arXiv subjects

Viktoria Fodor

Publications and source records attributed to Viktoria Fodor.

At least 19 recordsLinked to original sources

arXiv2026

Fixed Points Without Fixed Diffusion: Implicit Neural Sheaves for Convergent Test-Time Computation

Implicit Graph Neural Networks (IGNNs) define node representations as fixed points of graph neural operators, enabling effectively infinite-depth propagation, iteration-independent parameterization, and flexible test-time computation. Yet these benefits depend on the equilibrium being unique and reached by fixed-point iteration. Existing constructions often impose constraints on recurrent updates to obtain these guarantees, limiting the transformations available at equilibrium. This raises a central question: can IGNNs gain expressiveness through richer, edge-dependent transformations while retaining the inherent strengths of their equilibrium formulation? We introduce SheafDEQ, a subhomogeneous deep-equilibrium architecture with adaptive neural-sheaf propagation. Its learned, matrix-valued sheaf restriction maps can align, mix, or reverse neighbouring representations. Under mild regularity conditions, we prove that SheafDEQ admits a unique equilibrium reached globally by fixed-point iteration from any positive initial state. Contractivity further guarantees convergence under bounded communication staleness. We evaluate SheafDEQ on distributed-inference tasks requiring repeated nonlocal aggregation and on community detection whose rewiring increasingly favours cross-community interactions. SheafDEQ improves over implicit baselines on Sums, MNIST Terrain, and Coordinates, and on community detection as connectivity becomes increasingly heterophilic. SheafDEQ remains competitive with recurrent models without equilibrium guarantees. Continued-iteration diagnostics show decreasing residuals and retained test accuracy through 100 iterations, unlike the finite-horizon control, while delayed-update experiments show low sensitivity to bounded communication staleness.

cs.LG↗

arXiv2026

From Euclidean to Graph-Structured Data: A Survey of Collaborative Learning

The conventional approach to machine learning, that is, collecting data, training models, and performing inference in a single location, faces fundamental limitations, including scalability and privacy, that restrict its applicability. To address these challenges, recent research has explored collaborative learning approaches, including federated learning and decentralized learning, where individual agents perform training and inference locally, with limited collaboration. Most collaborative learning research focuses on Euclidean data with regular, grid-like structure (e.g., images, text). However, these approaches fail to capture the relational patterns in many real-world applications, best represented by graphs. Learning on graphs relies on message-passing mechanisms to propagate information between connected nodes, making it conceptually well-suited for collaborative environments where agents must exchange information. Yet, the opportunities and challenges of learning on graph-structured data in collaborative settings remain largely underexplored. This survey provides a comprehensive investigation of collaborative learning from Euclidean to graph-structured data, aiming to consolidate this emerging field. We begin by reviewing its foundational principles for Euclidean data, organizing them along three core dimensions: learning effectiveness, efficiency, and privacy preservation. We then extend the discussion to graph-structured data, introducing a taxonomy of graph distribution scenarios, characterizing associated statistical heterogeneities, and developing standardized problem formulations and algorithmic frameworks. Finally, we systematically identify open challenges and promising research directions.

cs.LG↗

arXiv2026

Deep Neural Sheaf Diffusion

Deep Graph Neural Networks (GNNs) are essential for capturing complex dependencies in graph-structured data. However, scaling GNNs to depth remains challenging, as stacking layers leads to representation collapse and diminishing sensitivity due to repeated aggregation. While Neural Sheaf Diffusion (NSD) provides strong theoretical guarantees against such collapse, these guarantees do not translate to practice: as depth increases, the disagreement signal of the sheaf Laplacian vanishes, limiting the contribution of deeper layers. We identify mechanisms that hinder NSD effectiveness at depth and propose \emph{Deep Neural Sheaf Diffusion} (DNSD), which replaces the sheaf Laplacian with a sheaf adjacency operator to maintain informative signals across layers. This is complemented by normalization, odd nonlinearities, and gating. To provide a principled explanation of the expected performance improvement, we contrast sheaf diffusion to graph attention mechanisms, highlighting that DNSD replaces scalar attention scores with matrix-valued edge functions and normalizes node representations rather than attention scores. We demonstrate empirically that DNSD effectively utilizes deep aggregation in graph tasks, outperforming GNN and NSD baselines with up to 30pp accuracy on synthetic long-range datasets, and consistently outperforming them on real-world benchmarks. These results position sheaf-based architectures as a promising building block for graph foundation models by supporting effective deep architectures.

