Wireless Ad Hoc Federated Learning (WAFL)

• Wireless Ad Hoc Federated Learning is a decentralized framework where wireless nodes train local models and exchange parameters via opportunistic, serverless links.
• It leverages over-the-air aggregation, peer-to-peer updates, and dynamic clustering to tackle non-IID data, intermittent connectivity, and mobility challenges.
• Empirical results show WAFL outperforms self-training in tasks like MNIST classification while enhancing resilience against adversarial attacks.

Searching arXiv for recent and foundational papers on wireless ad hoc federated learning, over-the-air FL, and clustered/decentralized wireless FL. Wireless Ad Hoc Federated Learning (WAFL) denotes a fully distributed federated learning paradigm for wireless ad hoc and opportunistic networks in which devices keep private data local, exchange model parameters directly with nearby peers over device-to-device links, and train without a central parameter server. In the serverless formulation introduced for opportunistic wireless nodes, each node maintains its own model rather than a single global model, and model synchronization is weak and local rather than global and server-mediated (Ochiai et al., 2022). Across the broader wireless FL literature, WAFL can also be interpreted as the ad hoc, infrastructure-less extension of wireless federated learning in which cluster heads, mobile aggregators, or elected leaders temporarily implement aggregation functions that are otherwise assigned to a base station or edge server (Niknam et al., 2019, Bouzinis et al., 2021). Related work spans fully decentralized WAFL (Ochiai et al., 2022), resilience analysis under model poisoning (Tezuka et al., 2022), clustered and semi-decentralized over-the-air aggregation (Madhan-Sohini et al., 2022), graph-based federated learning for low probability of detection in wireless ad hoc networks (Krishnan et al., 2023), mobility-driven stochastic ADMM in infrastructure-less settings (Parsons et al., 2023), and mission-oriented WAFL-ViT deployments on campus building-recognition datasets (Taniguchi et al., 5 Dec 2025).

1. Definition and architectural scope

WAFL is defined in the fully decentralized setting as a collaborative learning framework in which mobile or wireless nodes train models without any central server, exchanging model parameters only with neighbors they opportunistically encounter over wireless links (Tezuka et al., 2022, Ochiai et al., 2022). In this formulation, each node owns a local dataset $D^{(n)}$ and maintains local model parameters $\theta^{(n)}$, while the neighbor set $nbr(n)$ is determined by wireless proximity and satisfies symmetric connectivity, $k \in nbr(n) \Leftrightarrow n \in nbr(k)$ (Tezuka et al., 2022, Ochiai et al., 2022). The architectural consequence is that there is no single global model repository; instead, each node’s model evolves through repeated local exchanges and local training until it becomes a generalized model reflecting information that has diffused through the network (Tezuka et al., 2022).

The wider wireless FL literature uses a more canonical server-based formulation in which an aggregator collects local models and redistributes a global model (Niknam et al., 2019, Bouzinis et al., 2021, Qin et al., 2020). Within that literature, WAFL is the case in which the aggregator role is replaced by a cluster head, mobile gateway, UAV, or rotating coordinator, and aggregation may occur via peer-to-peer, multi-hop, or hierarchical communication rather than a fixed base station (Niknam et al., 2019, Bouzinis et al., 2021). This suggests that WAFL is best treated not as a separate optimization problem family, but as a change in communication and orchestration assumptions around the same federated objective.

Several sub-architectures fall under the WAFL umbrella. The fully decentralized peer-to-peer form exchanges parameters only among neighbors (Ochiai et al., 2022). A semi-decentralized clustered form uses cluster heads that aggregate locally and then coordinate with each other, which is communication-efficient relative to fully decentralized consensus and does not require a single powerful server (Madhan-Sohini et al., 2022). A mobility-assisted form uses a mobile server following a random walk over a graph of intermittently reachable clients, which remains infrastructure-less even though a server exists as a moving entity rather than fixed infrastructure (Parsons et al., 2023). Mission-oriented WAFL for IoT sensor systems specializes the same peer-to-peer parameter exchange mechanism to application-specific datasets and tasks such as campus building recognition (Taniguchi et al., 5 Dec 2025).

