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After training complex deep learning models, a common task is to compress the model to reduce compute and storage demands. When compressing, it is desirable to preserve the original model's per-example decisions (e.g., to go beyond top-1…

Machine Learning · Computer Science 2022-10-18 Jerry Chee , Megan Renz , Anil Damle , Christopher De Sa

At the core of any inference procedure in deep neural networks are dot product operations, which are the component that require the highest computational resources. A common approach to reduce the cost of inference is to reduce its memory…

Machine Learning · Computer Science 2018-12-19 Simon Wiedemann , Klaus-Robert Müller , Wojciech Samek

The Nystr\"{o}m method is routinely used for out-of-sample extension of kernel matrices. We describe how this method can be applied to find the singular value decomposition (SVD) of general matrices and the eigenvalue decomposition (EVD) of…

Numerical Analysis · Computer Science 2013-05-02 Arik Nemtsov , Amir Averbuch , Alon Schclar

We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^{\delta})$ many non-zero entries for a given value…

Data Structures and Algorithms · Computer Science 2025-08-15 Huck Bennett , Karthik Gajulapalli , Alexander Golovnev , Evelyn Warton

The large sparse linear systems arising from the finite element or finite difference discretization of elliptic PDEs can be solved directly via, e.g., nested dissection or multifrontal methods. Such techniques reorder the nodes in the grid…

Numerical Analysis · Mathematics 2013-02-26 Adrianna Gillman , Per-Gunnar Martinsson

Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…

Data Structures and Algorithms · Computer Science 2023-07-27 Antares Chen , Lorenzo Orecchia , Erasmo Tani

Pattern-matching-based document-compression systems (e.g. for faxing) rely on finding a small set of patterns that can be used to represent all of the ink in the document. Finding an optimal set of patterns is NP-hard; previous compression…

Data Structures and Algorithms · Computer Science 2016-01-19 Qin Zhang , John Danskin , Neal Young

Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a well-designed sensing matrix can reduce the coherence between the…

Information Theory · Computer Science 2010-09-09 Kevin Rosenblum , Lihi Zelnik-Manor , Yonina C. Eldar

We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…

Numerical Analysis · Mathematics 2018-05-08 Daria A. Sushnikova , Ivan V. Oseledets

Matrix and tensor-guided parametrization for Natural Language Processing (NLP) models is fundamentally useful for the improvement of the model's systematic efficiency. However, the internal links between these two algebra structures and…

Computation and Language · Computer Science 2024-10-07 Mingxue Xu , Sadia Sharmin , Danilo P. Mandic

We present two new algebraic multilevel hierarchical matrix algorithms to perform fast matrix-vector product (MVP) for $N$-body problems in $d$ dimensions, namely efficient $\mathcal{H}^2_{*}$ (fully nested algorithm, i.e., $\mathcal{H}^2$…

Numerical Analysis · Mathematics 2026-04-13 Ritesh Khan , Sivaram Ambikasaran

Homomorphic encryption (HE) enables computation over encrypted data but incurs a substantial overhead. For sparse-matrix vector multiplication, the widely used Halevi and Shoup (2014) scheme has a cost linear in the number of occupied…

Cryptography and Security · Computer Science 2026-04-07 Kemal Mutluergil , Deniz Elbek , Kamer Kaya , Erkay Savaş

Deep learning models incorporating linear SSMs have gained attention for capturing long-range dependencies in sequential data. However, their large parameter sizes pose challenges for deployment on resource-constrained devices. In this…

Machine Learning · Computer Science 2025-07-31 Hiroki Sakamoto , Kazuhiro Sato

Model compression is a crucial part of deploying neural networks (NNs), especially when the memory and storage of computing devices are limited in many applications. This paper focuses on two model compression techniques: low-rank…

Machine Learning · Computer Science 2024-08-16 Chenyang Li , Jihoon Chung , Mengnan Du , Haimin Wang , Xianlian Zhou , Bo Shen

We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…

Optimization and Control · Mathematics 2021-03-12 Burak Kocuk

The aim of this paper is to design a band-limited optimal input with power constraints for identifying a linear multi-input multi-output system. It is assumed that the nominal system parameters are specified. The key idea is to use the…

Systems and Control · Computer Science 2017-06-14 Shravan Mohan , Mithun Im , Bharath Bhikkaji

This study proposes a novel method for simplifying inequality constraints in Higher-Order Binary Optimization (HOBO) formulations. The proposed method addresses challenges associated with Quadratic Unconstrained Binary Optimization (QUBO)…

Optimization and Control · Mathematics 2025-01-22 Yuichiro Minato

In memory-constrained algorithms we have read-only access to the input, and the number of additional variables is limited. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose space…

Computational Geometry · Computer Science 2014-06-26 Luis Barba , Matias Korman , Stefan Langerman , Kunikiko Sadakane , Rodrigo Silveira

Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of electronic storage…

Information Theory · Computer Science 2022-09-07 Ahmed Hareedy , Beyza Dabak , Robert Calderbank

We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate…

Numerical Analysis · Computer Science 2017-07-04 Chenhan D. Yu , James Levitt , Severin Reiz , George Biros