different views of the data (e.g., the red, green and blue channels of a color image, or the left and right channels of a stereo audio track).
+
+These properties are not exploited when an affine transformation is applied; in
+fact, all the axes are treated in the same way and the topological information
+is not taken into account. Still, taking advantage of the implicit structure of
+the data may prove very handy in solving some tasks, like computer vision and
+speech recognition, and in these cases it would be best to preserve it. This is
+where discrete convolutions come into play.
+
+A discrete convolution is a linear transformation that preserves this notion of
+ordering. It is sparse (only a few input units contribute to a given output
+unit) and reuses parameters (the same weights are applied to multiple locations
+in the input).
+
+
+
+
 !split
 ===== Regular NNs don’t scale well to full images =====
 
@@ -623,3 +658,4 @@ learn the identity function under some constraints.
 
 
 
+