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Interaction of Geometry & Machine Learning

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Title: Interaction of Geometry & Machine Learning

Summary:

In this module of the Topics in Robotics PhD course, we will focus on exploring aspects of the role of geometry in machine learning. Three main topics, in particular, will be spectral theory on graphs, manifolds and generic data and applications to dimensionality reduction and geometric deep learning as well as low dimensional geometric representations for robotics applications (planning & RL).

Following the overview lectures (preliminary schedule below), pairs of participants will be required to define a small practical project that will involve presenting the underlying methodology for the project based on existing research (such as a specific research paper) and the groups will implement and evaluate their approach and present the results to the other participants.

Course Lecturers:

Florian Pokorny
fpokorny (at) kth.se

Anastasiia Varava
varava (at) kth.se

Preliminary Schedule (to be discussed/confirmed):

Zoom link (log in with your KTH credentials): https://kth-se.zoom.us/j/64500004938

Lecture 1 - Topology crash course: 2020-11-10, 13:00-15:00, via Zoom

  • What is a topological space?
  • Introduction to foundational concepts of topology
  • Continuity and convergence in topological spaces
  • Topological manifolds

Lecture 2 - Manifolds of various types: 2020-11-17, 13:00-15:00, via Zoom

  • What types of manifolds can we use for ML? Review of foundational concepts.
  • Smooth structures, PL structures, C^k structures, Riemannian manifolds
  • Operators on Riemannian manifolds
  • The manifold hypothesis in ML

Lecture 3 - Introduction to spectral methods: 2020-12-01, 13:00-15:00, via Zoom

NOTE CHANGED DATE! - MOVED BY ONE WEEK!

  • Foundations of Laplacians and their eigenfunctions
  • Examples of spectral theory on manifolds, graphs, ...

Lecture 4 - Connections to dimensionality reduction in ML: 2020-12-08, 13:00-15:00, via Zoom

  • Connections and convergence results of ML dimensionality methods and relation to spectral theory

Lecture 5 - Geometric Deep Learning & Related Topics: 2020-12-15, 13:00-15:00, via Zoom

  • Geometric Deep Learning & Spectral Methods

Lecture 6 - Dimensionality Reduction & Robotics Applications: 2020-12-?, ?-?, via Zoom

  • Dimensionality Reduction for Robotics with applications to Reinforcement Learning & Motion Planning

Project Proposal Presentation/Discussion: 2021-?-?, 13:00-15:00

Final Project Presentation Slots: 2021-03-?, 13:00-15:00

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