no code implementations • 21 Aug 2024 • Chenyang Li, Zhao Song, Zhaoxing Xu, Junze Yin

Leverage scores have become essential in statistics and machine learning, aiding regression analysis, randomized matrix computations, and various other tasks.

no code implementations • 8 May 2024 • YIngyu Liang, Heshan Liu, Zhenmei Shi, Zhao Song, Zhuoyan Xu, Junze Yin

We then design a fast algorithm to approximate the attention matrix via a sum of such $k$ convolution matrices.

no code implementations • 21 Apr 2024 • Zhihang Li, Zhao Song, Weixin Wang, Junze Yin, Zheng Yu

Leverage score is a fundamental problem in machine learning and theoretical computer science.

no code implementations • 26 Nov 2023 • Zhihang Li, Zhao Song, Zifan Wang, Junze Yin

Our main results involve analyzing the convergence properties of an approximate Newton method used to minimize the regularized training loss.

no code implementations • 24 Nov 2023 • Zhao Song, Junze Yin, Ruizhe Zhang

However, the running times of these algorithms depend on some quantum linear algebra-related parameters, such as $\kappa(A)$, the condition number of $A$.

no code implementations • 30 Oct 2023 • Zhao Song, Guangyi Xu, Junze Yin

In this paper, we offer a theoretical analysis of the expressive capabilities of polynomial attention.

no code implementations • 23 Sep 2023 • Zhao Song, Weixin Wang, Junze Yin

The Hessian is shown to be positive semidefinite, and its structure is characterized as the sum of a low-rank matrix and a diagonal matrix.

no code implementations • 14 Sep 2023 • Yeqi Gao, Zhao Song, Weixin Wang, Junze Yin

$A_3$ is a matrix in $\mathbb{R}^{n \times d}$, $\mathsf{A}_{j_0} \in \mathbb{R}^{n \times d^2}$ is the $j_0$-th block of $\mathsf{A}$.

no code implementations • 28 Aug 2023 • Zhao Song, Junze Yin, Lichen Zhang

Given an input matrix $A\in \mathbb{R}^{n\times d}$ with $n\gg d$ and a response vector $b$, we first consider the matrix exponential of the matrix $A^\top A$ as a proxy, and we in turn design algorithms for two types of regression problems: $\min_{x\in \mathbb{R}^d}\|(A^\top A)^jx-b\|_2$ and $\min_{x\in \mathbb{R}^d}\|A(A^\top A)^jx-b\|_2$ for any positive integer $j$.

no code implementations • 21 Aug 2023 • Yeqi Gao, Zhao Song, Junze Yin

It is likely that only two types of people would be interested in setting up a practical system for it: $\bullet$ Those who prefer to use a decentralized ChatGPT-like software.

no code implementations • 7 Jun 2023 • Zhao Song, Mingquan Ye, Junze Yin, Lichen Zhang

For weighted low rank approximation, this improves the runtime of [LLR16] from $n^2 k^2$ to $n^2k$.

no code implementations • 6 Jun 2023 • Xiang Chen, Zhao Song, Baocheng Sun, Junze Yin, Danyang Zhuo

Many machine learning algorithms require large numbers of labeled data to deliver state-of-the-art results.

no code implementations • 1 Jun 2023 • Yichuan Deng, Zhao Song, Junze Yin

Tensor decomposition is a fundamental method used in various areas to deal with high-dimensional data.

no code implementations • 27 May 2023 • Song Bian, Zhao Song, Junze Yin

Many convex optimization problems with important applications in machine learning are formulated as empirical risk minimization (ERM).

no code implementations • 15 May 2023 • Zhao Song, Weixin Wang, Chenbo Yin, Junze Yin

But in \textsc{FastPostponedGreedy} algorithm, the status of each node is unknown at first.

no code implementations • 1 May 2023 • Yeqi Gao, Zhao Song, Junze Yin

LLMs have shown great promise in improving the accuracy and efficiency of these tasks, and have the potential to revolutionize the field of natural language processing (NLP) in the years to come.

no code implementations • 21 Feb 2023 • Yuzhou Gu, Zhao Song, Junze Yin, Lichen Zhang

Moreover, our algorithm runs in time $\widetilde O(|\Omega| k)$, which is nearly linear in the time to verify the solution while preserving the sample complexity.

no code implementations • 1 Feb 2023 • Zhao Song, Mingquan Ye, Junze Yin, Lichen Zhang

One popular approach for solving such $\ell_2$ regression problem is via sketching: picking a structured random matrix $S\in \mathbb{R}^{m\times n}$ with $m\ll n$ and $SA$ can be quickly computed, solve the ``sketched'' regression problem $\arg\min_{x\in \mathbb{R}^d} \|SAx-Sb\|_2$.

no code implementations • 28 Nov 2022 • Jiehao Liang, Somdeb Sarkhel, Zhao Song, Chenbo Yin, Junze Yin, Danyang Zhuo

We propose a new algorithm \textsc{FastKmeans++} that only takes in $\widetilde{O}(nd + nk^2)$ time, in total.

no code implementations • 8 Aug 2022 • Jiehao Liang, Zhao Song, Zhaozhuo Xu, Junze Yin, Danyang Zhuo

In this work, we focus on the dynamic maintenance of KDE data structures with robustness to adversarial queries.

no code implementations • 5 Aug 2022 • Hang Hu, Zhao Song, Runzhou Tao, Zhaozhuo Xu, Junze Yin, Danyang Zhuo

Online bipartite matching is a fundamental problem in online algorithms.

no code implementations • 24 Nov 2020 • Baihe Huang, Zhao Song, Runzhou Tao, Junze Yin, Ruizhe Zhang, Danyang Zhuo

On the current InstaHide challenge setup, where each InstaHide image is a mixture of two private images, we present a new algorithm to recover all the private images with a provable guarantee and optimal sample complexity.

Cannot find the paper you are looking for? You can
Submit a new open access paper.

Contact us on:
hello@paperswithcode.com
.
Papers With Code is a free resource with all data licensed under CC-BY-SA.