2. Optimization formulations and local-update rules

The canonical FL objective used in wireless FL is the weighted sum of local losses. In one tutorial formulation, each client $k$ has local loss

$$F_k(w) = \frac{1}{|D_k|} \sum_{(x,y)\in D_k} \ell(w; x, y),$$

and the global objective is

$$\min_{w} F(w) \triangleq \min_w \sum_{k=1}^K p_k F_k(w),$$

with $p_k = \frac{|D_k|}{\sum_j |D_j|}$ or related importance weights (Niknam et al., 2019). In another wireless FL formulation, with user set $\mathcal{N}=\{1,2,\dots,N\}$, local dataset

$$\mathcal{D}_n = \{ (\boldsymbol{x}_{n,k}, y_{n,k}) \}_{k=1}^{D_n},$$

local loss

$\theta^{(n)}$0

and global loss

$\theta^{(n)}$1

the FL objective is

$\theta^{(n)}$2

(Bouzinis et al., 2021). These formulations remain conceptually valid in WAFL; what changes is how the averaging or consensus is implemented.

In fully decentralized WAFL, the characteristic model-mixing rule is a local weak-synchronization update rather than server-side averaging. For node $\theta^{(n)}$3,

$\theta^{(n)}$4

with $\theta^{(n)}$5 in the resilience analysis and $\theta^{(n)}$6 in the benchmark paper’s generalized discussion (Tezuka et al., 2022, Ochiai et al., 2022). This averaging step is followed by local mini-batch optimization, e.g.

$\theta^{(n)}$7

after which $\theta^{(n)}$8 is updated to $\theta^{(n)}$9 (Tezuka et al., 2022). In the WAFL benchmark implementation, an important procedural rule is that local adjustment is performed only when a node has neighbors; if $nbr(n)$0, the node skips local adjustment to avoid re-overfitting to highly non-IID local data (Ochiai et al., 2022).

Other WAFL-relevant formulations relax consensus in different ways. In the random-walk stochastic ADMM formulation for infrastructure-less environments, each client keeps a personalized model $nbr(n)$1, and instead of requiring global consensus, neighboring models satisfy hard inequality constraints

$nbr(n)$2

which is explicitly designed to support heterogeneity and personalization without introducing a global regularization center (Parsons et al., 2023). In clustered wireless FL, each cluster seeks a consensus model via local OTA aggregation and inter-cluster mixing, and under smooth strongly convex objectives the cluster updates converge to the global minimizer at $nbr(n)$3 (Madhan-Sohini et al., 2022).

A distinct WAFL-specific specialization appears in WAFL-ViT. There the collaborative object is not the full Vision Transformer but the MLP head $nbr(n)$4, while the backbone remains fixed. The ad hoc mixing rule is

$nbr(n)$5

with $nbr(n)$6 determined by current ad hoc connectivity (Taniguchi et al., 5 Dec 2025). This indicates that WAFL need not exchange full models; it can operate on task-specific trainable submodules.

3. Communication substrates: opportunistic links, over-the-air aggregation, and hierarchy

WAFL is defined by the fact that communication is wireless, local, and often intermittent. In the opportunistic-network formulation, nodes communicate in Wi-Fi ad hoc mode or Bluetooth, discover neighbors when within radio range, exchange model parameters using UDP multicast, and can segment a serialized model across multiple UDP packets for reassembly at the application layer (Ochiai et al., 2022). The benchmark paper explicitly evaluates static topologies such as static_line, static_tree, static_ringstar, and static_dense, as well as dynamic random waypoint and community-structured environments, all with 10 nodes and time-varying contact graphs (Ochiai et al., 2022). This grounds WAFL in the delay/disruption-tolerant networking regime rather than the cellular regime.

