Insights & Ideas
from Experts in the Field
Next Lectures:
Franca Hoffmann & Holger Hoos
Date/Time: December 17, from 4 pm CET
Location: Senatssaal, LMU Munich, Geschwister-Scholl-Platz 1, Munich
Franca Hoffmann - Dynamics of Strategic Agents and Algorithms as PDEs
Abstract
In many situations when a population interfaces with an algorithm, the algorithm may update its parameters based on the population’s behavior to achieve a given objective, and simultaneously strategic agents in a population may change their behavior in response to the algorithm’s actions. This interplay can generate complex dynamics that we would like to be able to understand and predict. The mathematical theory to do so is still nascent. We consider two particular settings; one, where the objective of the algorithm and population are aligned, and two, where the algorithm and population have opposing goals. Using ideas from game theory, we propose a framework for two-player infinite-dimensional games with cooperative or competitive structure that are able to capture such dynamics between strategic agents and algorithms. These games take the form of coupled partial differential equations in which players optimize over a space of measures, driven by either a gradient descent or gradient descent-ascent in Wasserstein-2 space. Under sufficient convexity assumptions, we are able to characterize the properties of the Nash equilibrium of the system and the behavior of solutions after a long time. We illustrate how our framework can accurately model real-world data and show via synthetic examples how it captures sophisticated distribution changes which cannot be modeled with simpler methods.
Bio
Franca obtained her master’s in mathematics from Imperial College London (UK) and holds a PhD from the Cambridge Centre for Analysis at University of Cambridge (UK). She held the position of von Kármán instructor at Caltech from 2017 to 2020, then joined University of Bonn (Germany) as Bonn Junior Professor and Quantum Leap Africa in Kigali, Rwanda (African Institute for Mathematical Sciences) as AIMS-Carnegie Research Chair in Data Science, before arriving at the California Institute of Technology as Assistant Professor in 2022.
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Holger Hoos - Learning, reasoning and optimisation: Adversarial robustness of neural networks
Abstract
Over the last decade, machine learning methods, notably neural networks, have played a key role in enabling major progress in artificial intelligence and its applications. Unfortunately, despite their excellent performance in many use cases, neural networks have been shown to be sensitive to input perturbations, including adversarial attacks. In this presentation, I will give an introduction to neural network robustness and explain how work in this area effectively combines AI methods from machine learning, optimisation and automated reasoning. I will explain the concept of robustness verification and introduce local robustness distributions, which afford a rigorous and nuanced assessment of neural network robustness against input perturbations. I will give examples from image and audio classification and briefly discuss connections to questions of bias and fairness, as well as the way in which this line of work relates to the broader effort of my group towards safe, dependable and sustainable AI.
Bio
Holger H. Hoos holds an Alexander von Humboldt professorship in AI at RWTH Aachen University (Germany), where he also leads the AI Center, as well as a professorship in machine learning at Universiteit Leiden (the Netherlands) and an adjunct professorship in computer science at the University of British Columbia (Canada). He is a Fellow of the Association of Computing Machinery (ACM), the Association for the Advancement of Artificial Intelligence (AAAI) and the European AI Association (EurAI), past president of the Canadian Association for Artificial Intelligence, former editor-in-chief of the Journal of Artificial Intelligence Research (JAIR) and chair of the board of CLAIRE, an organization that seeks to strengthen European excellence in AI research and innovation (claire-ai.org).
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On a monthly basis, we invite top-level AI researchers to give us a glimpse into their work and the future of AI. Join us for our next lecture!
Our lectures consist of a short presentation followed by a Q&A to enable a lively discussion with our speakers. Each lecture lasts about one hour and most lectures will be streamed live on our YouTube channel. Recordings will be available afterwards.
Monday, November 25th, 5:15 pm
Location: Große Aula, Raum E 120, 1. OG, Geschwister-Scholl-Platz 1, 80539 München, LMU München
This event is open to everyone, registration is not required.
Insights & Ideas
from Experts in the Field
Next Lectures:
Helmut Bölcskei - The Mathematical Universe behind Deep Neural Networks
Monday, November 25th, 5:15 pm
Location: Große Aula, Raum E 120, 1. OG, Geschwister-Scholl-Platz 1, 80539 München, LMU München
This event is open to everyone, registration is not required.
Abstract
Deep neural networks have led to breakthrough results in numerous practical machine learning tasks. In this lecture, we will attempt a journey through the mathematical universe behind these practical successes, elucidating the theoretical underpinnings of deep neural networks in functional analysis, harmonic analysis, complex analysis, approximation theory, dynamical systems, Kolmogorov complexity, optimal transport, fractal geometry, mathematical logic, and automata theory.
Bio
Helmut Bölcskei is a professor of Mathematical Information Science at ETH Zurich. Since 2021 he has also been a Principal Investigator at the Lagrange Mathematics and Computing Research Center, Paris, France.
He received his degrees from Vienna University of Technology, Vienna, Austria, was a postdoctoral researcher in the Information Systems Laboratory, Department of Electrical Engineering, and in the Department of Statistics, Stanford University, Stanford, CA. He was in the founding team of Iospan Wireless Inc., a Silicon Valley-based startup company (acquired by Intel Corporation in 2002) specialized in multiple-input multiple-output (MIMO) wireless systems for high-speed Internet access, and was a co-founder of Celestrius AG, Zurich, Switzerland. He was a visiting researcher at Philips Research Laboratories Eindhoven, The Netherlands, ENST Paris, France, and the Heinrich Hertz Institute Berlin, Germany. His research interests are in applied mathematics, machine learning theory, mathematical signal processing, data science, and statistics.
He received the 2001 IEEE Signal Processing Society Young Author Best Paper Award, the 2006 IEEE Communications Society Leonard G. Abraham Best Paper Award, the 2010 Vodafone Innovations Award, the ETH “Golden Owl” Teaching Award, is a Fellow of the IEEE, a 2011 EURASIP Fellow, was a Distinguished Lecturer (2013-2014) of the IEEE Information Theory Society, an Erwin Schrödinger Fellow (1999-2001) of the Austrian National Science Foundation (FWF), was included in the 2014 Thomson Reuters List of Highly Cited Researchers in Computer Science, was the 2016 Padovani Lecturer of the IEEE Information Theory Society, and received a 2021 Rothschild Fellowship from the Isaac Newton Institute for Mathematical Sciences, Cambridge University, UK. He served as editor-in-chief of the IEEE Transactions on Information Theory and is the founding editor-in-chief of the Springer journal “Mathematical Foundations of Machine Learning”. He has been a delegate for faculty appointments of the president of ETH Zurich since 2008.