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Basic Information About 6.S966/8.S301

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56-154 Mondays and Wednesdays at 2:30-4:00pm. Check Calendar for schedule for specific weeks affected by holidays!

Course Description

Introduces the use of group representation theory to construct symmetry-preserving algorithms for machine learning. Emphases the connection between topics in math and physics and machine learning. Students will implement core mathematical concepts in code to build algorithms that can operate on graphs, geometry, scientific data, and other structured data to preserve the symmetries of these domains. Topics covered include: Euclidean and permutation groups, group representations: regular, reducible, and irreducible, tensor products, statistics and sampling of group representation vector spaces, and symmetry-breaking mechanisms.

Learning Objectives

  • Deepen understanding of linear algebra
  • Learn about the mathematics of groups and group representations
  • Use these concepts in code to create symmetr-preserving algorithms (e.g. machine learning)
  • Be able to identify ways in which algorithms preserve or break symmetry
  • Learn common existing techniques in symmetry-equivariant neural networks
  • Build Intuition for how symmetry changes how you articulate tasks and algorithms for such tasks
  • First ~1/2 of class, learn basics and broadly applicable tools through Lectures, Readings, Polls, and Exercises
  • Second ~1/2 of class, deepen understanding in an area of your choosing (Literature Review + Project) and share / discuss these topics with classmates (Workshops)

Terms and Conditions

NO COMPUTER POLICY: No phones / tablets / laptops in class! This includes use for taking digital notes! If you need an accomodation, see section on "Disabilities and Accomodation" toward the bottom of this page.

This course is not:

  • a formal math class on group representation theory (but 18.715 is!)
  • an Intro. to ML class (but 6.3900 is!)
  • a course best practices for geometry deep learning

Syllabus is subject to change! The current version is available on the Calendar page.

Bugs: As this is a new course, there are bound to be bugs in the Exercises. We would great appreciate your help in identifying these! Please post any Bugs you find publically in Piazza. This will avoid duplication of notification. Thanks in advance!


18.06 Linear Algebra OR 18.061 Linear Algebra with Optimization

6.100 (6.0001) Introduction to Computer Science Programming in Python

6.1200 (6.006) Introduction to Algorithms

Course Website

All course materials will be available through this website and accessible through the Calendar page.


In a typical week, we will have two lectures. Readings will be released for the week Monday morning at the latest. Lecture notes / slides will be made available after class. We are not planning on making lecture recordings available except for special circumstances.

Graded Assignments

Please see the Grading Policy page.

Office Hours

Information on Office Hours are posted on the Office Hours page (subsection of Information header).


We will use Piazza as the course discussion forum where you can ask questions and get them answered by the course staff.

Illness and Personal Issues

If you are sick you should not attend lecture or in-person office hours -- we will excuse attendance points for illness so you will not be penalized; contact symm4ml-instructors@mit.edu for consideration. Also, if you have personal issues impacting your attendance, or other personal difficulties affecting your progress on assignments, please see a Dean in Student Support Services, and then you and the Dean should contact Prof. Tess Smidt at tsmidt@mit.edu for assistance and handling of the situation.

Disabilities and Accommodations

We are committed to the principle of equal access, and we are more than willing to make arrangements to help accommodate students with disabilities or related challenges. In general, knowing about the kind of help you need earlier in the semester means that we'll be better prepared to provide that help effectively, in coordination with Disability and Access Services. If you have a disability and are not planning to use accommodations, it is still recommended that you meet with DAS staff to familiarize yourself with their services and resources. If you have been approved for accommodations by DAS, 6.S966 staff are ready to assist with implementation. Please send these approved requests to Prof. Tess Smidt at tsmidt@mit.edu to inform us, and we will work to implement these accommodations.