A second communication substrate is over-the-air computation. In analog over-the-air FL with a central server, the wireless multiple-access channel is modeled as

$nbr(n)$7

where $nbr(n)$8 is the transmitted analog representation of the local parameter vector and $nbr(n)$9 is an unknown positive fading coefficient (Oksuz et al., 2023). The FedCOTA scheme uses two simultaneous uplink transmissions: local parameter vectors

$k \in nbr(n) \Leftrightarrow n \in nbr(k)$0

followed by server aggregation

$k \in nbr(n) \Leftrightarrow n \in nbr(k)$1

with

$k \in nbr(n) \Leftrightarrow n \in nbr(k)$2

(Oksuz et al., 2023). The key point is that this does not require channel estimation at the server or complex encoding-decoding schemes, since the normalization transmission implicitly cancels unknown scale factors (Oksuz et al., 2023). Although the architecture there is centralized, the paper explicitly notes that the same local aggregate

$k \in nbr(n) \Leftrightarrow n \in nbr(k)$3

could be computed by any node receiving simultaneous neighbor transmissions, which is directly relevant to cluster-based WAFL (Oksuz et al., 2023).

Clustered OTA wireless FL provides the clearest bridge from centralized OTA FL to WAFL. In the semi-decentralized clustered architecture, $k \in nbr(n) \Leftrightarrow n \in nbr(k)$4 clients are partitioned into $k \in nbr(n) \Leftrightarrow n \in nbr(k)$5 non-overlapping clusters, each with a cluster-head acting as a temporary local aggregator (Madhan-Sohini et al., 2022). Intra-cluster OTA aggregation at cluster-head $k \in nbr(n) \Leftrightarrow n \in nbr(k)$6 is

$k \in nbr(n) \Leftrightarrow n \in nbr(k)$7

and decoding yields

$k \in nbr(n) \Leftrightarrow n \in nbr(k)$8

(Madhan-Sohini et al., 2022). Cluster-heads then run an inter-cluster consensus step via a symmetric doubly stochastic mixing matrix $k \in nbr(n) \Leftrightarrow n \in nbr(k)$9: $k$0 (Madhan-Sohini et al., 2022). This is explicitly presented as a server-free or weak-server architecture suitable for D2D, fog/IoT, and wireless sensor networks, and the communication complexity scales as $k$1 rather than $k$2 for fully decentralized client-to-client exchanges (Madhan-Sohini et al., 2022). This suggests that clustered hierarchy is a central systems pattern for WAFL rather than a mere optimization heuristic.

A related two-tier AirComp design studies subordinate devices, lead devices, and a parameter server. There, subordinate devices send normalized gradients to lead devices, and lead devices send merged results to the PS using a second AirComp stage (Guo et al., 2022). While the presence of a PS places the model outside strict serverless WAFL, the lead-device mechanism and dynamic clustering rules transfer naturally to multi-hop WAFL, where lead devices can be interpreted as ad hoc cluster heads (Guo et al., 2022).

Weighted over-the-air aggregation adds a further layer of WAFL relevance. WAFeL formulates aggregation as

$k$3

and derives an equalizer

$k$4

that minimizes OTA estimation error without requiring CSIT on channel gains (Azimi-Abarghouyi et al., 2024). This suggests a path for channel-aware but transmitter-simple WAFL aggregation inside clusters.

4. Heterogeneity, topology, and mobility

Heterogeneity is central to WAFL at three levels: statistical heterogeneity, systems heterogeneity, and topology heterogeneity. The wireless FL surveys emphasize that local datasets are typically non-IID, unbalanced, and massively distributed (Niknam et al., 2019, Bouzinis et al., 2021). In the original WAFL benchmark, the data split is strongly non-IID: for node $k$5, about 90% of training samples belong to class $k$6, with the remaining 10% distributed over other labels without overlap, so each node is heavily specialized yet collectively the global distribution is balanced (Ochiai et al., 2022). This makes local training strongly biased and turns model exchange into the primary mechanism for global generalization.

Systems heterogeneity appears in computing speed, bandwidth, and energy. WHALE-FL studies compute and communication heterogeneity through per-round compute and transmission delays $k$7 and $k$8, a maximum subnetwork size $k$9, and a utility

$$F_k(w) = \frac{1}{|D_k|} \sum_{(x,y)\in D_k} \ell(w; x, y),$$0

that is combined with a training-efficiency term to drive adaptive subnetwork scheduling (Su et al., 2024). Although WHALE-FL is written for a centralized wireless network, the paper explicitly states that in WAFL “device–server rate” can be replaced by “effective end-to-end rate over the selected multi-hop path,” preserving the latency formulas and subnetwork logic (Su et al., 2024). A plausible implication is that adaptive model-width selection is a practical way to cope with multi-hop overhead in WAFL.

