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arXiv 2025年

作者： Hagemann, Niklas Kneib, Thomas Möllenhoff, Kathrin Institute of Medical Statistics and Computational Biology Faculty of Medicine University of Cologne Germany Division of Mathematics Department of Mathematics and Computer Science University of Cologne Germany Chair of Statistics and Campus Institute Data Science Georg August University Göttingen Germany

A central focus in survival analysis is examining how covariates influence survival time. These covariate effects are often found to be either time-varying, heterogeneous - such as being specific to patients, treatments, or subgroups - or exhibit both characteristics simultaneously. While the standard model, the Cox proportional hazards model, allows neither time-varying nor heterogeneous effects, several extensions to the Cox model as well as alternative modeling frameworks have been introduced. However, no unified framework for incorporating heterogeneously time-varying effects of covariates has been proposed. Such effects occur when a covariate influences survival not only in a heterogeneous and time-varying manner, but when the time-variation is also heterogeneous. We propose to model such effects by introducing heterogeneously time-varying coefficients to piecewise exponential additive mixed models. We deploy functional random effects, also known as factor smooths, to model such coefficients as the interaction effect of heterogeneity and timevariation. Our approach allows for non-linear time-effects due to being based on penalized splines and uses an efficient random effects basis to model the heterogeneity. Using a penalized basis prevents overfitting in case of absence of such effects. In addition, the penalization mostly solves the problem of choosing the number of intervals which is usually present in unregularized piecewise exponential approaches. We demonstrate the superiority of our approach in comparison to competitors by means of a simulation study. Finally, the practical application and relevance are outlined by presenting a brain tumor case study. © 2025, CC BY.

关键词： Regression analysis

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Surrogate-based multilevel Monte Carlo methods for uncertainty quantification in the Grad-Shafranov free boundary problem

arXiv

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arXiv 2025年

作者： Elman, Howard C. Liang, Jiaxing Sánchez-Vizuet, Tonatiuh Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Department of Computational Applied Mathematics & Operations Research Rice University United States Department of Mathematics The University of Arizona United States

We explore a hybrid technique to quantify the variability in the numerical solutions to a free boundary problem associated with magnetic equilibrium in axisymmetric fusion reactors amidst parameter uncertainties. The method aims at reducing computational costs by integrating a surrogate model into a multilevel Monte Carlo method. The resulting surrogate-enhanced multilevel Monte Carlo methods reduce the cost of simulation by factors as large as 104 compared to standard Monte Carlo simulations involving direct numerical solutions of the associated Grad-Shafranov partial differential equation. Accuracy assessments also show that surrogate-based sampling closely aligns with the results of direct computation, confirming its effectiveness in capturing the behavior of plasma boundary and geometric *** Codes 65Z05, 65C05, 62P35, 35R35, 35R60 Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

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Towards the Question of Packet Recovery at the Transport Layer

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Moscow University computational mathematics and Cybernetics 2025年第1期49卷 16-29页

作者： Borisov, A. V. Gurov, S. I. Semenikhin, K. V. Smelyanskiy, R. L. Stepanov, E. P. Federal Research Center ‘‘Computer Science and Control’’ of the Russian Academy of Sciences Moscow Russia Department of Computational Mathematics and Cybernetics Moscow State University Moscow Russia Moscow Aviation Institute (National Research University) Moscow Russia

A problem of using Forward Error Correction (FEC) codes at the transport layer for packet recovery is considered. This problem aims at avoiding multiple transmission of the same packet, reducing data transmission delay, and preventing a waste of network resources. The main idea of FEC coding methods is the introduction of redundancy into the transmitted data, which makes possible to recover lost data at the receiver end. The paper studies various FEC methods applied at the transport layer to select the most promising, in terms of computational complexity in encoding transmitted data and decoding it at the receiver end, as well as the effect of redundancy on data transmission delay and loss level in the transport connection. The redundancy level in the selected FEC schemes is evaluated taking into account the constraints on losses in the transport connection and quality-of-service characteristics.

