[b]Artificial Neural Networks[/b] (ANNs) are a specific tool for implementing ML. [br][br]Mathematically, ANNs are composite functions made up of simple mathematical functions like linear ([math]y=mx+b[/math]) and exponential ([math]y=e^x[/math]) functions. Calculus is used to "train" these composite functions to do various tasks.[br][br]In the applet below you can see an ANN perform machine learning with the push of a button. Each time you press the button, backpropagation "learns" how to select weights (w's) to get [math]out_{o1}[/math] and [math]out_{o2}[/math] to better target [math]o_1[/math] and [math]o_2[/math]. Each press of the button logs one epoch (or learning cycle). Backpropagation is the name for the calculus optimization problem the network is solving.[br][br]TRY IT! If anything goes wrong, click the refresh button in the top right of the applet. We'll discuss what's going on as a group.[br]

The inputs together with your targets are often called [b]training data[/b].[br][br]The [b]biases[/b] are optional fixed numbers that get added to the net's. They are user-specified parameters, and are not considered "learnable". They are set to 0 in the applet for simplicity.[br][br]The E's on the right are [b]errors (or loss)[/b], or a measurement of how close the computed outputs are to your targets. In this example we're using mean square error for an error.[br][br]The [b]learning rate[/b] adjusts the impact of each epoch of backpropagation on the weights. Higher learning rates have a bigger impact. Careful though! A learning rate too high might accidentally jump your ANN into a very bad error!

An ANN takes input data, and uses it compute outputs that [b]target[/b] numbers you specify. [br][br]An ANN usually starts its life doing a very bad job of computing outputs close to your targets, but ANNs use calculus to "[b]learn[/b]" how to get their calculated outputs closer to your specified targets. [br][br]You're can see an ANN below. I know it looks insanely complicated, but I promise it's not too bad. :)[br][br]There are two inputs, [math]i_1=2[/math] and [math]i_2=3[/math]. Do you see them on the left? You can change them if you want, but don't just yet.[br][br]There are two targets, [math]o_1=0.2[/math] and [math]o_2=0.3[/math]. Do you seem them on the right? You can also change these, but don't just yet.[br][br]The two outputs the ANN has computed are [math]out_{o1}=0.65596[/math] and [math]out_{o2}=0.68926[/math]. Do you seem them in the gray boxes? You can't change these. These have been computed by the ANN.[br][br]You don't need to know too much about what's in between (all the w's and net's and 1/(1+e^-x)'s), but I'll talk about them a little bit. If anyone's curious you can read more [url=https://docs.paperspace.com/machine-learning/wiki/weights-and-biases]here[/url].[br][br]The cool thing about ANNs is that they use calculus to LEARN how to adjust the w's to get the computed outputs, [math]out_{o1}[/math] and [math]out_{o2}[/math], closer to your targets, [math]o_1[/math] and [math]o_2[/math]. It's called [b]backpropagation[/b], and each iteration of backpropagation is called an [b]epoch[/b].