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<h2>What is this?</h2>

<h5>Cost function</h5>

<p>This is implementation of neural network with back-propagation. There aren't any special tricks, it's as simple neural

network as it gets. The cost is defined as \(C = \frac{1}{2 \times sampleCnt}\sum^{sampleCnt}_{m=1}(\sum^{outputSize}_{n=1}(neruon_n-target_n)^2)\).

In words: Error is defined as \((value - target)^2\). To get error of neural network for one training sample, you

simply add errors of all output neurons. The total cost is then defined as average error of all training samples.

</p>

<h5>Forward propagation</h5>

<p>

Let's say that the value of connection is the connection's weight (how wide it is) times the first connected neuron. To calculate

the value of some neuron you add the values of all incoming connections and apply the

<ahref="https://www.desmos.com/calculator/dw9fmqwlmn">sigmoid</a> function the that sum. Other activation functions are possible, but I have not implemented them yet.

</p>

<h5>Back propagation</h5>

<p>

This is implementation of neural network with back-propagation. blablabla

In the simplest way possible: The cost function defined above is a function dependend on weights of connections in the same

way as \(f(x, y) = x^2 + y^2\) is dependend on x and y. What you do is that you take derivation of C with respect

to each of the weights. Each of these derivatives tells you in which direction (up/down) will the cost change if

you increase/decrease the weight. So you take the old weight and substract a small step is a direction that decreases

the cost. In equation: \(w_{new} = w_{old} - rate \times \frac{\partial C}{\partial w_{old}}\). How to compute the

derivative is a little bit harder, but all you need to know is the

<i>chain rule</i>. I highly recommend

<ahref="https://www.youtube.com/watch?v=aircAruvnKk">3blue1brown's series</a> and

<ahref="https://web.archive.org/web/20150317210621/https://www4.rgu.ac.uk/files/chapter3%20-%20bp.pdf">this paper</a> for better understanding.

</p>

<h5>Inpiration</h5>

<p>

I got inspired by the

<ahref="https://playground.tensorflow.org">https://playground.tensorflow.org</a> and

<ahref="https://cs.stanford.edu/people/karpathy/convnetjs/">https://cs.stanford.edu/people/karpathy/convnetjs/</a>, but I wanted something simpler and build it myself from the