Video Lectures

In this talk I will describe the notion of "agreement tests" that are motivated by PCPs but stand alone as a combinatorial property-testing question. I will show that high dimensional expanders support agreement tests, thereby derandomizing direct...

A theorist's dream is to show that hard instances/obstructions for an (optimal) algorithm can be used as gadgets to prove tight hardness reductions (which proves optimality of the algorithm). An example of such a result is that of Prasad Raghavendra...

The purpose of the talk is to discuss a class of pseudo-metrics that can be defined on the set of objects of a triangulated category whose morphisms are endowed with a notion of weight. In case the objects are Lagrangian submanifolds (possibly...

This talk surveys the role of margins in the analysis of deep networks. As a concrete highlight, it sketches a perceptron-based analysis establishing that shallow ReLU networks can achieve small test error even when they are quite narrow, sometimes...

In this talk I will describe the notion of "agreement tests" that are motivated by PCPs but stand alone as a combinatorial property-testing question. I will show that high dimensional expanders support agreement tests, thereby derandomizing direct...

Consider the p-biased distribution over 0,1n, in which each coordinate independently is sampled according to a p-biased bit. A sharp-threshold result studies the behavior of Boolean functions over the hypercube under different p-biased measures, and...

Why deep learning models, trained on many machine learning tasks, can obtain nearly perfect predictions of unseen data sampled from the same distribution but are extremely vulnerable to small perturbations of the input? How can adversarial training...

In this talk, I will discuss my two recent works on Energy-Based Models. In the first work, I discuss how we can reinterpret standard classification architectures as class conditional energy-based models and train them using recently proposed...

High dimensional expansion generalizes edge and spectral expansion in graphs to hypergraphs (viewed as higher dimensional simplicial complexes). It is a tool that allows analysis of PCP agreement rests, mixing of Markov chains, and construction of...

We provide geometric sufficient conditions for Reifenberg flat sets of any integer dimension in Euclidean space to be parametrized by a Lipschitz map with Hölder derivatives. The conditions use a Jones type square function and all statements are...