Mobility and topology create the third heterogeneity axis. The 6G wireless FL survey stresses that wireless links are time-varying, unreliable, and subject to handovers, battery shortages, and competing tasks, motivating adaptive scheduling and asynchronous FL (Bouzinis et al., 2021). WAFL intensifies these issues because the topology itself changes. The WAFL benchmark models mobility with random waypoint in areas of $$F_k(w) = \frac{1}{|D_k|} \sum_{(x,y)\in D_k} \ell(w; x, y),$$1, $$F_k(w) = \frac{1}{|D_k|} \sum_{(x,y)\in D_k} \ell(w; x, y),$$2, and $$F_k(w) = \frac{1}{|D_k|} \sum_{(x,y)\in D_k} \ell(w; x, y),$$3 meters and with community-structured environments where nodes belong to subsets of 10 communities and move between them (Ochiai et al., 2022). Accuracy degrades when contacts are sparse, but WAFL still outperforms self-training in these dynamic settings (Ochiai et al., 2022).

Dynamic clustering is one response to topology and heterogeneity. In the two-tier AirComp paper, clusters are formed using a minimax linkage criterion that combines geometric distance and data importance: $$F_k(w) = \frac{1}{|D_k|} \sum_{(x,y)\in D_k} \ell(w; x, y),$$4 with data importance measured by predictive entropy under the current model (Guo et al., 2022). Lead devices are selected by minimizing a weighted combination of average distance to cluster members, distance to PS, and local data importance (Guo et al., 2022). This suggests that topology-aware and data-aware cluster formation is an essential WAFL design dimension rather than a purely networking concern.

A different mobility treatment appears in the random-walk stochastic ADMM framework, where the mobile server’s movement is modeled as an irreducible, aperiodic Markov chain with transition matrix $$F_k(w) = \frac{1}{|D_k|} \sum_{(x,y)\in D_k} \ell(w; x, y),$$5 and mixing time $$F_k(w) = \frac{1}{|D_k|} \sum_{(x,y)\in D_k} \ell(w; x, y),$$6 (Parsons et al., 2023). The theoretical communication complexity depends on the spectral gap $$F_k(w) = \frac{1}{|D_k|} \sum_{(x,y)\in D_k} \ell(w; x, y),$$7, and faster mixing implies faster convergence (Parsons et al., 2023). This suggests that when mobility can be shaped, WAFL performance is partly a graph-design problem.

5. Security, privacy, and robustness

WAFL inherits the privacy motivation of FL—raw data remains local—but replaces the central trust anchor with distributed interactions. The wireless FL surveys emphasize secure aggregation, differential privacy, memorization risks, poisoning, membership inference, and other inference attacks as core challenges (Niknam et al., 2019, Bouzinis et al., 2021). In infrastructure-less WAFL, those challenges are amplified because any node may be malicious, and there may be no authoritative aggregator (Niknam et al., 2019, Bouzinis et al., 2021).

The most explicit robustness result concerns model poisoning. In the WAFL resilience analysis, the dynamics at node $$F_k(w) = \frac{1}{|D_k|} \sum_{(x,y)\in D_k} \ell(w; x, y),$$8 on a line topology are written as

$$F_k(w) = \frac{1}{|D_k|} \sum_{(x,y)\in D_k} \ell(w; x, y),$$9

where

$$\min_{w} F(w) \triangleq \min_w \sum_{k=1}^K p_k F_k(w),$$0

(Tezuka et al., 2022). Under persistent attack, equilibrium satisfies

$$\min_{w} F(w) \triangleq \min_w \sum_{k=1}^K p_k F_k(w),$$1

which the paper interprets as a force balance between poisoned influence and legitimate local training (Tezuka et al., 2022). In experiments with 10 nodes arranged in a static line and attacks inserted at one end, nodes directly encountered by the attacker are compromised, but farther nodes remain resilient, and after the attacker leaves, all nodes recover and often achieve higher final accuracy than no-attack runs (Tezuka et al., 2022). The paper explicitly states that “Most of the attack-experienced cases achieved higher accuracy than the no-attack-experienced cases” (Tezuka et al., 2022). This challenges the common misconception that fully decentralized FL is necessarily more fragile than centralized FL. In the reported setup, decentralization and weak synchronization are themselves a robustness mechanism.

