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The simplest form of an artificial neural network explained and demonstrated.
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# Simplest artificial neural network This is the simplest artificial neural network possible explained and demonstrated. ## This is part 1 of a series of github repos on neural networks - part 1 - simplest network (**you are here**) - [part 2 - backpropagation](https://github.com/gokadin/ai-backpropagation) - [part 3 - backpropagation-continued](https://github.com/gokadin/ai-backpropagation-continued) ## Table of Contents - [Theory](#theory) - [Mimicking neurons](#mimicking-neurons) - [A simple example](#a-simple-example) - [The error](#the-error) - [Gradient descent](#gradient-descent) - [Code example](#code-example) - [References](#references) ## Theory ### Mimicking neurons Artificial neural networks are inspired by the brain by having interconnected artificial neurons store patterns and communicate with each other. The simplest form of an artificial neuron has one or multiple inputs <img src="/tex/9fc20fb1d3825674c6a279cb0d5ca636.svg?invert_in_darkmode&sanitize=true" align=middle width=14.045887349999989pt height=14.15524440000002pt/> each having a specific weight <img src="/tex/c2a29561d89e139b3c7bffe51570c3ce.svg?invert_in_darkmode&sanitize=true" align=middle width=16.41940739999999pt height=14.15524440000002pt/> and one output <img src="/tex/deceeaf6940a8c7a5a02373728002b0f.svg?invert_in_darkmode&sanitize=true" align=middle width=8.649225749999989pt height=14.15524440000002pt/>.  At the simplest level, the output is the sum of its inputs times its weights. <p align="center"><img src="/tex/c2d2775d67e954682fac686e557baed2.svg?invert_in_darkmode&sanitize=true" align=middle width=88.33802834999999pt height=44.89738935pt/></p> ### A simple example The purpose of a network is to learn a certain output <img src="/tex/deceeaf6940a8c7a5a02373728002b0f.svg?invert_in_darkmode&sanitize=true" align=middle width=8.649225749999989pt height=14.15524440000002pt/> given certain input(s) <img src="/tex/332cc365a4987aacce0ead01b8bdcc0b.svg?invert_in_darkmode&sanitize=true" align=middle width=9.39498779999999pt height=14.15524440000002pt/> by approximating a complex function with many parameters <img src="/tex/31fae8b8b78ebe01cbfbe2fe53832624.svg?invert_in_darkmode&sanitize=true" align=middle width=12.210846449999991pt height=14.15524440000002pt/> that we couldn't come up with ourselves. Say we have a network with two inputs <img src="/tex/f9b6dcc9279f659321ac3e1098b0ba4f.svg?invert_in_darkmode&sanitize=true" align=middle width=59.69172164999999pt height=21.18721440000001pt/> and <img src="/tex/bf84a893effff44b6d014b2b60460585.svg?invert_in_darkmode&sanitize=true" align=middle width=59.69172164999999pt height=21.18721440000001pt/> and two weights <img src="/tex/4b4518f1b7f0fb1347fa21506ebafb19.svg?invert_in_darkmode&sanitize=true" align=middle width=18.32105549999999pt height=14.15524440000002pt/> and <img src="/tex/f7eb0e840408d84a0c156d6efb611f3e.svg?invert_in_darkmode&sanitize=true" align=middle width=18.32105549999999pt height=14.15524440000002pt/>. The idea is to adjust the weights in such a way that the given inputs produce the desired output. Weights are normally initialized randomly since we can't know their optimal value ahead of time, however for simplicity we will initialize them both to <img src="/tex/034d0a6be0424bffe9a6e7ac9236c0f5.svg?invert_in_darkmode&sanitize=true" align=middle width=8.219209349999991pt height=21.18721440000001pt/>.  If we calculate the output of this network, we will get <p align="center"><img src="/tex/48c4f6073c4655b74cebf396493c9228.svg?invert_in_darkmode&sanitize=true" align=middle width=322.4824614pt height=13.789957499999998pt/></p> ### The error If the output <img src="/tex/deceeaf6940a8c7a5a02373728002b0f.svg?invert_in_darkmode&sanitize=true" align=middle width=8.649225749999989pt height=14.15524440000002pt/> doesn't match the expected target value, then we have an erro
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