Events

Sample covariance matrices are among the most fundamental objects in random matrix theory and statistics. In this talk, I'll discuss recent work identifying the assumptions on random vectors that allow local laws to hold for their sample covariance matrices — these are matrices with iid rows sampled from a fixed distribution.

A local law says that the empirical eigenvalue distribution converges to its deterministic limit—in this case the deformed Marchenko–Pastur law—not just globally, but on short intervals which still contain a power of dimension many eigenvalues. This fine-grained control is essential for many applications, including universality for the local eigenvalue distributions.

The classical approach assumes the data vectors take a separable form g=Xw where w has independent entries—but this excludes many natural examples. We ask: what assumptions on g are really needed? It turns out that concentration of quadratic forms suffices for an optimal averaged local law, while a structural condition on cumulant tensors—interpolating between independence and generic dependence—suffices for the full anisotropic local law.

I'll discuss key examples where our assumptions can be verified: sign-invariant vectors, the 'random features model’ from machine learning, and some examples of spin-glass type. I'll also give a short overview of the proof, which introduces a tensor network framework for fluctuation averaging in the presence of higher-order cumulant structure. 

Joint with Jack Ma (Yale), Zhou Fan (Yale), Zhichao Wang (Berkeley)

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.

Financial systems are becoming increasingly digital and decentralized, demanding a practical fusion of distributed systems security and economic theory. A key enabler of this change, blockchain technology, promises more private and egalitarian economic mechanisms, built by facilitating consensus between pseudonymous actors. However, the theoretical security of these systems may mask significant real-world risks. In this talk, I will present recent advances in bridging this gap between theory and practice. First, I will discuss the resolution of a decade-old puzzle: the lack of observed attacks on major consensus mechanisms. I will then distill the lessons learnt into a holistic approach to designing robust mechanisms for distributed pseudonymous systems and demonstrate its adoption in practice using several lines of work.