A curated collection of resources and research related to the geometry of representations in the brain, deep networks, and beyond, collaboratively generated on the Symmetry and Geometry in Neural Representations Slack Workspace.
This is a collaborative work-in-progress. Please contribute via PRs!
- Group Theory: A Primer (2019)
Luciano da Fontoura Costa - Tensors in Computations (2021)
Lek-Heng Lim - Aspects of Harmonic Analysis and Representation Theory (2021)
Gallier & Quaintance - Basic concepts of representation theory (2013)
Amritanshu Prasad - Representation Theory of Finite Groups (2012)
Bemjamin Steinberg
- Essence of Group Theory *Beginner-Friendly
Mathemaniac - Abstract Algebra *Beginner-Friendly
Socratica - Euler's formula with introductory group theory *Intuition Building
3blue1brown - What is a Tensor?
XylyXylyX - Representation Theory
Math Doctor Bob - Category Theory for AI
Online Course, October 2022
- Lie Groups, Lie Algebras, and Representations (2003)
Brian C. Hall - Differential Geometry and Lie Groups: A Computational Perspective (2020)
Gallier & Quaintance - Introduction to Riemannian Geometry and Geometric Statistics: from basic theory to implementation with Geomstats (2022)
Nicolas Guigui, Nina Miolane, Xavier Pannec
- Geometry and Topology and Symmetry *Beginner-Friendly
Sean Carroll - Differential Geometry for Computer Science
Justin Solomon - Discrete Differential Geometry
CMU - What is a Manifold?
XylyXylyX - Manifolds
Robert Davie - Lie Groups and Lie Algebras
XylyXylyX - Lectures on Geometric Anatomy of Theoretical Physics
Frederic Schuller - Weekend with Bernie (Riemann)
Søren Hauberg @ DTU - Riemann and Gauss Meet Asimov: A Tutorial on Geometric Methods in Robot Learning, Optimization, and Control
IROS 2022
- Introduction to Differential Geometry and Machine Learning
Geomstats Jupyter notebooks - Differential Geometry for Machine Learning
Roger Grosse - Manifolds: A Gentle Introduction
Brian Keng
- Group Invariance Applications in Statistics (1989)
Morris Eaton - Group Theoretical Methods in Machine Learning (2008)
Risi Kondor, PhD Thesis - Pattern Theory: The Stochastic Analysis of Real-World Signals (2010)
David Mumford and Agnès Desolneux - Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges (2021)
Michael M. Bronstein, Joan Bruna, Taco Cohen, Petar Veličković - Equivariant Convolutional Networks (2021)
Taco Cohen, PhD Thesis - An Introduction to Optimization on Smooth Manifolds (2022)
Nicolas Boumal
- Geometric Deep Learning (2nd Edition)
Michael Bronstein, Joan Bruna, Taco Cohen, Petar Veličković @ AMMI - CSC 2547: Current Topics in Machine Learning Methods in 3D and Geometric Deep Learning (2021)
Animesh Garg @ University of Toronto - An Introduction to Group-Equivariant Deep Learning (2022)
Erik Bekkers @ UvA - Italian Summer School on Geometric Deep Learning (2022)
Cristian Bodnar, Michael Bronstein, Francesco Di Giovanni, Pim de Haan, Maurice Weiler - COMP760: Geometry and Generative Models (2022)
Joey Bose and Prakash Panangaden @ MILA
- Geometric foundations of Deep Learning
Michael Bronstein, Joan Bruna, Taco Cohen, and Petar Veličković - What does 2022 hold for Geometric & Graph ML?
Michael Bronstein - Geometric Machine Learning for Shape Analysis with Jupyter Notebooks
Nina Miolane
- Introduction to the Theory of Neural Computation (1991)
John Hertz, Anders Krogh, Richard G Palmer - Theoretical Neuroscience (2001)
Peter Dayan - Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (2006)
Eugene M. Izhikevich - Neuronal Dynamics: From single neurons to networks and models of cognition (2014)
Wulfram Gerstner, Werner M. Kistler, Richard Naud and Liam Paninsky - Principles of Neural Design (2015)
Peter Sterling & Simon Laughlin
- Rhythms of the Brain (2006)
Gyorgy Buzsaki - Networks of the Brain (2010)
Olaf Sporns - Models of the Mind: How Physics, Engineering and Mathematics Have Shaped Our Understanding of the Brain (2021)
Grace Lindsay
- OpenNeuro
- NeuroVault
- CRCNS
- NeuroData Without Borders
- Allen Brain Atlas
- Kavli Institute for Systems Neuroscience Grid Cell Database
- The Natural Scenes Dataset
- Geomstats
- Computation, statistics, and machine learning on non-Euclidean manifolds
- Giotto TDA
- Topological Data Analysis
- E3NN
- E(3)-equivariant neural networks
- equivariant-MLP
- Construct equivariant multilayer perceptrons for arbitrary matrix groups
- SHTOOLS
- Python library for computations involving spherical harmonics
- LieConv
- Generalizing convolutional neural networks for equivariance to Lie groups on arbitrary continuous data
- Open Neuroscience
- A database of open-source tools and software for neuroscience
- LieTorch
- Geometric machine learning and Lie analysis tools for PyTorch
- NeurIPS Workshop on Symmetry and Geometry in Neural Representations (2023)
- ICML Workshop on Topology, Algebra and Geometry in Machine Learning (2023)
- RSS Workshop on Symmetries in Robot Learning (2023)
- NeurIPS Workshop on Symmetry and Geometry in Neural Representations (2022)
- ICML Workshop on Topology, Algebra and Geometry in Machine Learning (2022)
- ICLR Workshop on Geometrical and Topological Representation Learning (2022)
- Workshop on Symmetry, Invariance and Neural Representations @ The Bernstein Conference (2022)