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Machine learning relies on its ability to generalize from limited data, yet a principled theoretical understanding of generalization remains incomplete. While binary classification is well understood in the classical PAC framework, even its natural extension to multiclass learning is substantially more challenging.

In this talk, I will present recent progress in multiclass learning that characterizes when generalization is possible and how much data is required, resolving a long-standing open problem on extending the Vapnik–Chervonenkis (VC) dimension beyond the binary setting. I will then turn to complementary results on efficient learning via boosting.  We extend boosting theory to multiclass classification, while maintaining computational and statistical efficiency even for unbounded label spaces.

Lastly, I will discuss generalization in sequential learning settings, where a learner interacts with an environment over time. We introduce a new framework that subsumes classically studied settings (bandits and statistical queries) together with a combinatorial parameter that bounds the number of interactions required for learning.

Bio: 

Nataly Brukhim is a postdoctoral researcher at the Institute for Advanced Study (IAS) and the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS). She received her Ph.D. in Computer Science from Princeton University, where she was advised by Elad Hazan, and was a student researcher at Google AI Princeton. She earned her M.Sc. and B.Sc. in Computer Science from Tel Aviv University.

While AI models are becoming an ever-increasing part of our lives, our understanding of their behavior in unexpected situations is drifting even further out of reach. This gap poses significant risks to users, model owners, and society at large.

In the first part of the talk, I will overview my research on detecting unexpected phenomena with and within deep learning models. Specifically, detecting (i) anomalous samples, (ii) unexpected model behavior, and (iii) unexpected security threats. In the second part of the talk, I will dive into my recent research on a specific type of unexpected security threat: attacks on image watermarks. I will review such attacks and present my recent work toward addressing them. I will conclude with a discussion of future research directions.

Bio:

Niv Cohen is a postdoctoral researcher at the school of Computer Science & Engineering at New York University. He received his Ph.D. in Computer Science from the Hebrew University in 2024. His research interests include representation learning, computer vision, and AI safety. He is a recipient of the VATAT Scholarship for Outstanding Postdoctoral Fellows in Data Science and the 2024 Blavatnik Prize for Outstanding Israeli Doctoral Students in Computer Science.

In this talk we present a new approximate functional equation for the Hardy Z function with exponentially decaying error. This formula makes it possible to define a variation space for Z(t) consisting of a family of functions Z_N(t,a) with parameters a = (a1, …, aN) on a fixed window [2n, 2N + 2]. In this space the original Hardy function Z(t) is extremely well approximated in the window by the special choice a = (1, …, 1). Within this variation space we single out a natural domain RH_N in which all functions Z_N(t,a) have only real zeros in the window. We show that RH_N has striking connections with random matrix theory. In particular a Brownian motion with Skorokhod type reflection at the boundary of RH_N induces a Dyson Brownian motion in the \beta=2 case, and modern universality results then yield the expected GUE local statistics for elements of RH_N. No prior knowledge in number theory would be required.

Many fossil materials have embedded signals that enable aspects of the past to be reconstructed. These signals however can be altered or lost due to processes that take place once the fossil material is buried (diagenesis). Thus extracting reliable signals can be a major challenge. Here I present a new approach to better understanding diagenesis that I apply to bone.