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Ludwig Schubert
183 lines
7.3 KiB
HTML
183 lines
7.3 KiB
HTML
<!--
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Copyright 2018 The Distill Template Authors
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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<!doctype html>
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<head>
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<script src="template.v2.js"></script>
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<meta charset="utf8">
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</head>
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<body>
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<distill-header></distill-header>
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<d-front-matter>
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<script id='distill-front-matter' type="text/json">{
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"title": "Why Momentum Really Works",
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"description": "Although \" extremely useful for visualizing high-dimensional data, t-SNE plots can sometimes be mysterious or misleading.",
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"published": "Jan 10, 2017",
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"authors": [
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{
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"author":"Chris Olah",
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"authorURL":"https://colah.github.io/",
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"affiliations": [{"name": "Google Brain"}]
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},
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{
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"author":"Ludwig Schubert",
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"authorURL":"https://shancarter.com/",
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"affiliations": [{"name": "Google Brain", "url": "https://g.co/brain"}]
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},
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{
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"author":"Shan Carter",
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"authorURL":"https://shancarter.com/",
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"affiliations": [
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{"name": "Google Brain", "url": "https://g.co/brain"},
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{"name": "NYT", "url": "https://nytimes.com"}
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]
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}
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],
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"katex": {
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"delimiters": [
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{"left": "$$", "right": "$$", "display": false}
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]
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}
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}</script>
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</d-front-matter>
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<d-title>
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<figure style="grid-column: page; margin: 1rem 0;"><img src="momentum.png"
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style="width:100%; border: 1px solid rgba(0, 0, 0, 0.2);" /></figure>
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<p>We often think of Momentum<d-cite key="mercier2011humans"></d-cite> as a means of dampening oscillations and
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speeding up the iterations, leading to faster convergence. But it has other interesting behavior. It allows a
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larger range of step-sizes to be used, and creates its own oscillations. What is going on?</p>
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</d-title>
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<d-byline></d-byline>
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<d-article>
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<a class="marker" href="#section-1" id="section-1"><span>1</span></a>
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<h2>A Brief Survey of Techniques</h2>
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<p>Before diving in: if you haven’t encountered t-SNE before, here’s what you need to know about the math behind it.
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The goal is to take a set of points in a high-dimensional space and find a faithful representation of those points
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in a lower-dimensional space, typically the 2D plane. The algorithm is non-linear and adapts to the underlying
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data, performing different transformations on different regions. Those differences can be a major source of
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confusion.</p>
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<p>This is the first paragraph of the article. Test a long — dash -- here it is.</p>
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<p>Test for owner's possessive. Test for "quoting a passage." And another sentence. Or two. Some flopping fins; for
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diving.</p>
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<aside>Some text in an aside, margin notes, etc...</aside>
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<p>Here's a test of an inline equation <d-math>c = a^2 + b^2</d-math>. Also with configurable katex standards just
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using inline '$' signs: $$x^2$$ And then there's a block equation:</p>
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<d-math block>
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c = \pm \sqrt{ \sum_{i=0}^{n}{a^{222} + b^2}}
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</d-math>
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<p>Math can also be quite involved:</p>
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<d-math block>
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\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}}
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{1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }
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</d-math>
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<a class="marker" href="#section-1.1" id="section-1.1"><span>1.1</span></a>
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<h3>Citations</h3>
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<p>
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<d-slider style="width: 200px;"></d-slider>
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</p>
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<p>We can<d-cite bibtex-key="mercier2011humans"></d-cite> also cite <d-cite
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key="gregor2015draw,mercier2011humans,openai2018charter"></d-cite> external publications. <d-cite
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key="dong2014image,dumoulin2016guide,mordvintsev2015inceptionism"></d-cite>. We should also be testing footnotes
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<d-footnote>This will become a hoverable footnote. This will become a hoverable footnote. This will become a
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hoverable footnote. This will become a hoverable footnote. This will become a hoverable footnote. This will
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become a hoverable footnote. This will become a hoverable footnote. This will become a hoverable footnote.
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</d-footnote>. There are multiple footnotes, and they appear in the appendix<d-footnote>Given I have coded them
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right. Also, here's math in a footnote: <d-math>c = \sum_0^i{x}</d-math>. Also, a citation. Box-ception<d-cite
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key='gregor2015draw'></d-cite>!</d-footnote> as well.</p>
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<a class="marker" href="#section-2" id="section-2"><span>2</span></a>
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<h2>Displaying code snippets</h2>
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<p>Some inline javascript:<d-code language="javascript">var x = 25;</d-code>. And here's a javascript code block.
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</p>
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<d-code block language="javascript">
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var x = 25;
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function(x){
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return x * x;
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}
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</d-code>
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<p>We also support python.</p>
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<d-code block language="python">
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# Python 3: Fibonacci series up to n
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def fib(n):
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a, b = 0, 1
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while a < n: print(a, end=' ' ) a, b=b, a+b </d-code>
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<p>And a table</p>
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<table>
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<thead>
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<tr>
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<th>First</th>
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<th>Second</th>
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<th>Third</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>23</td>
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<td>654</td>
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<td>23</td>
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</tr>
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<tr>
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<td>14</td>
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<td>54</td>
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<td>34</td>
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</tr>
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<tr>
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<td>234</td>
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<td>54</td>
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<td>23</td>
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</tr>
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</tbody>
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</table>
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<d-figure id="last-figure"></d-figure>
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<script>
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const figure = document.querySelector("d-figure#last-figure");
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const initTag = document.createElement("span");
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initTag.textContent = "initialized!"
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figure.appendChild(initTag);
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figure.addEventListener("ready", function () {
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const initTag = figure.querySelector("span");
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initTag.textContent = "ready"
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console.log('ready')
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});
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figure.addEventListener("onscreen", function () {
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const initTag = figure.querySelector("span");
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initTag.textContent = "onscreen"
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console.log('onscreen')
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});
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figure.addEventListener("offscreen", function () {
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const initTag = figure.querySelector("span");
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initTag.textContent = "offscreen!"
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console.log('offscreen')
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});
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</script>
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<p>That's it for the example article!</p>
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</d-article>
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<d-appendix>
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<h3>Contributions</h3>
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<p>Some text describing who did what.</p>
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<h3>Reviewers</h3>
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<p>Some text with links describing who reviewed the article.</p>
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<d-bibliography src="bibliography.bib"></d-bibliography>
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</d-appendix>
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<distill-footer></distill-footer>
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</body> |