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arXiv 2025年

作者： Arous, Gerard Ben Gheissari, Reza Huang, Jiaoyang Jagannath, Aukosh Courant Institute New York University United States Department of Mathematics Northwestern University United States Department of Statistics and Data Science University of Pennsylvania United States Department of Statistics and Actuarial Science Department of Applied Mathematics Cheriton School of Computer Science University of Waterloo Canada

We study the local geometry of empirical risks in high dimensions via the spectral theory of their Hessian and information matrices. We focus on settings where the data, (Y)n=1 ∈ d, are i.i.d. draws of a k-component Gaussian mixture model, and the loss depends on the projection of the data into a fixed number of vectors, namely xY, where x ∈ d×C are the parameters, and C need not equal k. This setting captures a broad class of problems such as classification by one and two-layer networks and regression on multi-index models. We prove exact formulas for the limits of the empirical spectral distribution and outlier eigenvalues and eigenvectors of such matrices in the proportional asymptotics limit, where the number of samples and dimension n, d → ∞ and n/d = ∈ (0, ∞). These limits depend on the parameters x only through the summary statistic of the (C + k) × (C + k) Gram matrix of the parameters and class means, G = (x, µ)(x, µ). It is known that under general conditions, when x is trained by stochastic gradient descent, the evolution of these same summary statistics along training converges to the solution of an autonomous system of ODEs, called the effective dynamics. This enables us to connect the spectral theory to the training dynamics. We demonstrate our general results by analyzing the effective spectrum along the effective dynamics in the case of multi-class logistic regression. In this setting, the empirical Hessian and information matrices have substantially different spectra, each with their own static and even dynamical spectral transitions. Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

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No Imputation Without Representation 35th

No Imputation Without Representation

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35th Benelux Conference on Artificial Intelligence and Machine Learning, BNAIC/Benelearn 2023

作者： Lenz, Oliver Urs Peralta, Daniel Cornelis, Chris Leiden Institute of Advanced Computer Science Leiden University Leiden Netherlands Research Group for Computational Web Intelligence Department of Applied Mathematics Computer Science and Statistics Ghent University Ghent Belgium Department of Information Technology Ghent University Ghent Belgium

ISBN: (纸本)9783031746499

By filling in missing values in datasets, imputation allows these datasets to be used with algorithms that cannot handle missing values by themselves. However, missing values may in principle contribute useful information that is lost through imputation. The missing-indicator approach can be used in combination with imputation to instead represent this information as a part of the dataset. There are several theoretical considerations why missing-indicators may or may not be beneficial, but there has not been any large-scale practical experiment on real-life datasets to test this question for machine learning predictions. We perform this experiment for three imputation strategies and a range of different classification algorithms, on the basis of twenty real-life datasets. In a follow-up experiment, we determine attribute-specific missingness thresholds for each classifier above which missing-indicators are more likely than not to increase classification performance. And in a second follow-up experiment, we evaluate numerical imputation of one-hot encoded categorical attributes. We reach the following conclusions. Firstly, missing-indicators generally increase classification performance. Secondly, with missing-indicators, nearest neighbour and iterative imputation do not lead to better performance than simple mean/mode imputation. Thirdly, for decision trees, pruning is necessary to prevent overfitting. Fourthly, the thresholds above which missing-indicators are more likely than not to improve performance are lower for categorical attributes than for numerical attributes. Lastly, mean imputation of numerical attributes preserves some of the information from missing values. Consequently, when not using missing-indicators it can be advantageous to apply mean imputation to one-hot encoded categorical attributes instead of mode imputation. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Adversarial machine learning

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Acyclic, star and injective colouring: A complexity picture for H-free graphs

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Journal of computer and System sciences 2025年 154卷

作者： Bok, Jan Jedličková, Nikola Martin, Barnaby Ochem, Pascal Paulusma, Daniël Smith, Siani Computer Science Institute Charles University Prague Czech Republic Department of Applied Mathematics Charles University Prague Czech Republic Department of Computer Science Durham University Durham United Kingdom LIRMM CNRS Université de Montpellier Montpellier France

A (proper) colouring is acyclic, star, or injective if any two colour classes induce a forest, star forest or disjoint union of vertices and edges, respectively. The corresponding decision problems are ACYCLIC COLOURING, STAR COLOURING and INJECTIVE COLOURING. We give almost complete complexity classifications for ACYCLIC COLOURING, STAR COLOURING and INJECTIVE COLOURING on H-free graphs (for each of the problems, we have one open case). Moreover, we give full complexity classifications if the number of colours k is fixed, that is, not part of the input. From our study it follows that for fixed k, the three problems behave in the same way, but this is no longer true if k is part of the input. To obtain several of our results we prove stronger complexity results that in particular involve the girth of a graph and the class of line graphs of multigraphs. © 2025 The Author(s)

