arXiv subjects

Andras Horvath

Publications and source records attributed to Andras Horvath.

15 recordsLinked to original sources

arXiv2026

A Perron-Frobenius strong threshold theorem for (A, B, P, {\phi}) balanced bilinear models, and the role of left and right Perron eigenvectors in mathematical epidemiology

This paper started as a review of seven results pertaining to a family of bilinear models with rank one NGM introduced by Fall, Iggidr, Sallet and Bonzi, which utilize the explicit eigenvectors of the NGM to compute the unique endemic equilibrium (EE), and Lyapunov functions at both the disease free equilibrium (DFE) and EE, and of results of Shuai and Van den Driessche (2013), which essentially deal with the same "DFE -EE stability exchange" in the non-rank one case, when the eigenvectors are not explicit. Recently, these results were complemented by Earn and McCluskey (2025), who proved as well a ``strong threshold theorem", namely that when the DFE is unstable, a second equilibrium which is globally asymptotically stable must exist. Below, we obtain in Theorem \ref{thm:TK_DFE} some results that extend beyond rank one. For example, a nontrivial positive equilibrium exists if and only if the spectral equation $\rho(\widetilde K(S))=1$, admits a strictly positive solution. Also, we showed that Bonzi-Iggidr-Sallet bilinear models with rank one NGM may be classified in two classes, with slight variations in the eigenvector formulas, and that extensions in the presence of feedback from infectious to susceptible are possible. Another takeout from the previous works, which we clarify in a revisit of the seven results in the rank one case, is that Lyapunov functions for both the DFE and the EE may be constructed using as weights the left Perron eigenvector $\pi(S)$ of the \NGM\ (NGM) $K=F(S) V^{-1}$, where $S$ denote all the non-infectious variables, and when a positive ODE leaves a siphon face, it does so along the right Perron eigenvector $w(S)$ of $\T K= V^{-1}F(S)$. The question of whether this continues to be true beyond rank one is explored in ongoing work.

math.DS↗

arXiv2026

Markov Chain Decoders Overcome the Heavy-Tail Limitations of Lipschitz Generative Models

Heavy-tailed distributions are prevalent in performance evaluation, network traffic, and risk modeling. This behavior poses a fundamental challenge for modern deep generative models. Standard Variational Autoencoders (VAEs) employ Gaussian decoder likelihoods and Lipschitz-constrained neural networks, a combination that is structurally incapable of producing heavy-tailed outputs: the Gaussian tail decays exponentially, and Lipschitz continuity prevents the decoder from amplifying rare events from the latent space input to sufficiently overcome this decay. We provide both a theoretical characterization of this limitation and a controlled empirical demonstration using synthetic Pareto data across a grid of tail indices $\alpha$ $\in$ {2, 3, 5, 30} and dimensions d $\in$ {1, 5, 10}. As a solution, we replace the Gaussian decoder with a Phase-Type (PH) distribution based on Markov chains, while keeping the encoder, latent space, and training procedure identical. PH distributions allow for arbitrarily precise approximations of any positive-valued distributions, including heavy-tailed families. Experiments showed that the PH-based model reduces tail Kolmogorov-Smirnov distance by up to x6 and extreme quantile error by up to x10 compared to the Gaussian baseline for heavy-tailed data. These results demonstrate that integrating Markov chain-based distributions into the decoder of a generative model institutes a principled and practically effective solution to the heavy-tail generation problem.

stat.ML↗

arXiv2025

On the Similarity between Epidemiologic Strains, Minimal Self-Replicable Siphons, and autocatalytic cores in (Chemical) Reaction Networks: Towards a Unifying Framework

