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https://github.com/neurreps/awesome-neural-geometry

A curated collection of resources and research related to the geometry of representations in the brain, deep networks, and beyond
https://github.com/neurreps/awesome-neural-geometry

List: awesome-neural-geometry

awesome-list deep-learning differential-geometry equivariance group-theory neural-computation neural-networks neuroscience papers symmetry topology

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A curated collection of resources and research related to the geometry of representations in the brain, deep networks, and beyond

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# Awesome Neural Geometry



[![PRs Welcome](https://img.shields.io/badge/PRs-Welcome-green)](https://github.com/neurreps/reading-list/pulls) [![Awesome](https://awesome.re/badge.svg)](https://awesome.re) ![Stars](https://img.shields.io/github/stars/neurreps/reading-list?color=yellow)  ![Forks](https://img.shields.io/github/forks/neurreps/reading-list?color=blue&label=Fork)



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](https://www.neurreps.org) Slack Workspace.



This is a collaborative work-in-progress. Please contribute via PRs!



[Join us on Slack!](https://communityinviter.com/apps/neurreps/join)



![](https://lh4.googleusercontent.com/vODs2cK98sKA9SVu_K2s-y8RFVmAXR8xEi4yGb6JBGBH73oFnpnhQSgb3C2qt2jFLLys2NY86l6lrPsFx2RpvV-Oqkqdf_TknI0ujQYyTeU2vCbaTgztq6xD-rhp4TJxGg=w1280)



## Contents



- [**Educational Resources**](#resources)

  - [Abstract Algebra + Group Theory](#grouptheory)

  - [Differential Geometry + Lie Groups](#diffgeo)

  - [Information Geometry](#infogeo)

  - [Topology](#topology)

  - [Geometric Machine Learning](#gdl)

  - [Computational Neuroscience](#neuro-resources)

- [**Datasets**](#datasets)

- [**Software Libraries**](#software)

- [**Conferences and Workshops**](#conferences)











# Educational Resources






### Abstract Algebra + Group Theory



#### Textbooks & Notes

* [**Group Theory: A Primer** (2019) 
 *Luciano da Fontoura Costa*](https://www.researchgate.net/profile/Luciano-Da-F-Costa/publication/334126746_Group_Theory_A_Primer_CDT-11/links/5da83b2f299bf1c1e4c8ffb4/Group-Theory-A-Primer-CDT-11.pdf)

* [**Tensors in Computations** (2021) 
 *Lek-Heng Lim*](https://arxiv.org/pdf/2106.08090.pdf)

* [**Aspects of Harmonic Analysis and Representation Theory** (2021) 
 *Gallier & Quaintance*](https://drive.google.com/file/d/1eK8B1UpTJTnCXV6DL4-blDaKo6XQk28r/view?usp=sharing)

* [**Basic concepts of representation theory** (2013) 
 *Amritanshu Prasad*](https://cel.archives-ouvertes.fr/cel-00963677/document)

* [**Representation Theory of Finite Groups** (2012) 
 *Bemjamin Steinberg*](https://drive.google.com/file/d/1fe1qnVAkCHEY1hn9sOvcA6Ocww66fMmP/view?usp=sharing)



#### Courses, Lectures, and Videos

* [**Essence of Group Theory**  **Beginner-Friendly* 
 *Mathemaniac*](https://youtube.com/playlist?list=PLDcSwjT2BF_VuNbn8HiHZKKy59SgnIAeO)

* [**Abstract Algebra** **Beginner-Friendly* 
 *Socratica*](https://youtube.com/playlist?list=PLi01XoE8jYoi3SgnnGorR_XOW3IcK-TP6)

* [**Euler's formula with introductory group theory** **Intuition Building* 
 *3blue1brown*](https://www.youtube.com/watch?v=mvmuCPvRoWQ&t=648s&ab_channel=3Blue1Brown)

* [**What is a Tensor?** 
 *XylyXylyX*](https://youtube.com/playlist?list=PLRlVmXqzHjUQARA37r4Qw3SHPqVXgqO6c)

* [**Representation Theory** 
 *Math Doctor Bob*](https://youtube.com/playlist?list=PL57457844458A5A1F)

