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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Yuhan Lin Shengxiang Deng Xudong Li School of Data Science Fudan University

ISBN: (数字)9798350368741

ISBN: (纸本)9798350368758

Deep Equilibrium (DEQ) models hold great promise for expanding the capabilities of neural networks and showcasing competitive performances with less memory cost. However, the backward propagation steps in their training process typically involve expensive Jacobian-inverse calculations, resulting in significantly higher computational costs than training conventional neural networks. Despite previous attempts to alleviate the burden, the trade-off between performance and efficiency remains unsatisfactory. In this study, we recast the training problem as a specific bilevel optimization problem. Then we propose BiDEQ, an efficient training algorithm based on penalty method to address the problem without calculating or approximating the hypergradient and matrix inverse in the backward propagation. Numerical experiments on various datasets demonstrate the superiority of our method over state-of-the-art methods for training DEQ models.

关键词： Training Jacobian matrices Backpropagation Computational modeling Neural networks Signal processing algorithms approximation algorithms Numerical models Computational efficiency Optimization

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Near-Optimal Dimension Reduction for Facility Location 25

Near-Optimal Dimension Reduction for Facility Location

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Proceedings of the 57th Annual ACM Symposium on Theory of Computing

作者： Lingxiao Huang Shaofeng H.-C. Jiang Robert Krauthgamer Di Yue Nanjing University Nanjing China Peking University Beijing China Weizmann Institute of Science Rehovot Israel

ISBN: (纸本)9798400715105

Oblivious dimension reduction, à la the Johnson-Lindenstrauss (JL) Lemma, is a fundamental approach for processing high-dimensional data. We study this approach for Uniform Facility Location (UFL) on a Euclidean input X ⊂ℝd, where facilities can lie in the ambient space (not restricted to X). Our main result is that target dimension m=Õ(є−2 ddim) suffices to (1+є)-approximate the optimal value of UFL on inputs whose doubling dimension is bounded by ddim. It significantly improves over previous results, that could only achieve O(1)-approximation [Narayanan, Silwal, Indyk, and Zamir, ICML 2021] or dimension m=O(є−2logn) for n=|X|, which follows from [Makarychev, Makarychev, and Razenshteyn, STOC 2019]. Our oblivious dimension reduction has immediate implications to streaming and offline algorithms, by employing known algorithms for low dimension. In dynamic geometric streams, it implies a (1+є)-approximation algorithm that uses O(є−1logn)Õ(ddim/є2) bits of space, which is the first streaming algorithm for UFL to utilize the doubling dimension. In the offline setting, it implies a (1+є)-approximation algorithm, which we further refine to run in time ((1/є)Õ(ddim) d + 2(1/є)Õ(ddim)) · Õ(n). Prior work has a similar running time but requires some restriction on the facilities [Cohen-Addad, Feldmann and Saulpic, JACM 2021]. Our main technical contribution is a fast procedure to decompose an input X into several k-median instances for small k. This decomposition is inspired by, but has several significant differences from [Czumaj, Lammersen, Monemizadeh and Sohler, SODA 2013], and is key to both our dimension reduction and our PTAS.

关键词： approximation algorithms

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Iterative Recovery algorithms for Complex-Valued Distributed Compressed Sensing

Iterative Recovery Algorithms for Complex-Valued Distributed...

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International ITG Conference on Source and Channel Coding (SCC)

作者： Elena Sterk Robert F.H. Fischer Institute of Communications Engineering Ulm University Germany

ISBN: (数字)9798331522896

ISBN: (纸本)9798331522902

Distributed compressed sensing aims at the joint reconstruction of sparse signals with a common support. In some applications, complex-valued signals and sensing matrices are present. In this paper, we investigate recovery algorithms for complex-valued distributed scenarios. To that end, we review a compact exposition of complex- and vector-valued MMSE estimators. These can be used in approximate-message-passing-type algorithms. We explain joint reconstruction via iterative algorithms and evaluate suitable recovery algorithms. The performance of these algorithms is evaluated by numerical simulations for different scenarios.

