Fri, 01 Mar 2024
16:00
L1

Departmental Colloquium: The role of depth in neural networks: function space geometry and learnability

Professor Rebecca Willett (University of Chicago)
Further Information

Rebecca Willett is a Professor of Statistics and Computer Science & the Faculty Director of AI at the Data Science Institute, with a courtesy appointment at the Toyota Technological Institute at Chicago. Her research is focused on machine learning foundations, scientific machine learning, and signal processing. She is the Deputy Director for Research at the NSF-Simons Foundation National Institute for Theory and Mathematics in Biology and a member of the Executive Committee for the NSF Institute for the Foundations of Data Science. She is the Faculty Director of the Eric and Wendy Schmidt AI in Science Postdoctoral Fellowship and helps direct the Air Force Research Lab University Center of Excellence on Machine Learning

Abstract

Neural network architectures play a key role in determining which functions are fit to training data and the resulting generalization properties of learned predictors. For instance, imagine training an overparameterized neural network to interpolate a set of training samples using weight decay; the network architecture will influence which interpolating function is learned. 

In this talk, I will describe new insights into the role of network depth in machine learning using the notion of representation costs – i.e., how much it “costs” for a neural network to represent some function f. Understanding representation costs helps reveal the role of network depth in machine learning. First, we will see that there is a family of functions that can be learned with depth-3 networks when the number of samples is polynomial in the input dimension d, but which cannot be learned with depth-2 networks unless the number of samples is exponential in d. Furthermore, no functions can easily be learned with depth-2 networks while being difficult to learn with depth-3 networks. 

Together, these results mean deeper networks have an unambiguous advantage over shallower networks in terms of sample complexity. Second, I will show that adding linear layers to a ReLU network yields a representation cost that favors functions with latent low-dimension structure, such as single- and multi-index models. Together, these results highlight the role of network depth from a function space perspective and yield new tools for understanding neural network generalization. 

Fri, 16 Feb 2024
16:00
L1

Conferences and networking

Naomi Andrew, Jane Coons, Antonio Esposito, Romain Ruzziconi
(Mathematical Institute (University of Oxford))
Abstract

Conferences and networking are important parts of academic life, particularly early in your academic career.  But how do you make the most out of conferences?  And what are the does and don'ts of networking?  Learn about the answers to these questions and more in this panel discussion by postdocs from across the Mathematical Institute.

Fri, 02 Feb 2024
16:00
L1

Graduate Jobs in finance and the recruitment process

Keith Macksoud, Executive Director at Options Group
(Options Group)
Abstract

Join us for a session with Keith Macksoud, Executive Director at global recruitment consultant Options Group in London and who previously has > 20 years’ experience in Prime Brokerage Sales at Morgan Stanley, Citi, and Deutsche Bank.  Keith will discuss the recruitment process for financial institutions, and how to increase your chances of a successful application. 

Keith will detail his finance background in Prime Brokerage and provide students with an exclusive look behind the scenes of executive search and strategic consulting firm Options Group. We will look at what Options Group does, how executive search firms work and the Firm’s 30-year track record of placing individuals at many of the industries’ largest and most successful global investment banks, investment managers and other financial services-related organisations. 

About Options Group

Options Group is a leading global executive search and strategic consulting firm specializing in financial services including capital markets, global markets, alternative investments, hedge funds, and private banking/wealth management.

https://www.optionsgroup.com/

Fri, 03 May 2024
16:00
L1

Talks on Talks

Abstract

What makes a good talk? This year, graduate students and postdocs will give a series talks on how to give talks! There may even be a small prize for the audience’s favourite.

If you’d like to have a go at informing, entertaining, or just have an axe to grind about a particularly bad talk you had to sit through, we’d love to hear from you (you can email Ric Wade or ask any of the organizers).
 

Fri, 08 Mar 2024
16:00
L1

Maths meets Stats

James Taylor (Mathematical Institute) and Anthony Webster (Department of Statistics)
Abstract

Speaker: James Taylor
Title: D-Modules and p-adic Representations

Abstract: The representation theory of finite groups is a beautiful and well-understood subject. However, when one considers more complicated groups things become more interesting, and to classify their representations is often a much harder problem. In this talk, I will introduce the classical theory, the particular groups I am interested in, and explain how one might hope to understand their representations through the use of D-modules - the algebraic incarnation of differential equations.

 

Speaker: Anthony Webster
Title: An Introduction to Epidemiology and Causal Inference

Abstract: This talk will introduce epidemiology and causal inference from the perspective of a statistician and former theoretical physicist. Despite their studies being underpinned by deep and often complex mathematics, epidemiologists are generally more concerned by seemingly mundane information about the relationships between potential risk factors and disease. Because of this, I will argue that a good epidemiologist with minimal statistical knowledge, will often do better than a highly trained statistician. I will also argue that causal assumptions are a necessary part of epidemiology, should be made more explicitly, and allow a much wider range of causal inferences to be explored. In the process, I will introduce ideas from epidemiology and causal inference such as Mendelian Randomisation and the "do calculus", methodological approaches that will increasingly underpin data-driven population research.  

Fri, 26 Jan 2024
16:00
L1

North meets South

Dr Cedric Pilatte (North Wing) and Dr Boris Shustin (South Wing)
Abstract

Speaker: Cedric Pilatte 
Title: Convolution of integer sets: a galaxy of (mostly) open problems

Abstract: Let S be a set of integers. Define f_k(n) to be the number of representations of n as the sum of k elements from S. Behind this simple definition lie fascinating conjectures that are very easy to state but seem unattackable. For example, a famous conjecture of Erdős and Turán predicts that if f_2 is bounded then it has infinitely many zeroes. This talk is designed as an accessible overview of these questions. 
 
Speaker: Boris Shustin

Title: Manifold-Free Riemannian Optimization

Abstract: Optimization problems constrained to a smooth manifold can be solved via the framework of Riemannian optimization. To that end, a geometrical description of the constraining manifold, e.g., tangent spaces, retractions, and cost function gradients, is required. In this talk, we present a novel approach that allows performing approximate Riemannian optimization based on a manifold learning technique, in cases where only a noiseless sample set of the cost function and the manifold’s intrinsic dimension are available.

Tue, 28 Nov 2023

16:00 - 17:00
L1

Euclidean Ramsey Theory

Imre Leader
(University of Cambridge)
Abstract

Euclidean Ramsey Theory is a natural multidimensional version of Ramsey Theory. A subset of Euclidean space is called Ramsey if, for any $k$, whenever we partition Euclidean space of sufficiently high dimension into $k$ classes, one class much contain a congruent copy of our subset. It is still unknown which sets are Ramsey. We will discuss background on this and then proceed to some recent results.

Mon, 20 Nov 2023
16:00
L1

Post-Quantum Cryptography (and why I’m in the NT corridor)

Patrick Hough
(University of Oxford)
Abstract

In this talk I will give a brief introduction to the field of post-quantum (PQ) cryptography, introducing a few of the most popular computational hardness assumptions. Second, I will give an overview of a recent work of mine on PQ electronic voting. I’ll finish by presenting a short selection of ‘exotic’ cryptographic constructions that I think are particularly hot at the moment (no, not blockchain). The talk will be definitionally light since I expect the area will be quite new to many and I hope this will make for a more engaging introduction.

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