Results 1281 - 1290 of 23832

Gibbs sampling is a crucial computational technique used in physics, statistics, and many
other scientific fields. While classical Gibbs sampling has been studied for decades and numerous results has been obtained, few results are known for quantum Gibbs sampling. I will In this talk, I will introduce the concept of quantum Gibbs sampling, discuss its motivation and potential applications, and highlight several open problems that I find particularly interesting.

I will talk about some open problems in practical quantum fault-tolerance as well as some theoretical directions.

A key puzzle in deep learning is how simple gradient methods find generalizable solutions without explicit regularization. This talk discusses the implicit regularization of gradient descent (GD) through the lens of statistical dominance. Using least squares as a clean proxy, we present two surprising findings.

First, GD dominates ridge regression. For any well-specified Gaussian least squares problem, the finite-sample excess risk of optimally stopped GD is no more than a constant times that of optimally tuned ridge regression. However, there is a natural subset of these problems where GD achieves a polynomially smaller excess risk. Thus, implicit regularization is statistically superior to explicit regularization, in addition to its computational advantages.

Second, GD and online stochastic gradient descent (SGD) are incomparable. We construct a sequence of well-specified Gaussian least squares problems where optimally stopped GD is polynomially worse than online SGD, and similarly vice versa. Our construction leverages a key insight from benign overfitting, revealing a fundamental separation between batch and online learning.