Related papers: Lifting Linear Sketches: Optimal Bounds and Advers…
Many recent prompting strategies for large language models (LLMs) query the model multiple times sequentially -- first to produce intermediate results and then the final answer. However, using these methods, both decoder and model are…
We propose new variants of the sketch-and-project method for solving large scale ridge regression problems. Firstly, we propose a new momentum alternative and provide a theorem showing it can speed up the convergence of sketch-and-project,…
We derive an implicit numerical scheme for the solution of advection equation where the roles of space and time variables are exchanged using the inverse Lax-Wendroff procedure. The scheme contains a linear weight for which it is always…
We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications,…
We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…
In this paper, we present a new algorithm for maintaining linear sketches in turnstile streams with faster update time. As an application, we show that $\log n$ \texttt{Count} sketches or \texttt{CountMin} sketches with a constant number of…
Recent work has developed methods for learning deep network classifiers that are provably robust to norm-bounded adversarial perturbation; however, these methods are currently only possible for relatively small feedforward networks. In this…
Matrix sketching, aimed at approximating a matrix $\boldsymbol{A} \in \mathbb{R}^{N\times d}$ consisting of vector streams of length $N$ with a smaller sketching matrix $\boldsymbol{B} \in \mathbb{R}^{\ell\times d}, \ell \ll N$, has…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
Matrix sketching is a powerful tool for reducing the size of large data matrices. Yet there are fundamental limitations to this size reduction when we want to recover an accurate estimator for a task such as least square regression. We show…
We present space-efficient linear sketches for estimating trimmed statistics of an $n$-dimensional frequency vector $x$, e.g., the sum of $p$-th powers of the largest $k$ frequencies (i.e., entries) in absolute value, or the $k$-trimmed…
We develop new $(1+\epsilon)$-approximation algorithms for finding the global minimum edge-cut in a directed edge-weighted graph, and for finding the global minimum vertex-cut in a directed vertex-weighted graph. Our algorithms are…
We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less…
In this paper, we address the problem of learning compact similarity-preserving embeddings for massive high-dimensional streams of data in order to perform efficient similarity search. We present a new online method for computing binary…
It is often desirable to reduce the dimensionality of a large dataset by projecting it onto a low-dimensional subspace. Matrix sketching has emerged as a powerful technique for performing such dimensionality reduction very efficiently. Even…
For an input graph $G$, an additive spanner is a sparse subgraph $H$ whose shortest paths match those of $G$ up to small additive error. We prove two new lower bounds in the area of additive spanners: 1) We construct $n$-node graphs $G$ for…
We consider the Survivable Network Design problem (SNDP) in the single-pass insertion-only streaming model. The input to SNDP is an edge-weighted graph $G = (V, E)$ and an integer connectivity requirement $r(uv)$ for each $u, v \in V$. The…
Deep neural network-based image compression has been extensively studied. However, the model robustness which is crucial to practical application is largely overlooked. We propose to examine the robustness of prevailing learned image…
Recently, Bessa et al. (PODS 2023) showed that sketches based on coordinated weighted sampling theoretically and empirically outperform popular linear sketching methods like Johnson-Lindentrauss projection and CountSketch for the ubiquitous…
An acknowledged weakness of neural networks is their vulnerability to adversarial perturbations to the inputs. To improve the robustness of these models, one of the most popular defense mechanisms is to alternatively maximize the loss over…