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Our goal is to compare two planar point sets by finding subsets of a given size such that a minimum-weight matching between them has the smallest weight. This can be done by a translation of one set that minimizes the weight of the…
Randomized algorithms have proven to perform well on a large class of numerical linear algebra problems. Their theoretical analysis is critical to provide guarantees on their behaviour, and in this sense, the stochastic analysis of the…
In this paper, we aim to study the optimal weak convergence order for the finite element approximation to a stochastic Allen-Cahn equation driven by multiplicative white noise. We first construct an auxiliary equation based on the…
The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…
The technique of abstracting abstract machines (AAM) provides a systematic approach for deriving computable approximations of evaluators that are easily proved sound. This article contributes a complementary step-by-step process for…
Various forms of regularization in learning tasks strive for different notions of simplicity. This paper presents a spectral regularization technique, which attaches a unique inductive bias to sequence modeling based on an intuitive concept…
This contribution revisits the classical approximate realization problem, which involves determining matrices of a state-space model based on estimates of a truncated series of Markov parameters. A Hankel matrix built up by these Markov…
The heightened emphasis on the regulation of deep generative models, propelled by escalating concerns pertaining to privacy and compliance with regulatory frameworks, underscores the imperative need for precise control mechanisms over these…
This paper is devoted to the study (common in many applications) of the black-box optimization problem, where the black-box represents a gradient-free oracle $\tilde{f} = f(x) + \xi$ providing the objective function value with some…
Real-world machine learning applications often have complex test metrics, and may have training and test data that are not identically distributed. Motivated by known connections between complex test metrics and cost-weighted learning, we…
We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…
The challenge of approximating functions in infinite-dimensional spaces from finite samples is widely regarded as formidable. We delve into the challenging problem of the numerical approximation of Sobolev-smooth functions defined on…
Recent research has revealed that natural language processing (NLP) models are vulnerable to adversarial examples. However, the current techniques for generating such examples rely on deterministic heuristic rules, which fail to produce…
Low-rank adaptation (LoRA) reduces the computational and memory demands of fine-tuning large language models (LLMs) by approximating updates with low-rank matrices. However, low-rank approximation in two-dimensional space fails to capture…
A major approach to saddle point optimization $\min_x\max_y f(x, y)$ is a gradient based approach as is popularized by generative adversarial networks (GANs). In contrast, we analyze an alternative approach relying only on an oracle that…
Although deep learning models have proven effective at solving problems in natural language processing, the mechanism by which they come to their conclusions is often unclear. As a result, these models are generally treated as black boxes,…
We study 4 problems in string matching, namely, regular expression matching, approximate regular expression matching, string edit distance, and subsequence indexing, on a standard word RAM model of computation that allows logarithmic-sized…
Lokshtanov et al.~[STOC 2017] introduced \emph{lossy kernelization} as a mathematical framework for quantifying the effectiveness of preprocessing algorithms in preserving approximation ratios. \emph{$\alpha$-approximate reduction rules}…
The Minimum Weighted Feedback Arc Set (MWFAS) problem is closely related to the task of deriving a global ranking from pairwise comparisons. Recent work by He et al. (ICML 2022) advanced the state of the art on ranking benchmarks using…