What makes Artificial Intelligence Intelligent? Math of course!

Is math really at the core of Artificial Intelligence? Yes, it is! Indeed, it is such a direct application of math that you may start to think that Artificial Intelligence (AI) is fundamentally applied math – between you, me and these four walls, that’s all it is, but don’t tell the “AI engineers”.

To understand how math makes AI work, you need to understand the basics of Artificial Intelligence. Lucky for you, I just so happen to write code for artificial intelligence and have been since 2004 when I invented an artificial neural network system (ANNS) for prosthetics. Just to be clear, I will not self-hijack this post into an AI post; I’ll only explain enough AI so you see the math in it.

The basic building blocks of AI are: Data, the Algorithm and the Teach-Learn-Infer process (TLIP). The Data is any information (words, images, etc.) that is fed into the AI as binary information (1s and 0s). The TLIP is how the system is taught to recognize the data, how it learns what the data is, and how it then infers from past learning to provide information. The core of the process is the Algorithm (algo). The algo is the sequence of steps the AI follows to operate on the data and runs it’s TLIP. At the core of the algo is the math that makes the decisions. NOTE: the TLIP acronym is my acronym, so most likely you will not find it elsewhere, but you will find the concept of train-learn-infer as standard.

The three, core math concepts that are currently used in AI are: Linear Algebra (Vectors & Matrices), Calculus (derivatives, optimization) and Probability & Statistics. These three work together to form the complex equations that create the activation functions and layers in AI/ML/ANNS. NOTE: If you are an Electrical Engineer (EE) or are studying EE, ALL the elements of AI are taught to you as your bread and butter, all you got to do is apply it. I encourage you to do so.

Thus, humble Algebra is at the core of AI. Let’s explore a simple creation of an activation function just to see how algebra does its magic.

Take the simple algebraic equation

 y = mx + c . . . eq’n (1)

This is the slope-intercept form of a straight line, commonly used in linear regression where 𝑦 the dependent variable (the output or prediction), 𝑥 is the independent variable (the input), 𝑚 is the slope of the line (the rate of change of 𝑦 with respect to 𝑥), and 𝑐 is the y-intercept (the value of 𝑦 when 𝑥 = 0)

Another way of writing equation (1) is:

 y = f(x) = mx + c, where f(x) is called a function of x. 

It is called a function because it represents the functionality that connects a value of x with a specific output value, in other words, it is a mathematical relationship. Using function notation, for any value x, f(x) maps x to one, corresponding output value using the process mx + c. For example:

This equation can be used to represent the basic input-output process of an artificial neuron by replacing the slope c with a weight w, and the intercept c with a bias b, where f(x) is the output and x is the input. The bias simply shifts the linear relationship relative to wx and allows the linear relationship to approximate:

 f(x) = mx + c becomes f(x) = wx + b

If you wanted to represent multiple artificial neurons up to some number of neurons n, you could write the equation as:

[ f(x1) = w1x1 + b1 ] + [ f(x2) = w2x2 + b2 ] + . . . + [ f(xn) = wnxn + bn ]

Simplifying for a simple artificial neuron model with n inputs:

 y =  f(w1x1 + w2x2 + w3x3 + . . . + wnxn + b ).

This is just an example of linear functions. In AI, there are non-linear functions, step functions, sigmoid functions, parametric and more, and it is all math!