Seyed Mohammad Azimi-Abarghouyi

Seyed Mohammad Azimi-Abarghouyi, Viktoria Fodor

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.

Seyed Mohammad Azimi-Abarghouyi, Lav R. Varshney

This paper introduces a federated learning framework that enables over-the-air computation via digital communications, using a new joint source-channel coding scheme. Without relying on channel state information at devices, this scheme employs lattice codes to both quantize model parameters and exploit interference from the devices. We propose a novel receiver structure at the server, designed to reliably decode an integer combination of the quantized model parameters as a lattice point for the purpose of aggregation. We present a mathematical approach to derive a convergence bound for the proposed scheme and offer design remarks. In this context, we suggest an aggregation metric and a corresponding algorithm to determine effective integer coefficients for the aggregation in each communication round. Our results illustrate that, regardless of channel dynamics and data heterogeneity, our scheme consistently delivers superior learning accuracy across various parameters and markedly surpasses other over-the-air methodologies.

Seyed Mohammad Azimi-Abarghouyi, Mehdi Bennis, Leandros Tassiulas

Federated learning (FL) is fundamentally a distributed optimization problem executed by communicating agents with local data, local computation, and partial system visibility. Once FL is viewed through that lens, hierarchy is not merely a scalability mechanism. It becomes the natural place to rethink how distributed optimization should be organized over real multi-tier networks. This article argues that hierarchical federated learning (HFL) should move beyond its common framing as a communication-saving protocol and instead be viewed as an architecture-aware design framework for networked AI. The framework is organized around three coupled design axes: architectural parameters, layer-wise optimization decomposition, and layer-wise communication realization. The first axis determines the coordination geometry of learning through hierarchy depth, layer asymmetry, and layered connectivity. The second determines how the global FL objective is decomposed across layers and highlights modular multi-layer optimization as a major opportunity beyond one dominant method everywhere. The third determines how the distributed optimization is physically realized under heterogeneous communication regimes, from interference-limited lower tiers to reliable upper tiers. A central message is that, in HFL, convergence becomes architecture-dependent: it is directly shaped by the chosen hierarchy, the assigned optimization roles, and the communication mechanisms that connect them. We develop this viewpoint using large-scale wireless edge intelligence as a flagship networked AI setting, then provide a comparative perspective on flat FL, two-tier HFL, and deep HFL together with a regime-oriented design map. The resulting perspective positions HFL as a practical methodology for designing future networked AI systems.

Seyed Mohammad Azimi-Abarghouyi, Leandros Tassiulas

This paper introduces a new federated learning scheme that leverages over-the-air computation. A novel feature of this scheme is the proposal to employ adaptive weights during aggregation, a facet treated as predefined in other over-the-air schemes. This can mitigate the impact of wireless channel conditions on learning performance, without needing channel state information at transmitter side (CSIT). We provide a mathematical methodology to derive the convergence bound for the proposed scheme in the context of computational heterogeneity and general loss functions, supplemented with design insights. Accordingly, we propose aggregation cost metrics and efficient algorithms to find optimized weights for the aggregation. Finally, through numerical experiments, we validate the effectiveness of the proposed scheme. Even with the challenges posed by channel conditions and device heterogeneity, the proposed scheme surpasses other over-the-air strategies by an accuracy improvement of 15% over the scheme using CSIT and 30% compared to the one without CSIT.

Seyed Mohammad Azimi-Abarghouyi, Nicola Bastianello, Karl H. Johansson et al.

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.

Amirreza Kazemi, Seyed Mohammad Azimi-Abarghouyi, Gabor Fodor et al.

Hierarchical federated learning (HFL) has emerged as a key architecture for large-scale wireless and Internet of Things systems, where devices communicate with nearby edge servers before reaching the cloud. In these environments, uplink bandwidth and latency impose strict communication limits, thereby making aggressive gradient compression essential. One-bit methods such as sign-based stochastic gradient descent (SignSGD) offer an attractive solution in flat federated settings, but existing theory and algorithms do not naturally extend to hierarchical settings. In particular, the interaction between majority-vote aggregation at the edge layer and model aggregation at the cloud layer, and its impact on end-to-end performance, remains unknown. To bridge this gap, we propose a highly communication-efficient sign-based HFL framework and develop its corresponding formulation for nonconvex learning, where devices send only signed stochastic gradients, edge servers combine them through majority-vote, and the cloud periodically averages the obtained edge models, while utilizing downlink quantization to broadcast the global model. We introduce the resulting scalable HFL algorithm, HierSignSGD, and provide the convergence analysis for SignSGD in a hierarchical setting. Our core technical contribution is a characterization of how biased sign compression, two-level aggregation intervals, and inter-cluster heterogeneity collectively affect convergence. Numerical experiments under homogeneous and heterogeneous data splits show that HierSignSGD, despite employing extreme compression, achieves accuracy comparable to or better than full-precision stochastic gradient descent while reducing communication cost in the process, and remains robust under aggressive downlink sparsification.