cs.LG↗

arXiv2025

Majority Vote Compressed Sensing

We consider the problem of non-coherent over-the-air computation (AirComp), where $n$ devices carry high-dimensional data vectors $\mathbf{x}_i\in\mathbb{R}^d$ of sparsity $\lVert\mathbf{x}_i\rVert_0\leq k$ whose sum has to be computed at a receiver. Previous results on non-coherent AirComp require more than $d$ channel uses to compute functions of $\mathbf{x}_i$, where the extra redundancy is used to combat non-coherent signal aggregation. However, if the data vectors are sparse, sparsity can be exploited to offer significantly cheaper communication. In this paper, we propose to use random transforms to transmit lower-dimensional projections $\mathbf{s}_i\in\mathbb{R}^T$ of the data vectors. These projected vectors are communicated to the receiver using a majority vote (MV)-AirComp scheme, which estimates the bit-vector corresponding to the signs of the aggregated projections, i.e., $\mathbf{y} = \text{sign}(\sum_i\mathbf{s}_i)$. By leveraging 1-bit compressed sensing (1bCS) at the receiver, the real-valued and high-dimensional aggregate $\sum_i\mathbf{x}_i$ can be recovered from $\mathbf{y}$. We prove analytically that the proposed MVCS scheme estimates the aggregated data vector $\sum_i \mathbf{x}_i$ with $\ell_2$-norm error $ε$ in $T=\mathcal{O}(kn\log(d)/ε^2)$ channel uses. Moreover, we specify algorithms that leverage MVCS for histogram estimation and distributed machine learning. Finally, we provide numerical evaluations that reveal the advantage of MVCS compared to the state-of-the-art.

eess.SP↗

arXiv2025

A Hierarchical Federated Learning Approach for the Internet of Things

This paper presents a novel federated learning solution, QHetFed, suitable for large-scale Internet of Things deployments, addressing the challenges of large geographic span, communication resource limitation, and data heterogeneity. QHetFed is based on hierarchical federated learning over multiple device sets, where the learning process and learning parameters take the necessary data quantization and the data heterogeneity into consideration to achieve high accuracy and fast convergence. Unlike conventional hierarchical federated learning algorithms, the proposed approach combines gradient aggregation in intra-set iterations with model aggregation in inter-set iterations. We offer a comprehensive analytical framework to evaluate its optimality gap and convergence rate, and give a closed form expression for the optimal learning parameters under a deadline, that accounts for communication and computation times. Our findings reveal that QHetFed consistently achieves high learning accuracy and significantly outperforms other hierarchical algorithms, particularly in scenarios with heterogeneous data distributions.

cs.LG↗

arXiv2024

Hierarchical Federated ADMM

In this paper, we depart from the widely-used gradient descent-based hierarchical federated learning (FL) algorithms to develop a novel hierarchical FL framework based on the alternating direction method of multipliers (ADMM). Within this framework, we propose two novel FL algorithms, which both use ADMM in the top layer: one that employs ADMM in the lower layer and another that uses the conventional gradient descent-based approach. The proposed framework enhances privacy, and experiments demonstrate the superiority of the proposed algorithms compared to the conventional algorithms in terms of learning convergence and accuracy. Additionally, gradient descent on the lower layer performs well even if the number of local steps is very limited, while ADMM on both layers lead to better performance otherwise.

cs.LG↗

arXiv2024

Scalable Hierarchical Over-the-Air Federated Learning

When implementing hierarchical federated learning over wireless networks, scalability assurance and the ability to handle both interference and device data heterogeneity are crucial. This work introduces a new two-level learning method designed to address these challenges, along with a scalable over-the-air aggregation scheme for the uplink and a bandwidth-limited broadcast scheme for the downlink that efficiently use a single wireless resource. To provide resistance against data heterogeneity, we employ gradient aggregations. Meanwhile, the impact of uplink and downlink interference is minimized through optimized receiver normalizing factors. We present a comprehensive mathematical approach to derive the convergence bound for the proposed algorithm, applicable to a multi-cluster wireless network encompassing any count of collaborating clusters, and provide special cases and design remarks. As a key step to enable a tractable analysis, we develop a spatial model for the setup by modeling devices as a Poisson cluster process over the edge servers and rigorously quantify uplink and downlink error terms due to the interference. Finally, we show that despite the interference and data heterogeneity, the proposed algorithm not only achieves high learning accuracy for a variety of parameters but also significantly outperforms the conventional hierarchical learning algorithm.

