Bounded Rationality (Posts about metric tensor)http://bjlkeng.github.io/enSat, 03 Aug 2024 01:42:51 GMTNikola (getnikola.com)http://blogs.law.harvard.edu/tech/rssManifolds: A Gentle Introductionhttp://bjlkeng.github.io/posts/manifolds/Brian Keng<div><p>Following up on the math-y stuff from my <a class="reference external" href="http://bjlkeng.github.io/posts/tensors-tensors-tensors/">last post</a>,
I'm going to be taking a look at another concept that pops up in ML: manifolds.
It is most well-known in ML for its use in the
<a class="reference external" href="https://www.quora.com/What-is-the-Manifold-Hypothesis-in-Deep-Learning">manifold hypothesis</a>.
Manifolds belong to the branches of mathematics of topology and differential
geometry. I'll be focusing more on the study of manifolds from the latter
category, which fortunately is a bit less abstract, more well behaved, and more
intuitive than the former. As usual, I'll go through some intuition,
definitions, and examples to help clarify the ideas without going into too much
depth or formalities. I hope you mani-like it!</p>
<p><a href="http://bjlkeng.github.io/posts/manifolds/">Read more…</a> (30 min remaining to read)</p></div>manifoldsmathjaxmetric tensorhttp://bjlkeng.github.io/posts/manifolds/Tue, 17 Apr 2018 11:24:57 GMTTensors, Tensors, Tensorshttp://bjlkeng.github.io/posts/tensors-tensors-tensors/Brian Keng<div><p>This post is going to take a step back from some of the machine learning
topics that I've been writing about recently and go back to some basics: math!
In particular, tensors. This is a topic that is casually mentioned in machine
learning papers but for those of us who weren't physics or math majors
(*cough* computer engineers), it's a bit murky trying to understand what's going on.
So on my most recent vacation, I started reading a variety of sources on the
interweb trying to piece together a picture of what tensors were all
about. As usual, I'll skip the heavy formalities (partly because I probably
couldn't do them justice) and instead try to explain the intuition using my
usual approach of examples and more basic maths. I'll sprinkle in a bunch of
examples and also try to relate it back to ML where possible. Hope you like
it!</p>
<p><a href="http://bjlkeng.github.io/posts/tensors-tensors-tensors/">Read more…</a> (23 min remaining to read)</p></div>bilinearcontravariancecovariancecovectorsgeometric vectorslinear transformationsmathjaxmetric tensortensorshttp://bjlkeng.github.io/posts/tensors-tensors-tensors/Tue, 13 Mar 2018 13:24:57 GMT