In theoretical computer science and the study of machine learning, the manifold hypothesis is the hypothesis that many high-dimensional data sets that occur in the real world actually lie along low-dimensional latent manifolds inside that high-dimensional space. As a consequence of the manifold hypothesis, many data sets that appear to initially require many variables to describe, can actually be described by a comparatively small number of variables, likened to the local coordinate system of the underlying manifold. It is suggested that this principle underpins the effectiveness of machine learning algorithms in describing high-dimensional data sets by considering a few common features. The manifold hypothesis is related to the effectiveness of nonlinear dimensionality reduction techniques in machine learning. Many techniques of dimensional reduction make the assumption that data lies along a low-dimensional submanifold, such as manifold sculpting, manifold alignment, and manifold regularization. (Wikipedia).
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Is string theory a unified theory?
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From playlist Science Unplugged: String Theory
What is the goal of string theory?
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From playlist Science Unplugged: String Theory
How does string theory suggest that space itself can tear?
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From playlist Science Unplugged: String Theory
Brian Greene explains the basic idea of String Theory in under 3 minutes. Thirty-five years ago string theory took physics by storm, promising the coveted unified theory of nature’s forces that Einstein valiantly sought but never found. In the intervening decades, string theory has brought
From playlist Science Shorts and Explainers
The multiverse hypothesis: Is our universe the only one?
Support me on Patreon: https://www.patreon.com/Sabine In the past decades, the idea that our universe is only one of many, has become popular among physicists. If there are several universes, their collection is called the “multiverse”, and physicists have a few theories for this that I e
From playlist Physics
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From playlist Science Unplugged: General Relativity
What is the shape of the universe?
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From playlist Science Unplugged: Cosmology
[Quiz] Eigenfaces, Domain adaptation, Causality, Manifold Hypothesis, Denoising Autoencoder
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From playlist AI Coffee Break Quiz question answers
Testing the manifold hypothesis - Hariharan Narayanan
PROGRAM: Data Assimilation Research Program Venue: Centre for Applicable Mathematics-TIFR and Indian Institute of Science Dates: 04 - 23 July, 2011 DESCRIPTION: Data assimilation (DA) is a powerful and versatile method for combining observational data of a system with its dynamical mod
From playlist Data Assimilation Research Program
Olivier Benoist: Algebraic approximation of submanifolds of real algebraic varieties
CONFERENCE Recording during the thematic meeting : "Real Aspects of Geometry" the November 1, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audi
From playlist Algebraic and Complex Geometry
Fitting manifolds to data - Charlie Fefferman
Workshop on Topology: Identifying Order in Complex Systems Topic: Fitting manifolds to data Speaker: Charlie Fefferman Affiliation: Princeton University Date: April 7, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
This lecture was held by Abel Laureate John Milnor at The University of Oslo, May 25, 2011 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2011 1. "Spheres" by Abel Laureate John Milnor, Institute for Mathematical
From playlist Abel Lectures
The Inner Equation for Generalized Standard Maps - Pau Martin
Pau Martin Universitat Poliecnica de Catalunya, Barcelona, Spain February 15, 2012 We study particular solutions of the "inner equation" associated to the splitting of separatrices on "generalized standard maps". An exponentially small complete expression for their difference is obtained.
From playlist Mathematics
Macroscopically minimal hypersurfaces - Hannah Alpert
Variational Methods in Geometry Seminar Topic: Macroscopically minimal hypersurfaces Speaker: Hannah Alpert Affiliation: Ohio State University Date: March 12, 2019 For more video please visit http://video.ias.edu
From playlist Variational Methods in Geometry
Fitting a manifold to noisy data by Hariharan Narayanan
DISCUSSION MEETING THE THEORETICAL BASIS OF MACHINE LEARNING (ML) ORGANIZERS: Chiranjib Bhattacharya, Sunita Sarawagi, Ravi Sundaram and SVN Vishwanathan DATE : 27 December 2018 to 29 December 2018 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore ML (Machine Learning) has enjoyed tr
From playlist The Theoretical Basis of Machine Learning 2018 (ML)
Cosmology and Relativity with Dr. Leah Jenks
Einstein's Theory of General Relativity has been tried and tested many times, and so far, Einstein was right. But we know his theory must be incomplete, as it still doesn't integrate with quantum mechanics. Where are physicists searching next for the future of cosmology and relativity? Dr.
From playlist Interviews
David Ben-Zvi: Geometric Langlands correspondence and topological field theory - Part 1
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
GPDE Workshop - External doubly stochastic measures and optimal transportation
Robert McCann University of Toronto February 23, 2009 For more videos, visit http://video.ias.edu
From playlist Mathematics
What are the candidates for a unified theory?
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From playlist Science Unplugged: Physics