cs.IT↗

arXiv2024

Hierarchical Over-the-Air Federated Learning with Awareness of Interference and Data Heterogeneity

cs.IT↗

arXiv2023

Optimal Receive Filter Design for Misaligned Over-the-Air Computation

Over-the-air computation (OAC) is a promising wireless communication method for aggregating data from many devices in dense wireless networks. The fundamental idea of OAC is to exploit signal superposition to compute functions of multiple simultaneously transmitted signals. However, the time- and phase-alignment of these superimposed signals have a significant effect on the quality of function computation. In this study, we analyze the OAC problem for a system with unknown random time delays and phase shifts. We show that the classical matched filter does not produce optimal results, and generates bias in the function estimates. To counteract this, we propose a new filter design and show that, under a bound on the maximum time delay, it is possible to achieve unbiased function computation. Additionally, we propose a Tikhonov regularization problem that produces an optimal filter given a tradeoff between the bias and noise-induced variance of the function estimates. When the time delays are long compared to the length of the transmitted pulses, our filter vastly outperforms the matched filter both in terms of bias and mean-squared error (MSE). For shorter time delays, our proposal yields similar MSE as the matched filter, while reducing the bias.

eess.SP↗

arXiv2023

Resource Dimensioning for Single-Cell Edge Video Analytics

Edge intelligence is an emerging technology where the base stations located at the edge of the network are equipped with computing units that provide machine learning services to the end users. To provide high-quality services in a cost-efficient way, the wireless and computing resources need to be dimensioned carefully. In this paper, we address the problem of resource dimensioning in a single-cell system that supports edge video analytics under latency and accuracy constraints. We show that the resource-dimensioning problem can be transformed into a convex optimization problem, and we provide numerical results that give insights into the trade-offs between the wireless and computing resources for varying cell sizes and for varying intensity of incoming tasks. Overall, we observe that the wireless and computing resources exhibit opposite trends; the wireless resources favor from smaller cells, where high attenuation losses are avoided, and the computing resources favor from larger cells, where statistical multiplexing allows for computing more tasks. We also show that small cells with low loads have high per-request costs, even when the wireless resources are increased to compensate for the low multiplexing gain at the servers.

eess.SP↗

arXiv2022

Wireless for Machine Learning

As data generation increasingly takes place on devices without a wired connection, machine learning (ML) related traffic will be ubiquitous in wireless networks. Many studies have shown that traditional wireless protocols are highly inefficient or unsustainable to support ML, which creates the need for new wireless communication methods. In this survey, we give an exhaustive review of the state-of-the-art wireless methods that are specifically designed to support ML services over distributed datasets. Currently, there are two clear themes within the literature, analog over-the-air computation and digital radio resource management optimized for ML. This survey gives a comprehensive introduction to these methods, reviews the most important works, highlights open problems, and discusses application scenarios.

eess.SP↗

arXiv2022

Modelling multi-cell edge video analytics

Edge intelligence is a scalable solution for analyzing distributed data, but it cannot provide reliable services in large-scale cellular networks unless the inherent aspects of fading and interference are also taken into consideration. In this paper, we present the first mathematical framework for modelling edge video analytics in multi-cell cellular systems. We derive the expressions for the coverage probability, the ergodic capacity, the probability of successfully completing the video analytics within a target delay requirement, and the effective frame rate. We also analyze the effect of the system parameters on the accuracy of the detection algorithm, the supported frame rate at the edge server, and the system fairness.

eess.SP↗

arXiv2021

Over-the-Air Federated Learning with Retransmissions (Extended Version)

Motivated by increasing computational capabilities of wireless devices, as well as unprecedented levels of user- and device-generated data, new distributed machine learning (ML) methods have emerged. In the wireless community, Federated Learning (FL) is of particular interest due to its communication efficiency and its ability to deal with the problem of non-IID data. FL training can be accelerated by a wireless communication method called Over-the-Air Computation (AirComp) which harnesses the interference of simultaneous uplink transmissions to efficiently aggregate model updates. However, since AirComp utilizes analog communication, it introduces inevitable estimation errors. In this paper, we study the impact of such estimation errors on the convergence of FL and propose retransmissions as a method to improve FL convergence over resource-constrained wireless networks. First, we derive the optimal AirComp power control scheme with retransmissions over static channels. Then, we investigate the performance of Over-the-Air FL with retransmissions and find two upper bounds on the FL loss function. Finally, we propose a heuristic for selecting the optimal number of retransmissions, which can be calculated before training the ML model. Numerical results demonstrate that the introduction of retransmissions can lead to improved ML performance, without incurring extra costs in terms of communication or computation. Additionally, we provide simulation results on our heuristic which indicate that it can correctly identify the optimal number of retransmissions for different wireless network setups and machine learning problems.

eess.SP↗

arXiv2020

Will Scale-free Popularity Develop Scale-free Geo-social Networks?