We aim to study boundary stability and persistence of positive odes in mathematical epidemiology models by importing structural tools from chemical reaction networks. This is largely a review work, which attempts to bring closer together the fields of mathematical epidemiology (ME), and chemical reaction networks (CRNs), based on several observations. We started by observing the conceptual correspondence between epidemiologic strains and both critical minimal siphons and minimal autocatalytic sets (cores) in an underlying CRN, and confirmed this in all the models we studied. We leverage this to provide a definition of the disease free equilibrium (DFE) face/infected set as the union of either all minimal siphons, or of all cores (they coincide always in our examples). Next, we provide a proposed definition of ME models, as models which have a unique boundary fixed point on the DFE face, and for which the Jacobian of the infected subnetwork admits a regular splitting, which allows defining the famous next generating matrix (NGM). We then define the interaction graph on minimal siphons (IGMS), whose vertices are minimal siphons, and whose edges indicate the existence of reactions producing species in one siphon from species in another. When this graph is acyclic, we say the model exhibits a Acyclic Minimal Siphon Decomposition (AMSD). For AMSD models whose minimal siphons partition the infection species, we show that the NGM is block triangular after permutation, which implies the classical max structure of the reproduction number R0 for multi-strain models. We implement algorithms to compute IGMS and detect AMSD in the Epid-CRN Mathematica package (https://github.com/florinav/EpidCRNmodels) (which contains already modules to identify minimal siphons, criticality, drainability, self-replicability, etc).

math.DS↗

arXiv2024

Stable Diffusion with Continuous-time Neural Network

Stable diffusion models have ushered in a new era of advancements in image generation, currently reigning as the state-of-the-art approach, exhibiting unparalleled performance. The process of diffusion, accompanied by denoising through iterative convolutional or transformer network steps, stands at the core of their implementation. Neural networks operating in continuous time naturally embrace the concept of diffusion, this way they could enable more accurate and energy efficient implementation. Within the confines of this paper, my focus delves into an exploration and demonstration of the potential of celllular neural networks in image generation. I will demonstrate their superiority in performance, showcasing their adeptness in producing higher quality images and achieving quicker training times in comparison to their discrete-time counterparts on the commonly cited MNIST dataset.

cs.CV↗

arXiv2023

Targeted Adversarial Attacks on Generalizable Neural Radiance Fields

Neural Radiance Fields (NeRFs) have recently emerged as a powerful tool for 3D scene representation and rendering. These data-driven models can learn to synthesize high-quality images from sparse 2D observations, enabling realistic and interactive scene reconstructions. However, the growing usage of NeRFs in critical applications such as augmented reality, robotics, and virtual environments could be threatened by adversarial attacks. In this paper we present how generalizable NeRFs can be attacked by both low-intensity adversarial attacks and adversarial patches, where the later could be robust enough to be used in real world applications. We also demonstrate targeted attacks, where a specific, predefined output scene is generated by these attack with success.

cs.LG↗

arXiv2023

Mitigating the Bias of Centered Objects in Common Datasets

Convolutional networks are considered shift invariant, but it was demonstrated that their response may vary according to the exact location of the objects. In this paper we will demonstrate that most commonly investigated datasets have a bias, where objects are over-represented at the center of the image during training. This bias and the boundary condition of these networks can have a significant effect on the performance of these architectures and their accuracy drops significantly as an object approaches the boundary. We will also demonstrate how this effect can be mitigated with data augmentation techniques.

cs.CV↗

arXiv2022

On the Feasibility and Generality of Patch-based Adversarial Attacks on Semantic Segmentation Problems

Deep neural networks were applied with success in a myriad of applications, but in safety critical use cases adversarial attacks still pose a significant threat. These attacks were demonstrated on various classification and detection tasks and are usually considered general in a sense that arbitrary network outputs can be generated by them. In this paper we will demonstrate through simple case studies both in simulation and in real-life, that patch based attacks can be utilised to alter the output of segmentation networks. Through a few examples and the investigation of network complexity, we will also demonstrate that the number of possible output maps which can be generated via patch-based attacks of a given size is typically smaller than the area they effect or areas which should be attacked in case of practical applications. We will prove that based on these results most patch-based attacks cannot be general in practice, namely they can not generate arbitrary output maps or if they could, they are spatially limited and this limit is significantly smaller than the receptive field of the patches.

