We often think of Momentum as a means of dampening oscillations and speeding up the iterations, leading to faster convergence. But it has other interesting behavior. It allows a larger range of step-sizes to be used, and creates its own oscillations. What is going on?

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A Brief Survey of Techniques

Before diving in: if you haven’t encountered t-SNE before, here’s what you need to know about the math behind it. The goal is to take a set of points in a high-dimensional space and find a faithful representation of those points in a lower-dimensional space, typically the 2D plane. The algorithm is non-linear and adapts to the underlying data, performing different transformations on different regions. Those differences can be a major source of confusion.

This is the first paragraph of the article. Test a long — dash -- here it is.

Test for owner's possessive. Test for "quoting a passage." And another sentence. Or two. Some flopping fins; for diving.

Some text in an aside, margin notes, etc...

Here's a test of an inline equation c = a^2 + b^2. Also with configurable katex standards just using inline '$' signs: $$x^2$$ And then there's a block equation:

c = \pm \sqrt{ \sum_{i=0}^{n}{a^{222} + b^2}}

Math can also be quite involved:

\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } } 1.1

Citations

We can also cite external publications. . We should also be testing footnotesThis will become a hoverable footnote. This will become a hoverable footnote. This will become a hoverable footnote. This will become a hoverable footnote. This will become a hoverable footnote. This will become a hoverable footnote. This will become a hoverable footnote. This will become a hoverable footnote.. There are multiple footnotes, and they appear in the appendixGiven I have coded them right. Also, here's math in a footnote: c = \sum_0^i{x}. Also, a citation. Box-ception! as well.

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Displaying code snippets

Some inline javascript:var x = 25;. And here's a javascript code block.

var x = 25; function(x){ return x * x; }

We also support python.

# Python 3: Fibonacci series up to n def fib(n): a, b = 0, 1 while a < n: print(a, end=' ') a, b = b, a+b

And a table

First	Second	Third
23	654	23
14	54	34
234	54	23

That's it for the example article!