“I think the brain is essentially a computer and consciousness is like a computer program. It will cease to run when the computer is turned off. Theoretically, it could be re-created on a neural network, but that would be very difficult, as it would require all one’s memories.”
– Stephen Hawking
Now that we had an introduction, it is time to introduce a basic computational model called the perceptron, which is a model in a collection of models called artificial neurons, in general. The perceptron was invented by Frank Rosenblatt in 1958. Rosenblatt defined the perceptron as a unit of computation that had a threshold Θ and received inputs i_1, i_2, …, i_n, which are multiplied by w_1, w_2, …, w_n respectively. He then proposed that all of the products be summed together and another constant called the bias was added, for which the perceptron would output 1 if the sum was greater than or equal to the threshold, and 0 if it was smaller.
In mathematical terms,
In other words, a perceptron is a unit consisting of something called a weight, which was multiplied by the input (sometimes called the activation), and if the product of the two was bigger than a number called the threshold, the perceptron would output a 1, or 0 if not.
Another way to think about this is, the threshold is a value for which classifies all events α as similar if the summation of the product of their inputs and a set of weights with another constant called the bias is higher than the threshold. This also could be thought of as an event with a point (x, y). The threshold would therefore be a line y = Θ, which separated two different sets of points. Here is a graphical representation:
Like the diagram, the perceptron can similarly “separate” two different inputs and classify or predict the output for that input. So, now that we have these two basic properties, we can start to understand why machine learning and artificial intelligence are important in the field of data science. For example, say you want to classify whether a 3 by 3 grid of inputs is a 0 or 1. This requires a method to separate different sets of inputs and identify common features. In the perceptron model, since the weights, biases, and threshold are the only unknown variables, these are the ones we need to figure out to have the desired classification result. Machine learning, therefore, can be defined as the method that achieves this task of finding ideal values for the weights, bias, and threshold. Do note that other models may not have a threshold, but require an activation function which we will discuss in later chapters.
This was a ground-breaking invention that inspired others after Rosenblatt and caused the first AI winter. An AI winter is a period when no or little progress was made in the field of artificial intelligence. After the invention of the perceptron, professor Marvin Minsky in his book Perceptrons proved that a single layer of these perceptrons wasn’t able to predict anything. This led to a misunderstanding which resulted in a decrease in research on the area. Minsky actually also wrote in the same book that a network of several layers would have the ability to approximate any function, which resulted in the Universal Approximation Theorem, stating that a neural network with multiple layers could approximate any continuous(predictable) function to any degree of accuracy.
Given this information, neural networks are just a collection or array of these perceptrons(although they may have a different type of neuron instead), connected through multiple layers. Usually, the first layer is called the input layer, the middle layers are called the hidden layers and the last layer is called the output layer. Below is a diagram of a neural network.
This network can be called a neural network with structure 3–4–2(appears in the layer order from left to right). The lines on the diagram show the different connections between neurons in the network, which are represented by orange circles. The connections can be referred to as weights, which (if you remember) are multiplied by the input or activation. It is important to note that the number of sets of weights should be one less than the number of layers and that there is only one bias per layer. Usually, there are no connections towards a bias, but biases are connected to the next layer’s neurons. Networks can be called “single-layered networks” when there are only two layers in them (input and output). We will talk more about neural networks in Chapter 4.
- A perceptron is a type of artificial neuron(I will be calling it a ‘neuron’ instead, throughout most of the book).
2. The perceptron is a computational model consisting of weights, a set of inputs or activations, biases, and a threshold.
3. The input to the perceptron is multiplied by the weight and a bias is added. If the result is bigger than another value the threshold, then the perceptron outputs a 1, otherwise, it outputs 0.
4. The perceptron model was invented by Frank Rosenblatt in 1958.
5. A perceptron in mathematical terms is:
where the output of the perceptron is:
where w_k and i_k are the weights and inputs at index k respectively. n is the total number of weights connected to the perceptron and Θ is the threshold value. The output is also alternatively expressed as:
6. Machine learning is a set of algorithms that finds ideal values for the weights, biases, and threshold.
7. A threshold is like a line that separates two different sets of labeled inputs.
8. Marvin Minsky in his book Perceptrons proved that a layer of perceptrons could not predict anything, he also stated that multiple layers of perceptrons were able to approximate any function. This led to an AI winter.
9. The Universal Approximation Theorem states that any continuous function can be approximated to any degree of accuracy using a multilayer neural network.
10. An AI winter is a period when there is little or no further advancement in the field of Artificial Intelligence. This usually is caused by a lack of sponsorship or money that motivates the research in the field of AI.
11. Perceptrons may not have a threshold or bias, but(in that case) will require an activation function(Chapter 3).
12. A network consists of several layers of neurons. Single-layer networks have two layers, the first called the input layer and the last called the output layer. Multi-layer networks also have hidden layers, which are the layers in between the input layer and the output layer.