(Fun)damental Uses of Math in AI: Symposia
Explore the mathematical foundations of learning and artificial intelligence through a workshop designed to make rigorous theory accessible to a broader research community.
Featuring perspectives on how concepts like “learning” and “intelligence” can be formally defined and studied, the program highlights the rich problems, structures, and connections shaping this field. Designed for mathematically-inclined researchers, this workshop welcomes participants who are curious about theoretical machine learning and AI, whether new to the area or looking to deepen their understanding.
This event was part of the Frontiers in Data Science and AI initiative at the Data Science Institute, Columbia University.
Event Details
Friday, May 1, 2026 (10:00 AM - 4:00 PM ET)
Davis Auditorium, CEPSR (4th Floor - Campus Level) - Campus Map
Speakers & Talk Information
Christos H. Papadimitriou, Donovan Family Professor of Computer Science; Provost’s Senior Faculty Teaching Scholar, Columbia Engineering
Complexity Obstacles to Learning
Abstract: I will present examples from my work where complexity arguments inform aspects of machine learning, such as continual learning, reinforcement learning, the transformer architecture, and learning equilibria in multi-player games. I will also contemplate the role of complexity theory in the age of AI.
Elisenda Grigsby, Professor, Math Department, Boston College
The Geometry, Topology, and Combinatorics of Neural Networks
Abstract: Deep neural networks are a class of parameterized functions that have proven remarkably successful at making predictions about unseen data from finite labeled data sets. They do so even in settings when classical intuition suggests that they ought to be overfitting (memorizing) the data. I will begin by advertising one of the theoretical questions animating the field: how do internal symmetries of the models impact their learning dynamics? Along the way I will emphasize the many ways in which geometry, topology, and combinatorics play a role in the field.
Alexandr Andoni, Associate Professor of Computer Science, Columbia Engineering
Nearest Neighbor Search Problems in LLMs
Abstract: Long a foundational primitive for classification and retrieval, high-dimensional Nearest Neighbor Search (NNS) keeps resurfacing in many roles across the modern LLM pipeline. This talk explores three such roles: as the retrieval engine powering RAG systems; as a Kernel Density Estimation (KDE) problem underlying the KV cache problem in transformers; and as a route toward a sub-quadratic attention mechanism. Along the way, I will highlight open problems where stronger algorithmic and mathematical tools could yield further progress.
Joan Bruna Estrach, Professor of Computer Science, Data Science, and Mathematics, Courant Institute, New York University
A Dynamic Perspective on High-Dimensional Learning
Abstract: Modern machine learning systems surprise us again and again by their ability to extract complex information out of high-dimensional observations, defying our intuition anchored in the curse of dimensionality. In this talk I will describe a mathematical framework aiming to address this challenge, in which measure transport takes centerpiece. I will first illustrate training dynamics and describe how functions with hidden low-dimensional structure can be provably learnt using gradient-descent methods. Then we will illustrate measure transport in the context of generative models, emphasizing their role in inverse problems.
Agenda
Friday, May 1, 2026
9:45 AM: Doors Open for Attendees (15 min prior)
10:00 AM: Part One Introductions: Daniel Hsu, Associate Professor of Computer Science, Columbia Engineering (5 min)
10:05 AM: Presentation: Christos H. Papadimitriou, Donovan Family Professor of Computer Science; Provost's Senior Faculty Teaching Scholar, Columbia Engineering (40 min talk; 10 min questions) - presenting remotely
10:55 AM: Break (10 min)
11:05 AM: Presentation: Elisenda Grigsby, Professor, Math Department, Boston College (40 min talk; 10 min questions)
12:00 PM: Lunch for Attendees in Mudd 407 (60 min)
1:00 PM: Part Two Introductions: Daniel Hsu, Associate Professor of Computer Science, Columbia Engineering (5 min)
1:05 PM: Presentation: Alexandr Andoni, Associate Professor of Computer Science, Columbia Engineering (40 min talk; 10 min questions)
1:55 PM: Break (5 min)
2:00 PM: Presentation: Joan Bruna Estrach, Professor of Computer Science, Data Science, and Mathematics, Courant Institute, New York University (40 min talk; 10 min questions)
2:50 PM: Research Project Discussion: Kriste Krstovski, Associate Research Scientist, Data Science Institute (10 min)
3:00 PM: Reception for Attendees in Mudd 407 (60 min)
DSI Frontiers Awardees: (Fun)damental AI and Math Series
- Ivan Corwin, Professor of Mathematics and Statistics, Arts & Sciences, Columbia University
- Andrew J. Blumberg, Herbert and Florence Irving Professor of Cancer Data Research (in the Herbert and Florence Irving Institute of Cancer Dynamics and in the Herbert Irving Comprehensive Cancer Center) and Professor of Mathematics and Computer Science
- Kriste Krstovski, Associate Research Scientist, Data Science Institute
- Daniel Hsu, Associate Professor of Computer Science, Columbia Engineering
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