McCulloch-Pitts Neuron — Mankind’s First Mathematical Model Of A Biological Neuron

 

Source: McCulloch-Pitts Neuron — Mankind’s First Mathematical Model Of A Biological Neuron

 

McCulloch-Pitts Neuron — Mankind’s First Mathematical Model Of A Biological Neuron

It is very well known that the most fundamental unit of deep neural networks is called an artificial neuron/perceptron. But the very first step towards the perceptron we use today was taken in 1943 by McCulloch and Pitts, by mimicking the functionality of a biological neuron.

Note: The concept, the content, and the structure of this article were largely based on the awesome lectures and the material offered by Prof. Mitesh M. Khapra on NPTEL’s Deep Learning course. Check it out!

Biological Neurons: An Overly Simplified Illustration

A Biological Neuron — Wikipedia

Dendrite: Receives signals from other neurons

Soma: Processes the information

Axon: Transmits the output of this neuron

Synapse: Point of connection to other neurons

Basically, a neuron takes an input signal (dendrite), processes it like the CPU (soma), passes the output through a cable like structure to other connected neurons (axon to synapse to other neuron’s dendrite). Now, this might be biologically inaccurate as there is a lot more going on out there but on a higher level, this is what is going on with a neuron in our brain — takes an input, processes it, throws out an output.

Our sense organs interact with the outer world and send the visual and sound information to the neurons. Let’s say you are watching Friends. Now the information your brain receives is taken in by the “laugh or not” set of neurons that will help you make a decision on whether to laugh or not. Each neuron gets fired/activated only when its respective criteria (more on this later) is met like shown below.

Not real.

Of course, this is not entirely true. In reality, it is not just a couple of neurons which would do the decision making. There is a massively parallel interconnected network of 10¹¹ neurons (100 billion) in our brain and their connections are not as simple as I showed you above. It might look something like this:

Still not real but closer.

Now the sense organs pass the information to the first/lowest layer of neurons to process it. And the output of the processes is passed on to the next layers in a hierarchical manner, some of the neurons will fire and some won’t and this process goes on until it results in a final response — in this case, laughter.

This massively parallel network also ensures that there is a division of work. Each neuron only fires when its intended criteria is met i.e., a neuron may perform a certain role to a certain stimulus, as shown below.

Division of work

It is believed that neurons are arranged in a hierarchical fashion (however, many credible alternatives with experimental support are proposed by the scientists) and each layer has its own role and responsibility. To detect a face, the brain could be relying on the entire network and not on a single layer.

Sample illustration of hierarchical processing. Credits: Mitesh M. Khapra’s lecture slides

Now that we have established how a biological neuron works, lets look at what McCulloch and Pitts had to offer.

Note: My understanding of how the brain works is very very very limited. The above illustrations are overly simplified.

McCulloch-Pitts Neuron

The first computational model of a neuron was proposed by Warren MuCulloch (neuroscientist) and Walter Pitts (logician) in 1943.

This is where it all began..

It may be divided into 2 parts. The first part, takes an input (ahem dendrite ahem), performs an aggregation and based on the aggregated value the second part, f makes a decision.

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