Материал из MachineLearning.

Версия 19:46, 1 августа 2021 (править) Strijov (Обсуждение | вклад) (→Theme 1: Surface differential geometry) ← К предыдущему изменению		Версия 20:04, 1 августа 2021 (править) (отменить) Strijov (Обсуждение | вклад) (→Fourier for fun and practice nD) К следующему изменению →
Строка 62:		Строка 62:
	== Fourier for fun and practice nD==		== Fourier for fun and practice nD==
		+
		+	See:
		+	* Fourier analysis on Manifolds 5G page 49
		+	* Spectral analysis on meshes
	== Geometric Algebra ==		== Geometric Algebra ==

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Версия 20:04, 1 августа 2021

Основная статья: Численные методы обучения по прецедентам (практика, В.В. Стрижов)

Содержание 1 General principles 2 Syllabus and goals 3 Theme 1: 3.1 Message 3.2 Basics 3.3 Application 3.4 Code 4 Theme 1: Manifolds 5 Code 6 Theme 1: ODE and flows 7 Theme 1: PDE 8 Fourier for fun and practice 1D 9 Fourier for fun and practice nD 10 Geometric Algebra 11 Theme 1: High order splines 12 Theme 1: Topological data analysis 13 Theme 1: Homology versus homotopy 14 Fundamental theorems

• Geometric deep learning
• Functional data analysis
• Applied mathematics for machine learning

General principles

1. The experiment and measurements defines axioms i

Syllabus and goals

Theme 1:

Message

Basics

Application

Code

https://papers.nips.cc/paper/2018/file/69386f6bb1dfed68692a24c8686939b9-Paper.pdf

Theme 1: Manifolds

Code

Surface differential geometry Coursera code video for Image and Video Processing

Theme 1: ODE and flows

• Neural Ordinary Differential Equations (source paper and code)
• W: Flow-based generative model
• Flows at deepgenerativemodels.github.io
• Знакомство с Neural ODE на хабре

Goes to BME

• Variational Inference with Normalizing Flows (source paper)
• Flow-based deep generative models

Theme 1: PDE

(after RBF)

Fourier for fun and practice 1D

Fourier Code

Fourier for fun and practice nD

See:

• Fourier analysis on Manifolds 5G page 49
• Spectral analysis on meshes

Geometric Algebra

experior product and quaternions

Theme 1: High order splines

Theme 1: Topological data analysis

Theme 1: Homology versus homotopy

W: Homology

Fundamental theorems

W: Inverse function theorem and Jacobian