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Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…

Machine Learning · Statistics 2025-05-20 Riccardo Grazzi , Massimiliano Pontil , Saverio Salzo

A cornerstone of extremal graph theory due to Erd\H{o}s and Stone states that the edge density which guarantees a fixed graph $F$ as subgraph also asymptotically guarantees a blow-up of $F$ as subgraph. It is natural to ask whether this…

Combinatorics · Mathematics 2026-04-01 Richard Lang , Nicolás Sanhueza-Matamala

We provide a variant of cross-polytope locality sensitive hashing with respect to angular distance which is provably optimal in asymptotic sensitivity and enjoys $\mathcal{O}(d \ln d )$ hash computation time. Building on a recent result (by…

Data Structures and Algorithms · Computer Science 2016-09-22 Christopher Kennedy , Rachel Ward

The $\hybrid$ model was recently introduced by Augustine et al. \cite{DBLP:conf/soda/AugustineHKSS20} in order to characterize from an algorithmic standpoint the capabilities of networks which combine multiple communication modes.…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-08-05 Ioannis Anagnostides , Themis Gouleakis

We consider the problem of determining the maximal $\alpha \in (0,1]$ such that every matching $M$ of size $k$ (or at most $k$) in a bipartite graph $G$ contains an induced matching of size at least $\alpha |M|$. This measure was recently…

Data Structures and Algorithms · Computer Science 2018-09-11 Noga Alon , Jonathan D. Cohen , Thomas L. Griffiths , Pasin Manurangsi , Daniel Reichman , Igor Shinkar , Tal Wagner , Alexander Yu

This article develops, via the perspective of (arithmetic) algebraic geometry and category theory, different aspects of geometry of information. First, we describe in the terms of Eilenberg--Moore algebras over a Giry monad, the collection…

Algebraic Geometry · Mathematics 2022-12-20 N. C. Combe

The sparse Johnson-Lindenstrauss transform is one of the central techniques in dimensionality reduction. It supports embedding a set of $n$ points in $\mathbb{R}^d$ into $m=O(\varepsilon^{-2} \lg n)$ dimensions while preserving all pairwise…

Data Structures and Algorithms · Computer Science 2023-02-14 Mikael Møller Høgsgaard , Lion Kamma , Kasper Green Larsen , Jelani Nelson , Chris Schwiegelshohn

We are given a set of $n$ points that might be uniformly distributed in the unit square $[0,1]^2$. We wish to test whether the set, although mostly consisting of uniformly scattered points, also contains a small fraction of points sampled…

Statistics Theory · Mathematics 2007-06-13 Ery Arias-Castro , David L. Donoho , Xiaoming Huo

Let $G$ be a graph and $T$ a certain connected subgraph of $G$. The $T$-structure connectivity $\kappa(G; T)$ (or resp., $T$-substructure connectivity $\kappa^{s}(G; T)$) of $G$ is the minimum number of a set of subgraphs…

Combinatorics · Mathematics 2018-03-23 Dong Li , Xiaolan Hu , Huiqing Liu

Designing good error correcting codes whose generator matrix has a support constraint, i.e., one for which only certain entries of the generator matrix are allowed to be non-zero, has found many recent applications, including in distributed…

Information Theory · Computer Science 2018-01-25 Hikmet Yildiz , Babak Hassibi

Working in the setting of i.i.d. last-passage percolation on $\mathbb{R}^D$ with no assumptions on the underlying edge\hyp{}weight distribution, we arrive at the notion of grid entropy - a Subadditive Ergodic Theorem limit of the entropies…

Probability · Mathematics 2023-12-14 Alexandru Gatea

In coding theory, a common question is to understand the threshold rates of various local properties of codes, such as their list decodability and list recoverability. A recent work Levi, Mosheiff, and Shagrithaya (FOCS 2025) gave a novel…

Information Theory · Computer Science 2025-10-16 Joshua Brakensiek , Yeyuan Chen , Manik Dhar , Zihan Zhang

Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…

Algebraic Topology · Mathematics 2026-02-27 Pepijn Roos Hoefgeest , Lucas Slot

Moving scientific computation from high-performance computing (HPC) and cloud computing (CC) environments to devices on the edge, i.e., physically near instruments of interest, has received tremendous interest in recent years. Such edge…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-10-11 Christopher J. Vogl , Zachary Atkins , Alyson Fox , Agnieszka Miedlar , Colin Ponce

We study the design of robust subexponential algorithms for classical connectivity problems on intersection graphs of similarly sized fat objects in $\mathbb{R}^d$. In this setting, each vertex corresponds to a geometric object, and two…

Data Structures and Algorithms · Computer Science 2025-12-04 Malory Marin , Jean-Florent Raymond , Rémi Watrigant

We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…

Numerical Analysis · Mathematics 2026-05-26 Allen Paul , Neill Campbell , Tony Shardlow

We proposed a new criterion \textit{noise-stability}, which revised the classical rigidity theory, for evaluation of MDS algorithms which can truthfully represent the fidelity of global structure reconstruction; then we proved the…

Computational Geometry · Computer Science 2022-07-15 Zishuo Zhao

The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…

Machine Learning · Computer Science 2024-10-23 Ipsita Ghosh , Abiy Tasissa , Christian Kümmerle

Graphs are fundamental tools for modeling pairwise interactions in complex systems. However, many real-world systems involve multi-way interactions that cannot be fully captured by standard graphs. Hypergraphs, which generalize graphs by…

Metric Geometry · Mathematics 2024-12-04 Tom Needham , Ethan Semrad

We derive an algorithm for compression of the currents and varifolds representations of shapes, using ridge leverage score (RLS) sampling, and the theory of Nystrom approximation in Reproducing Kernel Hilbert Spaces. Our method is faster…

Numerical Analysis · Mathematics 2026-03-18 Allen Paul , Neill Campbell , Tony Shardlow