# Colloquium Details

## Covariant and compositional neural network architectures for learning from graphs, images and physical systems

**Speaker:**
Risi Kondor, University of Chicago

**Location:**
60 Fifth Avenue 150

**Date:**
January 30, 2019, 2 p.m.

**Host:** Subhash Khot

**Synopsis:**

The reason that convolutional neural networks are so effective in image recognition and related tasks is that they reflect the translational symmetry of natural images. In this talk we explore the generalization of this architecture in multiple directions: graph neural networks that respect symmetry with respect to permuting the vertices, spherical CNNs that are equivariant to rotations of the sphere, and N-body networks for learning atomic forces in a way that is covariant to rotating the atomic neighborhood. We find that the common thread in each of these cases is the appearance of group representations, leading to the concept of Fourier space neural networks and Fourier space (Clebsch-Gordan) nonlinearities. We present results on learning the properties of molecules, spherical image recognition, and learning the energy of molecular configurations. The work presented in this talk was done in collaboration with Brandon Anderson, Zhen Lin, Truong Son Hy, Horace Pan, and Shubhendu Trivedi.

**Speaker Bio:**

Risi Kondor is an Associate Professor at The University of Chicago in Computer Science, Statistics, and the Computational and Applied Mathematics Initiative. Risi obtained his B.A. in Mathematics and Theoretical Physics from Cambridge, followed by an M.Sc. in Machine Learning from Carnegie Mellon and a PhD from Columbia, and postdoc positions at the Gatsby Unit (UCL) and Caltech.

Risi is interested in bringing mathematical methods to bear on large scale learning problems. One example of this type of work are adaptive multresolution methods (in particular, Multiresolution Matrix Factorization) for discovering latent structure in large datasets. Another example are specialized neural network architectures that learn from data with specific symmetries, such as graphs (permutation symmetry) or physical systems (translational and rotational symmetry).

**Notes:**

Refreshments will be offered starting 15 minutes prior to the scheduled start of the talk.