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Found 15 papers, 4 papers with code
An Empirical Study on Challenging Math Problem Solving with GPT-4
Employing Large Language Models (LLMs) to address mathematical problems is an intriguing research endeavor, considering the abundance of math problems expressed in natural language across numerous science and engineering fields.
Learning-Augmented B-Trees
We study learning-augmented binary search trees (BSTs) and B-Trees via Treaps with composite priorities.
$\ell_2$-norm Flow Diffusion in Near-Linear Time
Diffusion is a fundamental graph procedure and has been a basic building block in a wide range of theoretical and empirical applications such as graph partitioning and semi-supervised learning on graphs.
Fully Dynamic Electrical Flows: Sparse Maxflow Faster Than Goldberg-Rao
We give an algorithm for computing exact maximum flows on graphs with $m$ edges and integer capacities in the range $[1, U]$ in $\widetilde{O}(m^{\frac{3}{2} - \frac{1}{328}} \log U)$ time.
Data Structures and Algorithms
A Matrix Chernoff Bound for Markov Chains and Its Application to Co-occurrence Matrices
Our result gives the first bound on the convergence rate of the co-occurrence matrix and the first sample complexity analysis in graph representation learning.
Faster Graph Embeddings via Coarsening
As computing Schur complements is expensive, we give a nearly-linear time algorithm that generates a coarsened graph on the relevant vertices that provably matches the Schur complement in expectation in each iteration.
A Study of Performance of Optimal Transport
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph.
Fast, Provably convergent IRLS Algorithm for p-norm Linear Regression
However, these algorithms often diverge for p > 3, and since the work of Osborne (1985), it has been an open problem whether there is an IRLS algorithm that is guaranteed to converge rapidly for p > 3.
Higher-Order Accelerated Methods for Faster Non-Smooth Optimization
We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods.
Iterative Refinement for $\ell_p$-norm Regression
We give improved algorithms for the $\ell_{p}$-regression problem, $\min_{x} \|x\|_{p}$ such that $A x=b,$ for all $p \in (1, 2) \cup (2,\infty).$ Our algorithms obtain a high accuracy solution in $\tilde{O}_{p}(m^{\frac{|p-2|}{2p + |p-2|}}) \le \tilde{O}_{p}(m^{\frac{1}{3}})$ iterations, where each iteration requires solving an $m \times m$ linear system, $m$ being the dimension of the ambient space.
SPALS: Fast Alternating Least Squares via Implicit Leverage Scores Sampling
In this paper, we show ways of sampling intermediate steps of alternating minimization algorithms for computing low rank tensor CP decompositions, leading to the sparse alternating least squares (SPALS) method.
Spectral Sparsification of Random-Walk Matrix Polynomials
Our work is particularly motivated by the algorithmic problems for speeding up the classic Newton's method in applications such as computing the inverse square-root of the precision matrix of a Gaussian random field, as well as computing the $q$th-root transition (for $q\geq1$) in a time-reversible Markov model.
Partitioning Well-Clustered Graphs: Spectral Clustering Works!
In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and (2) grouping the embedded points into k clusters via k-means algorithms.
Scalable Parallel Factorizations of SDD Matrices and Efficient Sampling for Gaussian Graphical Models
random samples for $n$-dimensional Gaussian random fields with SDDM precision matrices.
Uniform Sampling for Matrix Approximation
In addition to an improved understanding of uniform sampling, our main proof introduces a structural result of independent interest: we show that every matrix can be made to have low coherence by reweighting a small subset of its rows.
