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explain.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<!-- for displaying math as latex -->
<link rel="stylesheet" href="katex/katex.min.css">
<script src="katex/katex.min.js"></script>
<script src="katex/auto-render.min.js"></script>
<script src="js/explain.js"></script>
<style type="text/css">
#wrapper{
width: 980px;
margin-right: auto;
margin-left: auto;
margin-bottom: 200px;
}
canvas.bordered {
border: 1px solid #555;
}
</style>
<title>A Visual Explanation of Neural Networks</title>
</head>
<body>
<div id="wrapper">
<h3> Intelligence </h3>
<p> I've been fascinated by cognition for as long as I can remember. Intelligence is the defining charactistic of humankind, and so mysterious that there remain <a href="http://plato.stanford.edu/entries/dualism/#MinBodHisDua">active debates</a> among philosophers as to whether our minds are governed by the same natural laws as our physical bodies.</p>
<p> I've always felt that, to understand intelligence, we should study the brain.
<h3> Neurons </h3>
<p>An artificial neural network consists of many interconnected units of computation that are modeled after the <a href="https://en.wikipedia.org/wiki/Neuron">elecrically-activated cells</a> in our brains and spinal cords. They looks kind of like this:</p>
<p>Neurons recieve inputs from other activated neurons, and when the weighted sum of those inputs exceeds a threshold, it becomes active itself.</p>
<p>Mathematically speaking, the input to a neuron is the <a href="https://en.wikipedia.org/wiki/Linear_function">linear function</a> </p>
<p> $( f(x_0, x_1)=w_0 x_0 + w_1 x_1 )$ </p>
<p> where </p>
<p> $( x_0, x_1 )$ are the outputs of the incoming neurons, and</p>
<p> $( w_0, w_1 )$ are how much each of those inputs is weighted.</p>
<p>
<canvas id="part1_crtl" width="400" height="400"></canvas>
<canvas id="part1_actv" width="400" height="400" class="bordered"></canvas>
</p>
<p>
<!-- show a mathematical equation here -->
And messes of mathematical symbols.
</p>
<p>
These two representations of neural networks are at two different levels of abstraction.
<!-- make a comparison to python & dis? -->
</p>
<!--
- Linear transformations
- Applying a sigmoid
- Composing a graph of functions
- Graphs of graphs
- Gradients
- Gradient descent
- Putting it all together
-->
</div>
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renderMathInElement(document.body, options);
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</body>
</html>