关键词： Reviews approximation algorithms Numerical simulation Iterative algorithms Encoding Sensors Sparse matrices Compressed sensing

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Improved Fixed-Parameter Bounds for Min-Sum-Radii and Diameters k-Clustering and Their Fair Variants 39

Improved Fixed-Parameter Bounds for Min-Sum-Radii and Diamet...

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39th Annual AAAI Conference on Artificial Intelligence, AAAI 2025

作者： Banerjee, Sandip Bartal, Yair Gottlieb, Lee-Ad Hovav, Alon IDSIA USI-SUPSI Switzerland The Hebrew University of Jerusalem Israel Ariel University Israel

ISBN: (纸本)157735897X

We provide improved upper and lower bounds for the Min-Sum-Radii (MSR) and Min-Sum-Diameters (MSD) clustering problems with a bounded number of clusters k. In particular, we propose an exact MSD algorithm with running-time nO(k). We also provide (1 + Ε) approximation algorithms for both MSR and MSD with running-times of O(kn) + (1/Ε)O(dk) in metrics spaces of doubling dimension d. Our algorithms extend to k-center, improving upon previous results, and to α-MSR, where radii are raised to the α power for α > 1. For α-MSD we prove an exponential time ETH-based lower bound for α > log 3. All algorithms can also be modified to handle outliers. Moreover, we can extend the results to variants that observe fairness constraints, as well as to the general framework of mergeable clustering, which includes many other popular clustering variants. We complement these upper bounds with ETH-based lower bounds for these problems, in particular proving that nO(k) time is tight for MSR and α-MSR even in doubling spaces, and that 2o(k) bounds are impossible for MSD. Copyright © 2025, Association for the Advancement of Artificial Intelligence (***). All rights reserved.

关键词： approximation algorithms

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Fair Division Beyond Monotone Valuations

arXiv

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arXiv 2025年

作者： Barman, Siddharth Verma, Paritosh Indian Institute of Science India Purdue University United States

This paper studies fair division of divisible and indivisible items among agents whose cardinal preferences are not necessarily monotone. We establish the existence of fair divisions and develop approximation algorithms to compute them. We address two complementary valuation classes, subadditive and nonnegative, which go beyond monotone functions. Considering both the division of cake (divisible resources) and allocation of indivisible items, we obtain fairness guarantees in terms of (approximate) envy-freeness (EF) and equability (EQ). In the context of envy-freeness, we prove that an EF division of a cake always exists under cake valuations that are subadditive and globally nonnegative (i.e., the value of the entire cake for every agent is nonnegative, but parts of the cake can be burnt). This result notably complements the nonexistence of EF allocations for burnt cakes known for more general valuations. For envy-freeness in the indivisible-items setting, we establish the existence of EF3 allocations for subadditive and globally nonnegative valuations;again, such valuations can be non-monotone and can impart negative value to specific item subsets. In addition, we obtain universal existence of EF3 allocations under nonnegative valuations. We study equitability under nonnegative valuations. Here, we prove that EQ3 allocations always exist when the agents’ valuations are nonnegative (and possibly non-monotone). Also, in the indivisible-items setting, we develop an approximation algorithm that, for given nonnegative valuations, finds allocations that are equitable within additive margins. Our results have combinatorial implications. For instance, the developed results imply: (i) The universal existence of proximately dense subgraphs: Given any graph G = (V, E) and integer k (at most |V |), there always exists a partition V1, V2, . . ., Vk of the vertex set such that the edge densities within the parts, Vi, are additively within four of each other, and (ii) The univer

关键词： approximation algorithms

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Min-max coverage problems on tree-like metrics

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Procedia Computer Science 2023年 223卷 148-156页

