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The Max-k-Cut problem is a fundamental combinatorial optimization challenge that generalizes the classic NP-complete Max-Cut problem. While relaxation techniques are commonly employed to tackle Max-k-Cut, they often lack guarantees of…

Optimization and Control · Mathematics 2025-06-12 Yeqing Qiu , Ye Xue , Akang Wang , Yiheng Wang , Qingjiang Shi , Zhi-Quan Luo

Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…

Optimization and Control · Mathematics 2016-02-29 Farbod Roosta-Khorasani , Michael W. Mahoney

This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural…

Machine Learning · Statistics 2018-02-12 Léon Bottou , Frank E. Curtis , Jorge Nocedal

The problem of relevance ranking consists of sorting a set of objects with respect to a given criterion. Since users may prefer different relevance criteria, the ranking algorithms should be adaptable to the user needs. Two main approaches…

Machine Learning · Computer Science 2023-11-06 Leonardo Rigutini , Tiziano Papini , Marco Maggini , Franco Scarselli

Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…

Machine Learning · Computer Science 2023-10-20 Hongyuan Zhang , Xuelong Li

Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…

Optimization and Control · Mathematics 2024-03-08 David Newton , Raghu Bollapragada , Raghu Pasupathy , Nung Kwan Yip

It has been observed in practical applications and in theoretical analysis that over-parametrization helps to find good minima in neural network training. Similarly, in this article we study widening and deepening neural networks by a…

Numerical Analysis · Mathematics 2020-02-06 G. Welper

Sorting and permutation learning are key concepts in optimization and machine learning, especially when organizing high-dimensional data into meaningful spatial layouts. The Gumbel-Sinkhorn method, while effective, requires N*N parameters…

Machine Learning · Computer Science 2025-04-29 Kai Uwe Barthel , Florian Barthel , Peter Eisert

In high-dimensional statistics, variable selection recovers the latent sparse patterns from all possible covariate combinations. This paper proposes a novel optimization method to solve the exact L0-regularized regression problem, which is…

Methodology · Statistics 2022-06-02 Mingzhang Yin , Nhat Ho , Bowei Yan , Xiaoning Qian , Mingyuan Zhou

Feature attribution methods, or saliency maps, are one of the most popular approaches for explaining the decisions of complex machine learning models such as deep neural networks. In this study, we propose a stochastic optimization approach…

Machine Learning · Statistics 2018-07-17 Kouichi Ikeno , Satoshi Hara

We present a new method for scaling automatic configuration of computer networks. The key idea is to relax the computationally hard search problem of finding a configuration that satisfies a given specification into an approximate objective…

Networking and Internet Architecture · Computer Science 2022-11-04 Luca Beurer-Kellner , Martin Vechev , Laurent Vanbever , Petar Veličković

Neural algorithmic reasoning is an emerging area of machine learning focusing on building models that can imitate the execution of classic algorithms, such as sorting, shortest paths, etc. One of the main challenges is to learn algorithms…

Machine Learning · Computer Science 2023-11-02 Gleb Rodionov , Liudmila Prokhorenkova

We investigate how sorting algorithms efficiently overcome the exponential size of the permutation space. Our main contribution is a new continuous-time formulation of sorting as a gradient flow on the permutohedron, yielding an independent…

Data Structures and Algorithms · Computer Science 2025-04-24 Jonathan Landers

We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a…

Probability · Mathematics 2007-05-23 Svante Janson

Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the…

Machine Learning · Computer Science 2024-12-17 Naoki Sato , Hideaki Iiduka

Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal…

Machine Learning · Computer Science 2022-03-21 Felix Petersen , Christian Borgelt , Hilde Kuehne , Oliver Deussen

Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of…

Statistics Theory · Mathematics 2016-08-02 Nicolas Flammarion , Cheng Mao , Philippe Rigollet

Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…

Machine Learning · Computer Science 2020-06-11 Quentin Berthet , Mathieu Blondel , Olivier Teboul , Marco Cuturi , Jean-Philippe Vert , Francis Bach

We study sorting in the evolving data model, introduced by [AKMU11], where the true total order changes while the sorting algorithm is processing the input. More precisely, each comparison operation of the algorithm is followed by a…

Data Structures and Algorithms · Computer Science 2024-09-24 George Giakkoupis , Marcos Kiwi , Dimitrios Los

Seriation seeks to reconstruct a linear order between variables using unsorted, pairwise similarity information. It has direct applications in archeology and shotgun gene sequencing for example. We write seriation as an optimization problem…

Optimization and Control · Mathematics 2015-02-09 Fajwel Fogel , Rodolphe Jenatton , Francis Bach , Alexandre d'Aspremont