Perception Components - Introduction

Probably due to my background doing my PhD in a wireless laboratory, I’ve always preferred to think of neural networks as a series of components akin to what we see in a wireless radio. There are high-pass filters, low-pass filters, matched filters, gain, and so on.

This way of thinking about neural networks also impacts how I would approach the difficult task of teaching someone how to understand and use them. I wouldn’t begin a freshman signal analysis course with a discussion of how to optimize your tuning network before first introducing the components of a radio. In the same vein, I will not begin an introduction of neural networks with the mathematics of gradient descent1; instead I will begin with a discussion of components found in neural networks, what they do, and how they solve problems. Then when we proceed to outrageously large neural networks with millions of parameters a student may have some home of understand what it is that all of those numbers are getting up to.

Typical signal processing systems are concerned with decoding a signal from a noisy channel. Neural networks are typical used to do a similar task, but are also responsible for projecting data from an input space to an output space. Without getting too far ahead of ourselves, this means that neural networks can take as input a matrix or vector of any dimensionality and yield any one of those as an output. This diversity means that neural networks have different kinds of building blocks than what we see in a signal processing course. Our exploration of these components and their uses will begin with the lowest dimensional inputs. After we establish the functionality provided by neural network components in each situation we will increase the dimensionality and complexity of our examples.

  1. Stochastic gradient descent is of course important for neural networks, but it is not necessary. There may be other parameter update algorithms that yield the same or better results.