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Momentum visualization

Why Momentum Really Works

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?

1

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.

Here's a test of an inline equation c=a2+b2c = a^2 + b^2. And then there's a block equation:

c=±i=0na222+b2c = \pm \sqrt{ \sum_{i=0}^{n}{a^{222} + b^2}}

Math can also be quite involved:

1(ϕ5ϕ)e25π=1+e2π1+e4π1+e6π1+e8π1+\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 footnotes1 . There are multiple footnotes, and they appear in the appendix2 as well.

2

Displaying code snippets

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

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

We also support python.

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

FirstSecondThird
2365423
145434
2345423
initialized!

That's it for the example article!

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