* [**Category Theory for AI** 
 *Online Course, October 2022*](https://cats.for.ai/)










### Differential Geometry + Lie Groups



#### Textbooks & Notes

* [**Lie Groups, Lie Algebras, and Representations** (2003) 
 *Brian C. Hall*](https://link.springer.com/book/10.1007/978-3-319-13467-3)

* [**Differential Geometry and Lie Groups: A Computational Perspective** (2020) 
 *Gallier & Quaintance*](https://link.springer.com/book/10.1007/978-3-030-46040-2)

* [**Introduction to Riemannian Geometry and Geometric Statistics: from basic theory to implementation with Geomstats** (2022) 
 *Nicolas Guigui, Nina Miolane, Xavier Pannec*](https://hal.inria.fr/hal-03766900/)



#### Courses, Lectures, and Videos

* [**Geometry and Topology**](https://youtu.be/kp1k90zNVLc) and [**Symmetry**](https://youtu.be/yCxacFBLHIY) **Beginner-Friendly* 
 *Sean Carroll*

* [**Differential Geometry for Computer Science** 
 *Justin Solomon*](https://youtube.com/playlist?list=PLQ3UicqQtfNvPmZftPyQ-qK1wdXBxj86W)

* [**Discrete Differential Geometry** 
 CMU](https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS)

* [**What is a Manifold?** 
 *XylyXylyX*](https://youtube.com/playlist?list=PLRlVmXqzHjUQHEx63ZFxV-0Ortgf-rpJo)

* [**Manifolds** 
 *Robert Davie*](https://youtube.com/playlist?list=PLeFwDGOexoe8cjplxwQFMvGLSxbOTUyLv)

* [**Lie Groups and Lie Algebras** 
 *XylyXylyX*](https://youtube.com/playlist?list=PLRlVmXqzHjURZO0fviJuyikvKlGS6rXrb)

* [**Lectures on Geometric Anatomy of Theoretical Physics** 
 *Frederic Schuller*](https://youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic)

* [**Weekend with Bernie (Riemann)** 
 *Søren Hauberg @ DTU*](http://www2.compute.dtu.dk/~sohau/weekendwithbernie/)

* [**Riemann and Gauss Meet Asimov: A Tutorial on Geometric Methods in Robot Learning, Optimization, and Control** 
 *IROS 2022*](https://youtube.com/playlist?list=PL_oEZ6dld4ignAdbFvcP_LAJgNbdrNBKC)



#### Notebooks and Blogposts

* [**Introduction to Differential Geometry and Machine Learning** 
 *Geomstats Jupyter notebooks*](https://github.com/geomstats/geomstats/tree/master/notebooks)

* [**Differential Geometry for Machine Learning** 
 *Roger Grosse*](https://metacademy.org/roadmaps/rgrosse/dgml)

* [**Manifolds: A Gentle Introduction** 
 *Brian Keng*](https://bjlkeng.github.io/posts/manifolds/)










### Information Geometry



#### Primers

* [**The Many Faces of Information Geometry** (2022) 
 *Frank Nielsen*](https://www.ams.org/journals/notices/202201/rnoti-p36.pdf)







### Topology



#### Courses, Lectures, and Videos



* [**Computational Algebraic Topology** 
 Vidit Nanda](https://youtube.com/playlist?list=PLnLAqsCN_2ke8_EUd_KoJsLkPO0BKrrc6)



* [**Topological Data Analysis for Machine Learning** 
 Bastian Rieck](https://www.youtube.com/playlist?list=PLjFHG9gPsecYteKmbVbPhjiz2jHRtKT20)



#### Textbooks, Notes

* [**Elementary Applied Topology** 
 Robert Ghrist](https://www2.math.upenn.edu/~ghrist/notes.html)








### Geometric Machine Learning



#### Textbooks



* [**Group Invariance Applications in Statistics** (1989) 
 Morris Eaton](https://www.jstor.org/stable/4153172)

* [**Group Theoretical Methods in Machine Learning** (2008) 
 *Risi Kondor, PhD Thesis*](http://www.cs.columbia.edu/~jebara/papers/thesisKondor.pdf)