Empirical results show that spatial factors such as distance, population density and communication range affect our social activities, also reflected by the development of ties in social networks. This motivates the need for social network models that take these spatial factors into account. Therefore, in this paper we propose a gravity-low-based geo-social network model, where connections develop according to the popularity of the individuals, but are constrained through their geographic distance and the surrounding population density. Specifically, we consider a power-law distributed popularity, and random node positions governed by a Poisson point process. We evaluate the characteristics of the emerging networks, considering the degree distribution, the average degree of neighbors and the local clustering coefficient. These local metrics reflect the robustness of the network, the information dissemination speed and the communication locality. We show that unless the communication range is strictly limited, the emerging networks are scale-free, with a rank exponent affected by the spatial factors. Even the average neighbor degree and the local clustering coefficient show tendencies known in non-geographic scale-free networks, at least when considering individuals with low popularity. At high-popularity values, however, the spatial constraints lead to popularity-independent average neighbor degrees and clustering coefficients.

physics.soc-ph↗

arXiv2019

Dynamic Spectrum Sharing for Load Balancing in Multi-Cell Mobile Edge Computing

Large-scale mobile edge computing (MEC) systems require scalable solutions to allocate communication and computing resources to the users. In this letter we address this challenge by applying dynamic spectrum sharing among the base stations (BSs), together with local resource allocation in the cells. We show that the network-wide resource allocation can be transformed into a convex optimization problem, and propose a distributed, hierarchical solution with limited information exchange among the BSs. Numerical results demonstrate that the proposed solution is superior to other baseline algorithms, when wireless and computing resource allocation is not jointly optimized, or the wireless resources allocated to the BSs are fixed.

cs.IT↗

arXiv2017

Distributed Algorithms for Feature Extraction Off-loading in Multi-Camera Visual Sensor Networks

Real-time visual analysis tasks, like tracking and recognition, require swift execution of computationally intensive algorithms. Visual sensor networks can be enabled to perform such tasks by augmenting the sensor network with processing nodes and distributing the computational burden in a way that the cameras contend for the processing nodes while trying to minimize their task completion times. In this paper, we formulate the problem of minimizing the completion time of all camera sensors as an optimization problem. We propose algorithms for fully distributed optimization, analyze the existence of equilibrium allocations, evaluate the effect of the network topology and of the video characteristics, and the benefits of central coordination. Our results demonstrate that with sufficient information available, distributed optimization can provide low completion times, moreover predictable and stable performance can be achieved with additional, sparse central coordination.

cs.CV↗

arXiv2017

Performance Analysis of Reliable Video Streaming with Strict Playout Deadline in Multi-Hop Wireless Networks

Motivated by emerging vision-based intelligent services, we consider the problem of rate adaptation for high quality and low delay visual information delivery over wireless networks using scalable video coding. Rate adaptation in this setting is inherently challenging due to the interplay between the variability of the wireless channels, the queuing at the network nodes and the frame-based decoding and playback of the video content at the receiver at very short time scales. To address the problem, we propose a low-complexity, model-based rate adaptation algorithm for scalable video streaming systems, building on a novel performance model based on stochastic network calculus. We validate the model using extensive simulations. We show that it allows fast, near optimal rate adaptation for fixed transmission paths, as well as cross-layer optimized routing and video rate adaptation in mesh networks, with less than $10$\% quality degradation compared to the best achievable performance.

cs.MM↗

arXiv2015

Green Sensing and Access: Energy-Throughput Tradeoffs in Cognitive Networking

Limited spectrum resources and dramatic growth of high data rate applications have motivated opportunistic spectrum access utilizing the promising concept of cognitive networks. Although this concept has emerged primarily to enhance spectrum utilization and to allow the coexistence of heterogeneous network technologies, the importance of energy consumption imposes additional challenges, because energy consumption and communication performance can be at odds. In this paper, the approaches for energy efficient spectrum sensing and spectrum handoff, fundamental building blocks of cognitive networks is investigated. The tradeoff between energy consumption and throughput, under local as well as under cooperative sensing are characterized, and what further aspects need to be investigated to achieve energy efficient cognitive operation under various application requirements are discussed.

cs.IT↗