cs.CV↗

arXiv2020

Filtered Batch Normalization

It is a common assumption that the activation of different layers in neural networks follow Gaussian distribution. This distribution can be transformed using normalization techniques, such as batch-normalization, increasing convergence speed and improving accuracy. In this paper we would like to demonstrate, that activations do not necessarily follow Gaussian distribution in all layers. Neurons in deeper layers are more selective and specific which can result extremely large, out-of-distribution activations. We will demonstrate that one can create more consistent mean and variance values for batch normalization during training by filtering out these activations which can further improve convergence speed and yield higher validation accuracy.

cs.LG↗

arXiv2019

Application-level Studies of Cellular Neural Network-based Hardware Accelerators

As cost and performance benefits associated with Moore's Law scaling slow, researchers are studying alternative architectures (e.g., based on analog and/or spiking circuits) and/or computational models (e.g., convolutional and recurrent neural networks) to perform application-level tasks faster, more energy efficiently, and/or more accurately. We investigate cellular neural network (CeNN)-based co-processors at the application-level for these metrics. While it is well-known that CeNNs can be well-suited for spatio-temporal information processing, few (if any) studies have quantified the energy/delay/accuracy of a CeNN-friendly algorithm and compared the CeNN-based approach to the best von Neumann algorithm at the application level. We present an evaluation framework for such studies. As a case study, a CeNN-friendly target-tracking algorithm was developed and mapped to an array architecture developed in conjunction with the algorithm. We compare the energy, delay, and accuracy of our architecture/algorithm (assuming all overheads) to the most accurate von Neumann algorithm (Struck). Von Neumann CPU data is measured on an Intel i5 chip. The CeNN approach is capable of matching the accuracy of Struck, and can offer approximately 1000x improvements in energy-delay product.

cs.ET↗

arXiv2019

A mixed signal architecture for convolutional neural networks

Deep neural network (DNN) accelerators with improved energy and delay are desirable for meeting the requirements of hardware targeted for IoT and edge computing systems. Convolutional neural networks (CoNNs) belong to one of the most popular types of DNN architectures. This paper presents the design and evaluation of an accelerator for CoNNs. The system-level architecture is based on mixed-signal, cellular neural networks (CeNNs). Specifically, we present (i) the implementation of different layers, including convolution, ReLU, and pooling, in a CoNN using CeNN, (ii) modified CoNN structures with CeNN-friendly layers to reduce computational overheads typically associated with a CoNN, (iii) a mixed-signal CeNN architecture that performs CoNN computations in the analog and mixed signal domain, and (iv) design space exploration that identifies what CeNN-based algorithm and architectural features fare best compared to existing algorithms and architectures when evaluated over common datasets -- MNIST and CIFAR-10. Notably, the proposed approach can lead to 8.7$\times$ improvements in energy-delay product (EDP) per digit classification for the MNIST dataset at iso-accuracy when compared with the state-of-the-art DNN engine, while our approach could offer 4.3$\times$ improvements in EDP when compared to other network implementations for the CIFAR-10 dataset.

cs.CV↗

arXiv2018

A review of the deterministic and diffusion approximations for stochastic chemical reaction networks

This work reviews deterministic and diffusion approximations of the stochastic chemical reaction networks and explains their applications. We discuss the added value the diffusion approximation provides for systems with different phenomena, such as a deficiency and a bistability. It is advocated that the diffusion approximation can be considered as an alternative theoretical approach to study the reaction networks rather than a simulation shortcut. We discuss two examples in which the diffusion approximation is able to catch qualitative properties of reaction networks that the deterministic model misses. We provide an explicit construction of the original process and the diffusion approximation such that the distance between their trajectories is controlled and demonstrate this construction for the examples. We also discuss the limitations and potential directions of the developments.