作者： Eric Aaron Úrsula Hébert-Johnson Danny Krizanc Daniel Lokshtanov Colby College Waterville ME 04901 USA University of California Santa Barbara 93106 USA Wesleyan University Middletown CT 06457 USA

We consider a number of min-max coverage problems. In each problem, the input is an unweighted graph G and an integer k, and possibly some additional information, such as a root vertex r. In the Min-Max Path Cover problem, the task is to cover all vertices of the graph by k walks, minimizing the length of the longest walk. The variant of Min-Max Path Cover in which all walks start and end at the same prescribed root vertex r is called the k-Traveling Salesmen Problem. In the Min-Max Tree Cover problem, the task is to cover all vertices of the graph by k trees, minimizing the size (number of edges) of the largest tree. In the rooted version, Min-Max k-Rooted Tree Cover, the input also contains k roots r 1 , . . ., r k , and the i th tree must contain the root r i . These four problems are all known to be APX-hard and to admit a constant-factor approximation. In this paper, we initiate the systematic study of these problems on trees and, more generally, on graphs of constant treewidth. As opposed to most graph problems, all four of the above coverage problems remain NP-hard even when G is a tree. We obtain an n O(k) -time exact algorithm for all four problems on graphs of bounded treewidth. Our main contribution is a quasi-polynomial-time approximation scheme (QPTAS) for the k-Traveling Salesmen Problem, Min-Max Path Cover, and Min-Max Tree Cover on graphs of bounded treewidth.

关键词： approximation algorithms Parameterized algorithms Min-max coverage Treewidth Vehicle routing

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Multi-Pass Streaming Lower Bounds for Approximating Max-Cut

arXiv

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arXiv 2025年

作者： Fei, Yumou Minzer, Dor Wang, Shuo Department of EECS Massachusetts Institute of Technology United States Department of Mathematics Massachusetts Institute of Technology United States

In the Max-Cut problem in the streaming model, an algorithm is given the edges of an unknown graph G = (V, E) in some fixed order, and its goal is to approximate the size of the largest cut in G. Improving upon an earlier result of Kapralov, Khanna and Sudan, it was shown by Kapralov and Krachun that for all Ε > 0, no o(n) memory streaming algorithm can achieve a (1/2 + Ε)-approximation for Max-Cut. Their result holds for single-pass streams, i.e. the setting in which the algorithm only views the stream once, and it was open whether multi-pass access may help. The state-of-the-art result along these lines, due to Assadi and N, rules out arbitrarily good approximation algorithms with constantly many passes and n1−δ space for any δ > 0. We improve upon this state-of-the-art result, showing that any non-trivial approximation algorithm for Max-Cut requires either polynomially many passes or polynomially large space. More specifically, we show that for all Ε > 0, a k-pass streaming (1/2 + Ε)-approximation algorithm for Max-Cut requires ΩΕ (n1/3/k) space. This result leads to a similar lower bound for the Maximum Directed Cut problem, showing the near optimality of the algorithm of [Saxena, Singer, Sudan, Velusamy, SODA 2025]. Our lower bounds proceed by showing a communication complexity lower bound for the Distributional Implicit Hidden Partition (DIHP) Problem, introduced by Kapralov and Krachun. While a naive application of the discrepancy method fails, we identify a property of protocols called "globalness", and show that (1) any protocol for DIHP can be turned into a global protocol, (2) the discrepancy of a global protocol must be small. The second step is the more technically involved step in the argument, and therein we use global hypercontractive inequalities, and more specifically strong quantitative versions of the level d inequality for global functions. © 2025, CC BY.