关键词： Graphic methods

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CLEARING SECTIONS OF LATTICE LIABILITY NETWORKS

arXiv

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arXiv 2025年

作者： Ghrist, Robert Gould, Julian Lopez, Miguel Riess, Hans Department of Mathematics and Electrical & Systems Engineering University of Pennsylvania Philadelphia PA Department of Mathematics University of Pennsylvania Philadelphia PA Applied Mathematics & Computational Science University of Pennsylvania Philadelphia PA School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta GA

Modern financial networks involve complex obligations that transcend simple monetary debts: multiple currencies, prioritized claims, supply chain dependencies, and more. We present a mathematical framework that unifies and extends these scenarios by recasting the classical Eisenberg-Noe model of financial clearing in terms of lattice liability networks. Each node in the network carries a complete lattice of possible states, while edges encode nominal liabilities. Our framework generalizes the scalar-valued clearing vectors of the classical model to lattice-valued clearing sections, preserving the elegant fixed-point structure while dramatically expanding its descriptive power. Our main theorem establishes that such networks possess clearing sections that themselves form a complete lattice under the product order. This structure theorem enables tractable analysis of equilibria in diverse domains, including multi-currency financial systems, decentralized finance with automated market makers, supply chains with resource transformation, and permission networks with complex authorization structures. We further extend our framework to chain-complete lattices for term structure models and multivalued mappings for complex negotiation systems. Our results demonstrate how lattice theory provides a natural language for understanding complex network dynamics across multiple domains, creating a unified mathematical foundation for analyzing systemic risk, resource allocation, and network *** Codes 91G40, 06B23, 91D30, 68Q85 Copyright © 2025, The Authors. All rights reserved.

关键词： Lattice theory

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INJECTIVE ENVELOPES FOR LOCALLY C∗-ALGEBRAS

arXiv

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arXiv 2025年

作者： Joit, Maria A. Şimon, Gheorghe-Ionut Department of Mathematics Faculty of Applied Sciences University Po-litehnica of Bucharest 313 Spl. Independentei Bucharest060042 Romania Department of Mathematics Faculty of Mathematics and Computer Science University of Bucharest Str. Academiei nr. 14 Bucharest Romania

We introduce the notion of admissible injective envelope for a locally C∗-algebra and show that each object in the category whose objects are unital Fréchet locally C∗-algebras and whose morphisms are unital admissible local completely positive maps has a unique admissible injective envelope. The concept of admissible injectivity is stronger than that of injectivity. As a consequence, we show that a unital Fréchet locally W∗-algebras is injective if and only if the C∗-algebras from its Arens-Michael decomposition are injective. Copyright © 2025, The Authors. All rights reserved.

关键词： Algebra

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Regression and classification of Windkessel parameters from non-invasive cardiovascular quantities using a fully connected neural network

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Informatics in Medicine Unlocked 2025年 53卷

作者： Gdoura, Ahmed Bernhard, Stefan Departement of Life Science Engineering Technische Hochschule Mittelhessen University of Applied Sciences Giessen Germany Department of Mathematics and Computer Science Free University of Berlin Berlin Germany

Despite their simplicity, three-element Windkessel models (WK-3) provide an effective and straightforward representation of the aortic input impedance. The WK-3 model not only captures valuable information about the mechanical and structural characteristics of the aortic arch but also generates reliable estimations of the central blood pressure (cBP) wave, a significant cardiovascular risk indicator. However, fitting the parameters of the WK-3 model typically requires invasively collected data, which carries substantial risk and high cost for patients. This study aims to enable non-invasive impedance estimation of the WK-3 model using cardiovascular signals. As a proof of concept, we developed and trained a fully connected neural network (FCNN) on an in-silico dataset to predict the WK-3 parameters: characteristic impedance, peripheral arterial resistance, and arterial compliance. These predictions are based on non-invasive parameters, including zero-flow pressure intercept, heart rate, stroke volume, and left ventricular ejection time. The proposed model achieved an overall accuracy of 80% with an average area under the curve (AUC) of 0.91±0.11. The implementation and best-fitting model are available for download from this link. © 2025 The Authors

关键词： Asymptotic pressure BEC Classification Fully connected NN Heart rate LVET Regression Stroke volume WGM Windkessel τ

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A New Dominating Set Game on Graphs

arXiv

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arXiv 2025年

作者： Fiscus, Sean Hurlbert, Glenn Myzelev, Eric Pence, Travis Department of Mathematics Duke University DurhamNC United States Department of Mathematics and Applied Mathematics Virginia Commonwealth University RichmondVA United States Department of Mathematics University of Pennsylvania PhiladelphiaPA United States Department of Computer Science University of Wisconsin MadisonWI United States

We introduce a new two-player game on graphs, in which players alternate choosing vertices until the set of chosen vertices forms a dominating set. The last player to choose a vertex is the winner. The game fits into the scheme of several other known games on graphs. We characterize the paths and cycles for which the first player has the winning strategy. We also create tools for combining graphs in various ways (via graph powers, Cartesian products, graph joins, and other methods) for building a variety of graphs whose games are won by the second player, including cubes, multidimensional grids with an odd number of vertices, most multidimensional toroidal grids, various trees such as specialized caterpillars, the Petersen graph, and others. Finally, we extend the game to groups and show that the second player wins the game on abelian groups of even order with canonical generating set, among *** Codes 91A43, 05C57 Copyright © 2025, The Authors. All rights reserved.