math.PR↗

arXiv2015

Approximate analysis of biological systems by hybrid switching jump diffusion

In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has proposed two kinds of approximations. One is based on ordinary differential equations, while the other uses a diffusion process. The computational cost of the deterministic approximation is significantly lower, but the diffusion approximation retains stochasticity and is able to reproduce relevant random features like variance, bimodality, and tail behavior. In a recent paper, for particular stochastic Petri net models, we proposed a jump diffusion approximation that aims at being applicable beyond the limits of Kurtz's diffusion approximation, namely when the process reaches the boundary with non-negligible probability. Other limitations of the diffusion approximation in its original form are that it can provide inaccurate results when the number of objects in some groups is often or constantly low and that it can be applied only to pure density dependent Markov chains. In order to overcome these drawbacks, in this paper we propose to apply the jump-diffusion approximation only to those components of the model that are in density dependent form and are associated with high population levels. The remaining components are treated as discrete quantities. The resulting process is a hybrid switching jump diffusion. We show that the stochastic differential equations that characterize this process can be derived automatically both from the description of the original Markov chains or starting from a higher level description language, like stochastic Petri nets. The proposed approach is illustrated on three models: one modeling the so called crazy clock reaction, one describing viral infection kinetics and the last considering transcription regulation.

cs.PF↗

arXiv2014

Analysis of Petri Net Models through Stochastic Differential Equations

It is well known, mainly because of the work of Kurtz, that density dependent Markov chains can be approximated by sets of ordinary differential equations (ODEs) when their indexing parameter grows very large. This approximation cannot capture the stochastic nature of the process and, consequently, it can provide an erroneous view of the behavior of the Markov chain if the indexing parameter is not sufficiently high. Important phenomena that cannot be revealed include non-negligible variance and bi-modal population distributions. A less-known approximation proposed by Kurtz applies stochastic differential equations (SDEs) and provides information about the stochastic nature of the process. In this paper we apply and extend this diffusion approximation to study stochastic Petri nets. We identify a class of nets whose underlying stochastic process is a density dependent Markov chain whose indexing parameter is a multiplicative constant which identifies the population level expressed by the initial marking and we provide means to automatically construct the associated set of SDEs. Since the diffusion approximation of Kurtz considers the process only up to the time when it first exits an open interval, we extend the approximation by a machinery that mimics the behavior of the Markov chain at the boundary and allows thus to apply the approach to a wider set of problems. The resulting process is of the jump-diffusion type. We illustrate by examples that the jump-diffusion approximation which extends to bounded domains can be much more informative than that based on ODEs as it can provide accurate quantity distributions even when they are multi-modal and even for relatively small population levels. Moreover, we show that the method is faster than simulating the original Markov chain.

cs.PF↗

arXiv2012

On matrix exponential approximations of the infimum of a spectrally negative Levy process

We recall four open problems concerning constructing high-order matrix-exponential approximations for the infimum of a spectrally negative Levy process (with applications to first-passage/ruin probabilities, the waiting time distribution in the M/G/1 queue, pricing of barrier options, etc). On the way, we provide a new approximation, for the perturbed Cramer-Lundberg model, and recall a remarkable family of (not minimal order) approximations of Johnson and Taaffe, which fit an arbitrarily high number of moments, greatly generalizing the currently used approximations of Renyi, De Vylder and Whitt-Ramsay. Obtaining such approximations which fit the Laplace transform at infinity as well would be quite useful.

math.PR↗

arXiv2003

A Secure Infrastructure For System Console and Reset Access

During the last years large farms have been built using commodity hardware. This hardware lacks components for remote and automated administration. Products that can be retrofitted to these systems are either costly or inherently insecure. We present a system based on serial ports and simple machine controlled relays. We report on experience gained by setting up a 50-machine test environment as well as current work in progress in the area.

cs.DC↗