关键词： approximation algorithms

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Fusion of Information in Multiple Particle Filtering in the Presence of Unknown Static Parameters

Fusion of Information in Multiple Particle Filtering in the ...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Xiaokun Zhao Marija Iloska Yousef El-Laham Monica F. Bugallo Department of Electrical and Computer Engineering Stony Brook University Stony Brook NY USA

ISBN: (数字)9798350368741

ISBN: (纸本)9798350368758

An important and often overlooked aspect of particle filtering methods is the estimation of unknown static parameters. A simple approach for addressing this problem is to augment the unknown static parameters as auxiliary states that are jointly estimated with the time-varying parameters of interest. This can be impractical, especially when the system of interest is high-dimensional. Multiple particle filtering (MPF) methods were introduced to try to overcome the curse of dimensionality by using a "divide and conquer" approach, where the vector of unknowns is partitioned into a set of subvectors, each estimated by a separate particle filter. Each particle filter weighs its own particles by using predictions and estimates communicated from the other filters. Currently, there is no principled way to implement MPF methods where the particle filters share unknown parameters or states. In this work, we propose a fusion strategy to allow for the sharing of unknown static parameters in the MPF setting. Specifically, we study the systems which are separable in states and observations. It is proved that optimal Bayesian fusion can be obtained for state-space models with non-interacting states and observations. Simulations are performed to show that MPF with fusion strategy can provide more accurate estimates within fewer time steps comparing to existing algorithms.

关键词： Signal processing algorithms Estimation approximation algorithms Particle filters Vectors Acoustics State-space methods Partitioning algorithms Bayes methods Speech processing

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On Approximability of the Permanent of PSD Matrices 25

On Approximability of the Permanent of PSD Matrices

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Proceedings of the 57th Annual ACM Symposium on Theory of Computing

作者： Farzam Ebrahimnejad Ansh Nagda Shayan Oveis Gharan University of Washington Seattle USA University of California at Berkeley Berkeley USA

ISBN: (纸本)9798400715105

We study the complexity of approximating the permanent of a positive semidefinite matrix A∈ ℂn× *** first result is a new approximation algorithm for per(A) with approximation ratio e−(0.9999 + γ)n, exponentially improving upon the current best bound of e−(1+γ−o(1))n (Anari-Gurvits-Oveis Gharan-Saberi 2017, Yuan-Parrilo 2022). Here, γ ≈ 0.577 is Euler’s *** second result is a hardness result. We prove that it is NP-hard to approximate per(A) within a factor e−(γ−)n for any >0. This is the first exponential hardness of approximation for this problem. Along the way, we prove optimal hardness of approximation results for the ||·||2→ q “norm” problem of a matrix for all −1 < q < 2.

关键词： approximation algorithms

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Spectrum and RFI Sensing using 2.4 GHz Digital Multi-Beam Circular Apertures with 360 FoV

Spectrum and RFI Sensing using 2.4 GHz Digital Multi-Beam Ci...

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IEEE Space Hardware and Radio Conference (SHaRC)

作者： A. Madanayake B. Thevathasan C. Rathnayaka U. Kumarasiri S. Sivasankar V. Ariyarathna Department of Electrical and Computer Engineering Florida International University Miami USA

ISBN: (数字)9798331507367

ISBN: (纸本)9798331507374

Radio spectrum monitoring across 360-degree field-of-view (FoV) is a fundamental requirement for RF situational awareness. RF awareness demands sensed intelligence on the direction of arrival, frequency occupancy, modulation type signal power, and bandwidth for each waveform present. This article includes an end-to-end design and realization of an array processor, consisting of sixteen uniformly spaced antennas in a circular array at 2.4 GHz, providing 360-degrees FoV using digital multi-beam beamforming. The algorithms encapsulate a low-complexity multi-beam circular array processor with each RF beam being processed by an approximate discrete Fourier transform (ADFT) algorithm. All directional sensing covered by sixteen simultaneous RF beams are 100 MHz in baseband. A fully parallel systolic-array processor for multi-beams is realized using Xilinx Virtex-6 FPGA and CASPER toolchain.

关键词： Radio frequency Array signal processing Bandwidth Parallel processing approximation algorithms Hardware Sensors Monitoring Antenna arrays Radiofrequency interference

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