11 citations · 26 across the 25 of their papers we have counts for
28 papers
Hadamard Flattening and Gaussian Pooling Sketch for Least Squares with Coordinate-wise Guarantee
Zhao Song, Lichen Zhang
Randomized sketch-and-solve algorithms accelerate overconstrained regression by replacing the input with a smaller problem. Standard subspace embeddings guarantee that the…
A General Framework for Metropolis-Adjusted Dikin Walks: Dimension-Square Mixing on Polytopes and Log-Det Walks on Spectrahedra
Zhao Song, Lichen Zhang
We analyze exact-metric, Metropolis-adjusted Dikin walks by keeping the proposal determinant and reverse quadratic form together. Their leading uncentered terms cancel in the compl…
On the maximum number of edges of k-cacti
Yuanqiu Huang, Licheng Zhang
A cactus is a graph in which every edge lies on at most one cycle. In 2024, Zhang and Huang generalized this concept to the -cactus, defined as a graph in which every edge lies…
ArcFlow: Unleashing 2-Step Text-to-Image Generation via High-Precision Non-Linear Flow Distillation
Zihan Yang, Shuyuan Tu, Licheng Zhang +3
Diffusion models have achieved remarkable generation quality, but they suffer from significant inference cost due to their reliance on multiple sequential denoising steps, motivati…
Sublinear Time Quantum Algorithm for Attention Approximation
Zhao Song, Jianfei Xue, Jiahao Zhang +1
Given the query, key and value matrices , the attention module is defined as where wi…
Differential Privacy for Euclidean Jordan Algebra with Applications to Private Symmetric Cone Programming
Zhao Song, Jianfei Xue, Lichen Zhang
In this paper, we study differentially private mechanisms for functions whose outputs lie in a Euclidean Jordan algebra. Euclidean Jordan algebras capture many important mathematic…
Sublinear Time Quantum Sensitivity Sampling
Zhao Song, David P. Woodruff, Lichen Zhang
We present a unified framework for quantum sensitivity sampling, extending the advantages of quantum computing to a broad class of classical approximation problems. Our unified fra…
On Differential Privacy for Adaptively Solving Search Problems via Sketching
Shiyuan Feng, Ying Feng, George Z. Li +3
Recently differential privacy has been used for a number of streaming, data structure, and dynamic graph problems as a means of hiding the internal randomness of the data structure…
Log-concave Sampling from a Convex Body with a Barrier: a Robust and Unified Dikin Walk
Yuzhou Gu, Nikki Lijing Kuang, Yi-An Ma +2
We consider the problem of sampling from a -dimensional log-concave distribution for -Lipschitz , constrained to a convex body with an efficient…
On Differentially Private String Distances
Jerry Yao-Chieh Hu, Erzhi Liu, Han Liu +2
Given a database of bit strings , a fundamental data structure task is to estimate the distances between a given query with all the st…
Streaming Semidefinite Programs: Passes, Small Space and Fast Runtime
Zhao Song, Mingquan Ye, Lichen Zhang
We study the problem of solving semidefinite programs (SDP) in the streaming model. Specifically, constraint matrices and a target matrix , all of size together…
Solving Attention Kernel Regression Problem via Pre-conditioner
Zhao Song, Junze Yin, Lichen Zhang
The attention mechanism is the key to large language models, and the attention matrix serves as an algorithmic and computational bottleneck for such a scheme. In this paper, we def…
Faster Algorithms for Structured Linear and Kernel Support Vector Machines
Yuzhou Gu, Zhao Song, Lichen Zhang
Quadratic programming is a ubiquitous prototype in convex programming. Many machine learning problems can be formulated as quadratic programming, including the famous Support Vecto…
Efficient Algorithm for Solving Hyperbolic Programs
Yichuan Deng, Zhao Song, Lichen Zhang +1
Hyperbolic polynomials is a class of real-roots polynomials that has wide range of applications in theoretical computer science. Each hyperbolic polynomial also induces a hyperboli…
Efficient Alternating Minimization with Applications to Weighted Low Rank Approximation
Zhao Song, Mingquan Ye, Junze Yin +1
Weighted low rank approximation is a fundamental problem in numerical linear algebra, and it has many applications in machine learning. Given a matrix $M \in \mathbb{R}^{n \times n…
Convex Minimization with Integer Minima in Time
Haotian Jiang, Yin Tat Lee, Zhao Song +1
Given a convex function on with an integer minimizer, we show how to find an exact minimizer of using calls to a separation oracle and $O(n^4…
Low Rank Matrix Completion via Robust Alternating Minimization in Nearly Linear Time
Yuzhou Gu, Zhao Song, Junze Yin +1
Given a matrix , the low rank matrix completion problem asks us to find a rank- approximation of as for …
A Nearly-Optimal Bound for Fast Regression with Guarantee
Zhao Song, Mingquan Ye, Junze Yin +1
Given a matrix and a vector , we consider the regression problem with guarantees: finding a vector $x'\in \mathbb{R}^…
Sketching Meets Differential Privacy: Fast Algorithm for Dynamic Kronecker Projection Maintenance
Zhao Song, Xin Yang, Yuanyuan Yang +1
Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming alg…
Sketching for First Order Method: Efficient Algorithm for Low-Bandwidth Channel and Vulnerability
Zhao Song, Yitan Wang, Zheng Yu +1
Sketching is one of the most fundamental tools in large-scale machine learning. It enables runtime and memory saving via randomly compressing the original large problem into lower…
Dynamic Tensor Product Regression
Aravind Reddy, Zhao Song, Lichen Zhang
In this work, we initiate the study of \emph{Dynamic Tensor Product Regression}. One has matrices and a…
Accelerating Frank-Wolfe Algorithm using Low-Dimensional and Adaptive Data Structures
Zhao Song, Zhaozhuo Xu, Yuanyuan Yang +1
In this paper, we study the problem of speeding up a type of optimization algorithms called Frank-Wolfe, a conditional gradient method. We develop and employ two novel inner produc…
Speeding Up Sparsification using Inner Product Search Data Structures
Zhao Song, Zhaozhuo Xu, Lichen Zhang
We present a general framework that utilizes different efficient data structures to improve various sparsification problems involving an iterative process. We also provide insights…
Neural Architecture Search for Inversion
Cheng Zhan, Licheng Zhang, Xin Zhao +2
Over the year, people have been using deep learning to tackle inversion problems, and we see the framework has been applied to build relationship between recording wavefield and ve…