* [**Pattern Theory: The Stochastic Analysis of Real-World Signals** (2010) 
 *David Mumford and Agnès Desolneux*](https://www.routledge.com/Pattern-Theory-The-Stochastic-Analysis-of-Real-World-Signals/Mumford-Desolneux/p/book/9781568815794)

* [**Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges** (2021) 
 _Michael M. Bronstein, Joan Bruna, Taco Cohen, Petar Veličković_](https://arxiv.org/abs/2104.13478)

* [**Equivariant Convolutional Networks** (2021) 
 *Taco Cohen, PhD Thesis*](https://pure.uva.nl/ws/files/60770359/Thesis.pdf)

* [**An Introduction to Optimization on Smooth Manifolds** (2022) 
 *Nicolas Boumal*](https://sma.epfl.ch/~nboumal/book/IntroOptimManifolds_Boumal_2022.pdf)



#### Courses, Lectures, and Videos



* [**Geometric Deep Learning** (2nd Edition) 
  *Michael Bronstein, Joan Bruna, Taco Cohen, Petar Veličković @ AMMI*](https://www.youtube.com/watch?v=5c_-KX1sRDQ&list=PLn2-dEmQeTfSLXW8yXP4q_Ii58wFdxb3C)

* [**CSC 2547: Current Topics in Machine Learning Methods in 3D and Geometric Deep Learning** (2021) 
 *Animesh Garg @ University of Toronto*](https://youtube.com/playlist?list=PLki3HkfgNEsLrbI_r2iqNogmL5DW6HJXF)

* [**An Introduction to Group-Equivariant Deep Learning** (2022) 
 *Erik Bekkers @ UvA*](https://www.youtube.com/playlist?list=PL8FnQMH2k7jzPrxqdYufoiYVHim8PyZWd)

* [**Italian Summer School on Geometric Deep Learning** (2022) 
 *Cristian Bodnar, Michael Bronstein, Francesco Di Giovanni, Pim de Haan, Maurice Weiler*](https://www.youtube.com/playlist?list=PLn2-dEmQeTfRQXLKf9Fmlk3HmReGg3YZZ)

* [**COMP760: Geometry and Generative Models** (2022) 
 *Joey Bose and Prakash Panangaden @ MILA*](https://joeybose.github.io/Blog/GenCourse)



#### Notebooks and Blogposts

* [**Geometric foundations of Deep Learning** 
 *Michael Bronstein, Joan Bruna, Taco Cohen, and Petar Veličković*](https://towardsdatascience.com/geometric-foundations-of-deep-learning-94cdd45b451d)

* [**What does 2022 hold for Geometric & Graph ML?** 
 *Michael Bronstein*](https://towardsdatascience.com/predictions-and-hopes-for-geometric-graph-ml-in-2022-aa3b8b79f5cc)

* [**Geometric Machine Learning for Shape Analysis with Jupyter Notebooks** 
 *Nina Miolane*](https://github.com/bioshape-lab/ece594n/tree/main/lectures)










### Computational Neuroscience



#### Textbooks

* [**Introduction to the Theory of Neural Computation** (1991) 
 *John Hertz, Anders Krogh, Richard G Palmer*](https://drive.google.com/file/d/1jjAHNSZld1tjH0wiqXc9wCv3Y6h5sjok/view?usp=sharing)

* [**Theoretical Neuroscience** (2001) 
 *Peter Dayan*](http://www.gatsby.ucl.ac.uk/~lmate/biblio/dayanabbott.pdf)

* [**Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting** (2006) 
 *Eugene M. Izhikevich*](https://drive.google.com/file/d/1CXQCPl6MN8XSmoyo6J0TbdlWhBmaib62/view?usp=sharing)

* [**Neuronal Dynamics: From single neurons to networks and models of cognition** (2014) 
 *Wulfram Gerstner, Werner M. Kistler, Richard Naud and Liam Paninsky*](https://neuronaldynamics.epfl.ch/)

* [**Principles of Neural Design** (2015) 
 *Peter Sterling & Simon Laughlin*](https://drive.google.com/file/d/1cskdlUJBjAY5wH7GeZa2IxT9iSXZ_3_0/view?usp=sharing)