关键词： Graphic methods

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A Novel Methodology to Predict Flood and Landslide Disasters using Learning Assisted Artificial Intelligence (AI) Logic 3

A Novel Methodology to Predict Flood and Landslide Disasters...

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3rd International Conference on Electronics and Renewable Systems, ICEARS 2025

作者： Raj, G. Bhupal Patan, Muzeeb Khan Gupta, Ashwani Kumar Lakshmi, C. Gopinath, D. Yadav, Ajay Singh Sr University School of Agriculture Warangal India University of Technology and Applied Sciences College of Engineering and Technology Department of Eee Muscat Oman Chandigarh University Faculty of Business and Commerce Uttar Pradesh Unnao India Saveetha Engineering College Chennai India Department of Computer Science Karnataka Bengaluru India Srm Institute of Science and Technology Department of Mathematics Delhi-NCR Campus U.P Ghaziabad India

ISBN: (纸本)9798331509675

Comprehending the dynamics of flood and landslide prediction in current and adjacent regions is crucial for the formulation and advancement of effective predictive models, conservation, and management techniques. Conventional forecasting techniques, typically dependent on statistical models and empirical data, may prove inadequate because of the intrinsic complexities and variability of environmental elements. The complex interaction of climatic conditions, hydrological processes, geological attributes, and topographical aspects complicates precise forecasting. The constraints of traditional methods highlight the pressing necessity for more advanced and efficient predictive instruments. Artificial intelligence, especially machine learning (ML) and deep learning (DL), presents a robust paradigm that utilizes sophisticated algorithms to examine extensive datasets, discern intricate patterns, and produce more precise and prompt predictions. This proposed ViT-DL model prediction ability can greatly boost catastrophe preparedness, mitigation strategies, and ultimately, preserve lives and reduce economic damages. This study will comprehensively examine contemporary research trends, emphasizing the methodology used, model efficacy, related problems, and potential future research avenues in AI-based flood and landslide prediction. The experimental results of our proposed model produces 96.6% of Accuracy and 96.31% of Precision, comparision shows our model outperforms the overall accuracy to conventions model techniques. © 2025 IEEE.

关键词： Landslides

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Background subtraction based on tensor Robust principal component analysis with side information

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Signal, Image and Video Processing 2025年第8期19卷 1-11页

作者： Xu, Xin Chen, Lixia Wang, Xuewen School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin People’s Republic of China Center for Applied Mathematics of Guangxi (GUET) Guilin People’s Republic of China School of Computer Science and Information Security Guilin University of Electronic Technology Guilin China

In the field of video image processing, moving target detection remains a hot topic. To address the limitations of existing methods in complex environments, This paper proposes a novel TRPCA model based on Tensor Singular Value Decomposition (T-SVD), incorporating the advantages of side information. Firstly, by imposing $$\gamma $$ -norm constraints, the method incorporates feature side information into the background component processing, addresses the over-penalization issue caused by the nuclear norm in traditional RPCA. Secondly, for the foreground part, $$L_{1,1,2}$$ norm and tensor total variation (TTV) regularization constraints are applied to enhance the model’s sensitivity to tubal sparsity and spatiotemporal continuity, effectively reducing the interference of dynamic backgrounds on foreground extraction. To solve this model, we employ the Alternating Direction Method of Multipliers (ADMM). Extensive experiments on the datasets CDnet2014 and LASIESTA demonstrate that the proposed method achieves optimal or near-optimal performance in terms of F-measure for the majority of cases, highlighting its superiority in foreground detection precision.

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Exploring Local Interpretable Model-Agnostic Explanations for Speech Emotion Recognition with Distribution-Shift

arXiv

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arXiv 2025年

作者： Hjuler, Maja J. Clemmensen, Line H. Das, Sneha Dept. of Applied Mathematics and Computer Science Technical University of Denmark Lyngby2800 Denmark University Grenoble Alpes CNRS Grenoble INP LIG Grenoble38000 France School of Computer Science Queensland University of Technology BrisbaneQLD4000 Australia

We introduce EmoLIME1, a version of local interpretable model-agnostic explanations (LIME) for black-box Speech Emotion Recognition (SER) models. To the best of our knowledge, this is the first attempt to apply LIME in SER. EmoLIME generates high-level interpretable explanations and identifies which specific frequency ranges are most influential in determining emotional states. The approach aids in interpreting complex, high-dimensional embeddings such as those generated by end-to-end speech models. We evaluate EmoLIME, qualitatively, quantitatively, and statistically, across three emotional speech datasets, using classifiers trained on both hand-crafted acoustic features and Wav2Vec 2.0 embeddings. We find that EmoLIME exhibits stronger robustness across different models than across datasets with distribution shifts, highlighting its potential for more consistent explanations in SER tasks within a dataset. © 2025, CC BY.

关键词： Speech recognition

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