Seyed Mohammad Azimi-Abarghouyi, Carlo Fischione, Kaibin Huang

Over-the-Air Federated Learning (AirFL) is an emerging paradigm that tightly integrates wireless signal processing and distributed machine learning to enable scalable AI at the network edge. By leveraging the superposition property of wireless signals, AirFL performs communication and model aggregation of the learning process simultaneously, significantly reducing latency, bandwidth, and energy consumption. This article offers a tutorial treatment of AirFL, presenting a novel classification into three design approaches: CSIT-aware, blind, and weighted AirFL. We provide a comprehensive guide to theoretical foundations, performance analysis, complexity considerations, practical limitations, and prospective research directions.

Seyed Mohammad Azimi-Abarghouyi, Lav R. Varshney

This paper introduces a universal federated learning framework that enables over-the-air computation via digital communications, using a new joint source-channel coding scheme. Without relying on channel state information at devices, this scheme employs lattice codes to both quantize model parameters and exploit interference from the devices. A novel two-layer receiver structure at the server is designed to reliably decode an integer combination of the quantized model parameters as a lattice point for the purpose of aggregation. Numerical experiments validate the effectiveness of the proposed scheme. Even with the challenges posed by channel conditions and device heterogeneity, the proposed scheme markedly surpasses other over-the-air FL strategies.

Seyed Mohammad Azimi-Abarghouyi, Viktoria Fodor

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 learning method designed to address these challenges, along with a scalable transmission scheme that efficiently uses a single wireless resource through over-the-air computation. To provide resistance against data heterogeneity, we employ gradient aggregations. Meanwhile, the impact of interference is minimized through optimized receiver normalizing factors. For this, we model a multi-cluster wireless network using stochastic geometry, and characterize the mean squared error of the aggregation estimations as a function of the network parameters. We show that despite the interference and the data heterogeneity, the proposed scheme achieves high learning accuracy and can significantly outperform the conventional hierarchical algorithm.

Seyed Mohammad Azimi-Abarghouyi, Viktoria Fodor

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.

Seyed Mohammad Azimi-Abarghouyi

Over-the-air computation (AirComp) has traditionally been built on the principle of pre-embedding computation into transmitted waveforms or on exploiting massive antenna arrays, often requiring the wireless multiple-access channel (MAC) to operate under conditions that approximate an ideal computational medium. This paper introduces a new computation framework, termed out-of-air computation (AirCPU), which establishes a joint source-channel coding foundation in which computation is not embedded before transmission but is instead extracted from the wireless superposition by exploiting structured coding. AirCPU operates directly on continuous-valued device data, avoiding the need for a separate source quantization stage, and employs a multi-layer nested lattice architecture that enables progressive resolution by decomposing each input into hierarchically scaled components, all transmitted over a common bounded digital constellation under a fixed power constraint. We formalize the notion of decoupled resolution, showing that in operating regimes where the decoding error probability is sufficiently small, the impact of channel noise and finite constellation constraints on distortion becomes negligible, and the resulting computation error is primarily determined by the target resolution set by the finest lattice. For fading MACs, we further introduce collective and successive computation mechanisms, in addition to the proposed direct computation, which exploit multiple decoded integer-coefficient functions and side-information functions as structural representations of the wireless superposition to significantly expand the reliable operating regime; in this context, we formulate and characterize the underlying reliability conditions and integer optimization problems, and develop a structured low-complexity two-group approximation to address them.

Seyed Mohammad Azimi-Abarghouyi, Carlo Fischione

Almost all existing hierarchical federated learning (FL) models are limited to two aggregation layers, restricting scalability and flexibility in complex, large-scale networks. In this work, we propose a Multi-Layer Hierarchical Federated Learning framework (QMLHFL), which appears to be the first study that generalizes hierarchical FL to arbitrary numbers of layers and network architectures through nested aggregation, while employing a layer-specific quantization scheme to meet communication constraints. We develop a comprehensive convergence analysis for QMLHFL and derive a general convergence condition and rate that reveal the effects of key factors, including quantization parameters, hierarchical architecture, and intra-layer iteration counts. Furthermore, we determine the optimal number of intra-layer iterations to maximize the convergence rate while meeting a deadline constraint that accounts for both communication and computation times. Our results show that QMLHFL consistently achieves high learning accuracy, even under high data heterogeneity, and delivers notably improved performance when optimized, compared to using randomly selected values.