Related papers: How Robust are Linear Sketches to Adaptive Inputs?

Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…

This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…

Deep learning models are increasingly deployed in safety-critical tasks where predictions must satisfy hard constraints, such as physical laws, fairness requirements, or safety limits. However, standard architectures lack built-in…

Matrix sketching is a recently developed data compression technique. An input matrix A is efficiently approximated with a smaller matrix B, so that B preserves most of the properties of A up to some guaranteed approximation ratio. In so…

Given a persistence diagram with $n$ points, we give an algorithm that produces a sequence of $n$ persistence diagrams converging in bottleneck distance to the input diagram, the $i$th of which has $i$ distinct (weighted) points and is a…

Humans show high-level of abstraction capabilities in games that require quickly communicating object information. They decompose the message content into multiple parts and communicate them in an interpretable protocol. Toward equipping…

We present new adaptive sampling rules for the sketch-and-project method for solving linear systems. To deduce our new sampling rules, we first show how the progress of one step of the sketch-and-project method depends directly on a…

Sketch-based modeling strives to bring the ease and immediacy of drawing to the 3D world. However, while drawings are easy for humans to create, they are very challenging for computers to interpret due to their sparsity and ambiguity. We…

This paper presents a robust, distributed algorithm to solve general linear programs. The algorithm design builds on the characterization of the solutions of the linear program as saddle points of a modified Lagrangian function. We show…

Time series are difficult to monitor, summarize and predict. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). For scalability, we require fast…

Powerful deep learning tools, such as convolutional neural networks (CNN), are able to learn the input-output relationships of large complicated systems directly from data. Encoder-decoder deep CNNs are able to extract features directly…

Function approximation has been an indispensable component in modern reinforcement learning algorithms designed to tackle problems with large state spaces in high dimensions. This paper reviews recent results on error analysis for these…

Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…

We study the problem of constructing a linear sketch of minimum dimension that allows approximation of a given real-valued function $f \colon \mathbb{F}_2^n \rightarrow \mathbb R$ with small expected squared error. We develop a general…

We study classic streaming and sparse recovery problems using deterministic linear sketches, including l1/l1 and linf/l1 sparse recovery problems (the latter also being known as l1-heavy hitters), norm estimation, and approximate inner…

In this paper, we explore the unique modality of sketch for explainability, emphasising the profound impact of human strokes compared to conventional pixel-oriented studies. Beyond explanations of network behavior, we discern the genuine…

We revisit the well-studied problem of approximating a matrix product, $\mathbf{A}^T\mathbf{B}$, based on small space sketches $\mathcal{S}(\mathbf{A})$ and $\mathcal{S}(\mathbf{B})$ of $\mathbf{A} \in \R^{n \times d}$ and $\mathbf{B}\in…

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

Linear approximations to the decision boundary of a complex model have become one of the most popular tools for interpreting predictions. In this paper, we study such linear explanations produced either post-hoc by a few recent methods or…

Deep neural networks are capable of training fast and generalizing well within many domains. Despite their promising performance, deep networks have shown sensitivities to perturbations of their inputs (e.g., adversarial examples) and their…