About
This is the third edition of the Liverpool Discrete Mathematics Colloquium, an annual two-day event designed to strengthen links between Computer Science and Mathematics and to expose PhD students to current research topics.
The 2026 meeting has a focused format around mathematically rigorous analysis of black-box AI algorithms. The first day is devoted to Logics and Graph Neural Networks, while the second day focuses on Stochastic Gradient Descent. Each day will feature a 2 hour tutorial together with invited talks and time for discussion and networking.
Venue
TBC
Catering
There are tea/coffee breaks provided. Lunches are not provided, however there is the University of Liverpool refectory and plenty of local cafes and restaurants nearby.
There will be a conference dinner on the evening of the first day. All participants are welcome to attend, however non-speaking participants will have to cover the cost of their own meal. Details will be provided closer to the event.
Funding for Students
We urge all students to keep receipts for expenses as we may be able to refund some expenses after the conference.
Registration
Attendance at the Liverpool Discrete Mathematics Colloquium is expected to be free of charge. Registration will be required for planning purposes, and the form and deadline will be added here once available.
Tutorial Speakers
Logical Aspects of Graph Neural Networks
Steffen Dereich
Convergence of Stochastic Gradient Descent
Speakers
Carsten Lutz
Leipzig
Emily Jin
Oxford
Benjamin Dupuis
ENS Paris
Alex Mijatović
Warwick
Sarah Sachs
Bristol
Jonni Virtema
Glasgow
Schedule
Logics and Graph Neural Networks
Tuesday 8 September 2026
Stochastic Gradient Descent
Wednesday 9 September 2026
Talk Abstracts
Invited Talks
Jonni Virtema
Abstract to be added.
Carsten Lutz
Abstract to be added.
Emily Jin
Abstract to be added.
Benjamin Dupuis
Abstract to be added.
Alex Mijatović - Limit Theorems for Stochastic Gradient Descent with Infinite Variance
Stochastic gradient descent (SGD) algorithm is a classical algorithm that gained significant popularity from both empirical and theoretical perspectives. While its probabilistic properties are well-studied when the randomness is assumed to have a finite variance, there is a scarcity of research addressing its theoretical behaviour in the case of infinite variance. In this talk, I will describe the asymptotic behavior of SGD when the stochastic gradient has an infinite variance, specifically assuming the stochastic gradient is regularly varying with index $\alpha\in(1,2)$. The most recent limit theorems in this context were established in the classical paper Karsulina (1969) in the context of one-dimensional stochastic noise belonging to a restrictive class. We extend this result into the multi-dimensional case, covering a more general class of infinite variance distributions. This extension requires entirely different techniques, as the original method does not apply to the multi-dimensional case. Our results indicate that the asymptotic distribution of the stochastic gradient descent algorithm aligns with the Ornstein-Unlenbeck process driven by an additive process with jumps (instead of a Brownian motion). Additionally, we explore the applications of these results in linear regression and logistic regression models.
This joint work with Jose Blanchet and Wenhao Yang is to appear in the Annals of Applied Probability (2026).
Sarah Sachs
Abstract to be added.
Organisers
John Sylvester
Linglong Yuan
Viktor Zamaraev
Supported by
This event is supported by the Heilbronn Institute for Mathematical Research, Applied Probability Trust, EPSRC, and the University of Liverpool.