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A Comunication Framework for Compositional Generation

arXiv

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arXiv 2025年

作者： Elberg, Rafael Petrache, Mircea Parra, Denis Department of Computer Science PUC Chile Centro Nacional de Inteligencia Artificial CenIA Chile Department of Mathematics PUC Chile Institute for Mathematical and Computational Engineering PUC Chile

Compositionality and compositional generalization—the ability to understand novel combinations of known concepts—are central characteristics of human language and are hypothesized to be essential for human cognition. In machine learning, the emergence of this property has been studied in a communication game setting, where independent agents (a sender and a receiver) converge to a shared encoding policy from a set of states to a space of discrete messages, where the receiver can correctly reconstruct the states observed by the sender using only the sender’s messages. The use of communication games in generation tasks is still largely unexplored, with recent methods for compositional generation focusing mainly on the use of supervised guidance (either through class labels or text). In this work, we take the first steps to fill this gap, and we present a self-supervised generative communication game-based framework for creating compositional encodings in learned representations from pre-trained encoder-decoder models. In an Iterated Learning (IL) protocol involving a sender and a receiver, we apply alternating pressures for compression and diversity of encoded discrete messages, so that the protocol converges to an efficient but unambiguous encoding. Approximate message entropy regularization is used to favor compositional encodings. Our framework is based on rigorous justifications and proofs of defining and balancing the concepts of Eficiency, Unambiguity and Non-Holisticity in encoding. We test our method on the compositional image dataset Shapes3D, demonstrating robust performance in both reconstruction and compositionality metrics, surpassing other tested discrete message frameworks. © 2025, CC BY.

关键词： Encoding (symbols)

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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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Securing unmanned aerial vehicle—heterogeneous networks using functional encryption scheme

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Multimedia Tools and Applications 2025年 1-19页

作者： Gupta, Sachin Kumar Gupta, Parul Singh, Pawan Department of Electronics and Communication Engineering Central University of Jammu UT of Jammu and Kashmir Jammu181143 India Computer Science of Engineering J.B. Institute of Technology Uttarakhand Dehradun248197 India Department of Computer Science School of Mathematics Statistics and Computational Sciences Central University of Rajasthan Ajmer- 305817 Rajasthan India

In today's scenario, as the internet expands at a faster pace, the number of data consumers also increases at an exponential rate. As the range and number of users increased, a change from traditional homogeneous networks to heterogeneous networks is in demand. However, heterogeneous networks' primary focus is to give a higher quality of service criteria to users. Furthermore, in a heterogeneous network enabled by unmanned aerial vehicles, a large number of users and devices are active. In such a diverse environment, intruder nodes may efficiently operate and transmit numerous harmful actions throughout the network. As a result, the network's entire communication is open to many types of security threats. Therefore, to secure the communication, we used the functional encryption scheme, which allows us to protect the data against intrusion attacks. The whole procedure of establishing a functional encryption scheme in unmanned aerial vehicles integrated heterogeneous network is proposed in this study in two phases: the first phase between user equipment and micro base station, and the second phase between micro base station and unmanned aerial vehicles. The proposed approach is validated using the simulation tool namely Automated Validation of Internet Security Protocols and Applications. The outcome of the security validation ensures that the proposed methodology provides the desired security and robustness to the network. © The Author(s), under exclusive licence to Springer science+Business Media, LLC, part of Springer Nature 2025.

关键词： Network intrusion

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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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A THEORY OF INITIALISATION’S IMPACT ON SPECIALISATION

arXiv

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arXiv 2025年

作者： Jarvis, Devon Lee, Sebastian Dominé, Clémentine Carla Juliette Saxe, Andrew M. Mannelli, Stefano Sarao School of Computer Science and Applied Mathematics University of the Witwatersrand South Africa Center for Computational Neuroscience Flatiron Institute Simons Foundation Gatsby Computational Neuroscience Unit Sainsbury Wellcome Centre UCL United Kingdom Data Science and AI Computer Science and Engineering Chalmers University of Technology University of Gothenburg Sweden Machine Intelligence and Neural Discovery Institute University of the Witwatersrand South Africa CIFAR Azrieli Global Scholar CIFAR

