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Pure mathematics in AI

Anonymous Mon 30 Nov 20:09:35 2020 No.12404545 View Reply Original Report

Quoted By: >>12404592 >>12404608 >>12404742 >>12405036 >>12405042

Been seeing a lot of pure mathematics used in machine learning, like manifolds. What for?

Anonymous

Anonymous Mon 30 Nov 2020 20:19:09 No.12404592 Report

Quoted By:

>>12404545
dunno, probably something with high dimensional vector spaces and linear+nonlinear transformations on them.

Anonymous

Anonymous Mon 30 Nov 2020 20:22:54 No.12404608 Report

Quoted By:

>>12404545
machine learning is a lot of optimization, and staying on a manifold could be a form of constraint

Anonymous

Anonymous Mon 30 Nov 2020 21:04:36 No.12404742 Report

Quoted By:

>>12404545
Bcause e.g. in classification problems, it is usually assumed that each class to be represented by manifold of the feature space.
It useful, because if you feature space is 1000 dimensional, but what you carer about is actually 10 dimensional manifold, then you can reduce your dimensionality to 100 times which is efficiencient both statistically and computationally.

See here (chapter 5.11.3) for a high level description:
https://www.deeplearningbook.org/contents/ml.html

Anonymous

Anonymous Mon 30 Nov 2020 22:15:32 No.12405036 Report

Quoted By:

>>12404545
You have a 2D information space of all possibilities. You need to create a line to separate the results you want from those you don't. If your information space is multi-dimensional you need a manifold. It is just a sheet a straight line. It's bretty poring, but the results are obviously fairly impressive.

Anonymous

Anonymous Mon 30 Nov 2020 22:17:38 No.12405042 Report

Quoted By:

>>12404545
Manifold learning and dimensionality reduction are naturally problems stated in the language of functional analysis and algebraic topology. Yes, shocking, these pure fields of mathematics that every undergrad memes on despite being made to make sense of structure on abstract spaces that show up everywhere in science are practical. Shocking.

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