#### Books - General Audience

* [**Rhythms of the Brain** (2006) 
 *Gyorgy Buzsaki*](https://drive.google.com/file/d/1DtGEb54qJNS2wkny1FXM4b_dfT-b140y/view?usp=sharing)

* [**Networks of the Brain** (2010) 
 *Olaf Sporns*](https://drive.google.com/file/d/1MsGNsFVF7AxPtnyv1WnH-YnZMGvhUkHb/view?usp=sharing)

* [**Models of the Mind: How Physics, Engineering and Mathematics Have Shaped Our Understanding of the Brain** (2021) 
 *Grace Lindsay*](https://www.goodreads.com/en/book/show/50884536-models-of-the-mind)



#### Tutorials

* [**Generative Models for Neural Data Analysis** 
 *COSYNE Workshops 2023*](https://github.com/davindicode/cosyne-2023-generative-models)



#### Courses, Lectures, and Videos

* [**Neural Computation VS265** 
 *Bruno Olshausen @ UC Berkeley*](https://redwood.berkeley.edu/courses/vs265/)











# Datasets



### Open-Source Neuroscience Datasets

* [**OpenNeuro**](https://openneuro.org/)

* [**NeuroVault**](https://neurovault.org/)

* [**CRCNS**](https://crcns.org/data-sets)

* [**NeuroData Without Borders**](https://www.nwb.org/example-datasets/)

* [**Allen Brain Atlas**](https://portal.brain-map.org/)

* [**Kavli Institute for Systems Neuroscience Grid Cell Database**](https://www.ntnu.edu/kavli/research/grid-cell-data)

* [**The Natural Scenes Dataset**](http://naturalscenesdataset.org/)











# Software Libraries



* [**Geomstats**](https://geomstats.github.io/)

  * Computation, statistics, and machine learning on non-Euclidean manifolds

* [**Giotto TDA**](https://giotto-ai.github.io/gtda-docs/0.5.1/library.html)

  * Topological Data Analysis

* [**E3NN**](https://github.com/e3nn/e3nn)

  * E(3)-equivariant neural networks

* [**equivariant-MLP**](https://github.com/mfinzi/equivariant-MLP)

  * Construct equivariant multilayer perceptrons for arbitrary matrix groups

* [**SHTOOLS**](https://github.com/SHTOOLS/SHTOOLS)

  * Python library for computations involving spherical harmonics

* [**LieConv**](https://github.com/mfinzi/LieConv)

  * Generalizing convolutional neural networks for equivariance to Lie groups on arbitrary continuous data

* [**Open Neuroscience**](https://open-neuroscience.com/)

  * A database of open-source tools and software for neuroscience

* [**LieTorch**](https://gitlab.com/bsmetsjr/lietorch)

  * Geometric machine learning and Lie analysis tools for PyTorch

* [**pyRiemann**](https://github.com/pyRiemann/pyRiemann)

  * Machine learning for multivariate data through the Riemannian geometry of positive definite matrices











# Conferences and Workshops



* [**NeurIPS Workshop on Symmetry and Geometry in Neural Representations** (2023)](https://neurreps.org)

* [**ICML Workshop on Topology, Algebra and Geometry in Machine Learning** (2023)](https://www.tagds.com/events/conference-workshops/tag-ml23)

* [**RSS Workshop on Symmetries in Robot Learning** (2023)](https://sites.google.com/view/rss23-sym)

* [**NeurIPS Workshop on Symmetry and Geometry in Neural Representations** (2022)](https://www.neurreps.org/past-workshops)

* [**ICML Workshop on Topology, Algebra and Geometry in Machine Learning** (2022)](https://www.tagds.com/events/conference-workshops/tag-ml22)

* [**ICLR Workshop on Geometrical and Topological Representation Learning** (2022)](https://gt-rl.github.io/)

* [**Workshop on Symmetry, Invariance and Neural Representations @ The Bernstein Conference** (2022)](https://bernstein-network.de/bernstein-conference/program/satellite-workshops/symmetry-invariance-and-neural-representations/)