Related papers: Lazy Kronecker Product
We build upon the recent papers by Weinstein and Yu (FOCS'16), Larsen (FOCS'12), and Clifford et al. (FOCS'15) to present a general framework that gives amortized lower bounds on the update and query times of dynamic data structures. Using…
We study the Kronecker product regression problem, in which the design matrix is a Kronecker product of two or more matrices. Given $A_i \in \mathbb{R}^{n_i \times d_i}$ for $i=1,2,\dots,q$ where $n_i \gg d_i$ for each $i$, and $b \in…
Second order stochastic optimizers allow parameter update step size and direction to adapt to loss curvature, but have traditionally required too much memory and compute for deep learning. Recently, Shampoo [Gupta et al., 2018] introduced a…
The dynamic set cover problem has been subject to growing research attention in recent years. In this problem, we are given as input a dynamic universe of at most $n$ elements and a fixed collection of $m$ sets, where each element appears…
Kronecker PCA involves the use of a space vs. time Kronecker product decomposition to estimate spatio-temporal covariances. In this work the addition of a sparse correction factor is considered, which corresponds to a model of the…
In this paper, we study the $d$-dimensional update-query problem. We provide lower bounds on update and query running times, assuming a long-standing conjecture on min-plus matrix multiplication, as well as algorithms that are close to the…
We consider the problem of maintaining an (approximately) minimum vertex cover in an $n$-node graph $G = (V, E)$ that is getting updated dynamically via a sequence of edge insertions/deletions. We show how to maintain a…
Motivated by recent Linear Programming solvers, we design dynamic data structures for maintaining the inverse of an $n\times n$ real matrix under $\textit{low-rank}$ updates, with polynomially faster amortized running time. Our data…
This work proposes a Momentum-Enabled Kronecker-Factor-Based Optimizer Using Rank-1 updates, called MKOR, that improves the training time and convergence properties of deep neural networks (DNNs). Second-order techniques, while enjoying…
Using a noise covariance model based on a single Kronecker product of spatial and temporal covariance in the spatiotemporal analysis of MEG data was demonstrated to provide improvement in the results over that of the commonly used diagonal…
In this paper we introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive…
In the dynamic minimum set cover problem, a challenge is to minimize the update time while guaranteeing close to the optimal $\min(O(\log n), f)$ approximation factor. (Throughout, $m$, $n$, $f$, and $C$ are parameters denoting the maximum…
In this paper we propose a Kronecker-based modeling for identifying the spatial-temporal dynamics of large sensor arrays. The class of Kronecker networks is defined for which we formulate a Vector Autoregressive model. Its…
A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…
We analyze Newton's method with lazy Hessian updates for solving general possibly non-convex optimization problems. We propose to reuse a previously seen Hessian for several iterations while computing new gradients at each step of the…
We study the problem of efficiently correcting an erroneous product of two $n\times n$ matrices over a ring. Among other things, we provide a randomized algorithm for correcting a matrix product with at most $k$ erroneous entries running in…
Many of the recent trajectory optimization algorithms alternate between linear approximation of the system dynamics around the mean trajectory and conservative policy update. One way of constraining the policy change is by bounding the…
We formulate the predicted-updates dynamic model, one of the first beyond-worst-case models for dynamic algorithms, which generalizes a large set of well-studied dynamic models including the offline dynamic, incremental, and decremental…
Many convex problems in machine learning and computer science share the same form: \begin{align*} \min_{x} \sum_{i} f_i( A_i x + b_i), \end{align*} where $f_i$ are convex functions on $\mathbb{R}^{n_i}$ with constant $n_i$, $A_i \in…
Kronecker regression is a highly-structured least squares problem $\min_{\mathbf{x}} \lVert \mathbf{K}\mathbf{x} - \mathbf{b} \rVert_{2}^2$, where the design matrix $\mathbf{K} = \mathbf{A}^{(1)} \otimes \cdots \otimes \mathbf{A}^{(N)}$ is…