5 accepted papers
Softmax distributions are widely used in machine learning, including Large Language Models (LLMs), where the attention unit uses softmax distributions. We abstract the attention unit as the softmax model, where given a vector input, the model produces an output drawn from the softmax distribution (w…
We study the evolution of information in interactive decision making through the lens of a stochastic multi-armed bandit problem. Focusing on a fundamental example where a unique optimal arm outperforms the rest by a fixed margin, we characterize the optimal success probability and mutual informatio…
Quadratic programming is a ubiquitous prototype in convex programming. Many machine learning problems can be formulated as quadratic programming, including the famous Support Vector Machines (SVMs). Linear and kernel SVMs have been among the most popular models in machine learning over the past thre…
We consider the problem of sampling from a $d$-dimensional log-concave distribution $\pi(\theta) \propto \exp(-f(\theta))$ for $L$-Lipschitz $f$, constrained to a convex body (described by $n$ hyperplanes) equipped with a barrier function, contained in a ball of radius $R$ with a $w$-warm start. W…
Given a matrix $M\in \mathbb{R}^{m\times n}$, the low rank matrix completion problem asks us to find a rank-$k$ approximation of $M$ as $UV^\top$ for $U\in \mathbb{R}^{m\times k}$ and $V\in \mathbb{R}^{n\times k}$ by only observing a few entries specified by a set of entries $\Omega\subseteq [m]\tim…