Prior work has demonstrated a consistent tendency in neural networks engaged in continual learning tasks, wherein intermediate task similarity results in the highest levels of catastrophic interference. This phenomenon is attributed to the network’s tendency to reuse learned features across tasks. However, this explanation heavily relies on the premise that neuron specialisation occurs, i.e. the emergence of localised representations. Our investigation challenges the validity of this assumption. Using theoretical frameworks for the analysis of neural networks, we show a strong dependence of specialisation on the initial condition. More precisely, we show that weight imbalance and high weight entropy can favour specialised solutions. We then apply these insights in the context of continual learning, first showing the emergence of a monotonic relation between task-similarity and forgetting in non-specialised networks. Finally, we show that specialization by weight imbalance is beneficial on the commonly employed elastic weight consolidation regularisation technique. Copyright © 2025, The Authors. All rights reserved.

关键词： Neural networks

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Multiphysics simulations of microstructure influence on hysteresis and eddy current losses of electrical steel

arXiv

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arXiv 2025年

作者： Kühn, Patrick Yang, Yangyiwei Chen, Guanyu Foster, Shanelle N. Egger, Herbert Xu, Bai-Xiang Mechanics of Functional Materials Division Institute of Materials Science Technische Universität Darmstadt Darmstadt64287 Germany Department of Electrical and Computer Engineering Michigan State University MI48824 United States Johann Radon Institute for Computational and Applied Mathematics Linz Austria Institute for Numerical Mathematics Johannes Kepler University Linz Austria

Improving efficiency of electrical machines requires fundamental knowledge on the mechanisms behind magnetic and eddy current losses of the magnetic core materials, with Fe-Si alloy as a prototype. These losses are intrinsically influenced by the microstructure of the materials. This necessitates physics-based, microstructure-informed multiscale simulations. In the present paper, we utilised micromagnetic simulations and computational homogenization methods to calculate the effective hysteresis and effective conductivities of Fe-Si electrical steels. To demonstrate the methodology, binder-jet printed electrical steel material samples with different microstructure were investigated. The microstructure samples were digitized based on both the descriptor-based synthetic reconstruction and SEM-image-based digitization. More samples were generated with varying microstructure features such as grain size and grain boundary phases. The micromagnetic simulations were then performed to investigate the magnetic hysteresis and hysteresis loss. The eddy current loss was also evaluated by using the effective conductivity through computational homogenization. By performing parameter research on a series of synthetic microstructures, effects of average grain size and grain boundary (GB) phase thickness on the hysteresis loss and eddy current loss were unveiled. An average grain size around 120 µm has the lowest hysteresis loss, although the eddy current loss increases with the grain size. Increasing GB-phase thickness helps reduce both losses. Results indicate the potential to decrease loss of magnetic core materials by microstructure optimization. © 2025, CC BY.

关键词： Silicon alloys

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Solving Inverse Problems with Deep Linear Neural Networks: Global Convergence Guarantees for Gradient Descent with Weight Decay

arXiv

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arXiv 2025年

作者： Laus, Hannah Parkinson, Suzanna Charisopoulos, Vasileios Krahmer, Felix Willett, Rebecca Department of Mathematics Technical University of Munich Germany Germany Committee on Computational and Applied Mathematics University of Chicago United States Data Science Institute University of Chicago United States Technical University of Munich Germany Department of Computer Science University of Chicago United States Department of Statistics University of Chicago United States

Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few measurements generated via a known acquisition procedure. In particular, neural networks perform well empirically but have limited theoretical guarantees. In this work, we study an underdetermined linear inverse problem that admits several possible solution mappings. A standard remedy (e.g., in compressed sensing) establishing uniqueness of the solution mapping is to assume knowledge of latent low-dimensional structure in the source signal. We ask the following question: do deep neural networks adapt to this low-dimensional structure when trained by gradient descent with weight decay regularization? We prove that mildly overparameterized deep linear networks trained in this manner converge to an approximate solution that accurately solves the inverse problem while implicitly encoding latent subspace structure. To our knowledge, this is the first result to rigorously show that deep linear networks trained with weight decay automatically adapt to latent subspace structure in the data under practical stepsize and weight initialization schemes. Our work highlights that regularization and overparameterization improve generalization, while overparameterization also accelerates convergence during training. © 2025, CC BY.

关键词： Deep neural networks

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