One World Seminar Series on the 

Mathematics of Machine Learning

The One World Seminar Series on the Mathematics of Machine Learning is an online platform for research seminars, workshops and seasonal schools in theoretical machine learning. The focus of the series lies on theoretical advances in machine learning and deep learning as a complement to the one world seminars on probability, on Information, Signals and Data (MINDS), on methods for arbitrary data sources (MADS), and on imaging and inverse problems (IMAGINE).

The series was started during the Covid-19 epidemic in 2020 to bring together researchers from all over the world for presentations and discussions in a virtual environment. It follows in the footsteps of other community projects under the One World Umbrella which originated around the same time.

We welcome suggestions for speakers concerning new and exciting developments and are committed to providing a platform also for junior researchers. We recognize the advantages that online seminars provide in terms of flexibility, and we are experimenting with different formats. Any feedback on different events is welcome.

Next Event

Wed May 29

12 noon ET

On the hardness of learning under symmetries

We study the problem of learning equivariant neural networks via gradient descent. The incorporation of known symmetries ("equivariance") into neural nets has empirically improved the performance of learning pipelines, in domains ranging from biology to computer vision. However, a rich yet separate line of learning theoretic research has demonstrated that actually learning shallow, fully-connected (i.e. non-symmetric) networks has exponential complexity in the correlational statistical query (CSQ) model, a framework encompassing gradient descent. In this work, we ask: are known problem symmetries sufficient to alleviate the fundamental hardness of learning neural nets with gradient descent? We answer this question in the negative. In particular, we give lower bounds for shallow graph neural networks, convolutional networks, invariant polynomials, and frame-averaged networks for permutation subgroups, which all scale either superpolynomially or exponentially in the relevant input dimension. Therefore, in spite of the significant inductive bias imparted via symmetry, actually learning the complete classes of functions represented by equivariant neural networks via gradient descent remains hard.

Mailing List and Google Calendar

Sign up here to join our mailing list and receive announcements. If your browser automatically signs you into a google account, it may be easiest to join on a university account by going through an incognito window. With other concerns, please reach out to one of the organizers. 

Sign up here for our google calendar with all seminars.


Seminars are held online on Zoom. The presentations are recorded and video is made available on our youtube channel. A list of past seminars can be found here. All seminars, unless otherwise stated, are held on Wednesdays at 12 noon ET. The invitation will be shared on this site before the talk and distributed via email.


Wuyang Chen (UC Berkeley)

Bin Dong (Peking University)

Boumediene Hamzi (Caltech)

Issa Karambal (Quantum Leap Africa)

Qianxiao Li (National University of Singapore)

Matthew Thorpe (University of Warwick)

Tiffany Vlaar (University of Glasgow)

Stephan Wojtowytsch (University of Pittsburgh)

Former Board Members

Simon Shaolei Du (University of Washington)

Franca Hoffmann (Caltech)

Surbhi Goel (Microsoft Research NY)

Chao Ma (Stanford University)

Song Mei (UC Berkeley)

Philipp Petersen (University of Vienna)