Privacy through the wireless channel itself is another theme. Analog over-the-air ADMM uses fading-perturbed aggregated signals at the parameter server and proves privacy guarantees in the sense that local model trajectories cannot be uniquely reconstructed from the server’s observations, because the inverse problem remains underdetermined before and after convergence (Elgabli et al., 2020). The server only observes sums of terms such as

$$\min_{w} F(w) \triangleq \min_w \sum_{k=1}^K p_k F_k(w),$$2

plus noise, not individual local models (Elgabli et al., 2020). A plausible implication is that OTA WAFL can exploit channel randomness as a privacy resource, provided CSI and dual variables are not fully exposed to an aggregator.

Low probability of detection (LPD) provides a distinct, physical-layer notion of privacy. In federated graph learning for LPD, the task is to predict communication radii $$\min_{w} F(w) \triangleq \min_w \sum_{k=1}^K p_k F_k(w),$$3 that minimize the RF footprint

$$\min_{w} F(w) \triangleq \min_w \sum_{k=1}^K p_k F_k(w),$$4

subject to connectivity constraints $$\min_{w} F(w) \triangleq \min_w \sum_{k=1}^K p_k F_k(w),$$5 (Krishnan et al., 2023). Training is federated, with each worker holding local graph datasets and sharing only GNN parameters; pruning is used to reduce transmitted model size and hence RF visibility (Krishnan et al., 2023). This is not a general WAFL training architecture, but it is a concrete example of WAFL being used to optimize communication stealth rather than task accuracy alone.

6. Empirical performance and representative applications

The benchmark results for fully decentralized WAFL on highly partitioned non-IID MNIST provide one empirical anchor. Using a 2-layer fully connected network, batch size 32, Adam optimizer, learning rates $$\min_{w} F(w) \triangleq \min_w \sum_{k=1}^K p_k F_k(w),$$6 and $$\min_{w} F(w) \triangleq \min_w \sum_{k=1}^K p_k F_k(w),$$7, and 50 epochs of local pre-training followed by 5000 WAFL epochs, self-training achieves 84.66% test accuracy under the 90% non-IID split, while WAFL reaches 94.8–96.3% in most scenarios and centralized federated learning reaches 96.76% in the best setting (Ochiai et al., 2022). The paper summarizes this as WAFL achieving “higher accuracy of 94.8-96.3% than the self-training case of 84.7%” and showing that model parameters can converge from highly partitioned non-IID datasets over opportunistic networks without centralized mechanisms (Ochiai et al., 2022). Confusion matrices and a model convergence error

$$\min_{w} F(w) \triangleq \min_w \sum_{k=1}^K p_k F_k(w),$$8

show that WAFL reduces inter-model divergence while self-training causes divergence to grow (Ochiai et al., 2022).

Mission-oriented WAFL-ViT provides a second empirical anchor. On the CUBR campus-building dataset with 32 building classes, 10 devices, random waypoint mobility, and IID image distribution across devices, WAFL-ViT achieves 0.861 accuracy with standard deviation 0.007, outperforming SELF-ViT at 0.619, and also surpassing WAFL-ResNet, WAFL-VGG, and WAFL-MobileNet under the same collaborative setting (Taniguchi et al., 5 Dec 2025). The paper also reports WAFL-ResNet at 0.833, WAFL-VGG at 0.732, WAFL-MobileNet at 0.791, SELF-ResNet at 0.596, SELF-VGG at 0.498, and SELF-MobileNet at 0.561 (Taniguchi et al., 5 Dec 2025). This indicates that even under IID splits, decentralized collaboration in WAFL can substantially outperform isolated training, and that exchanging only ViT heads is sufficient for strong gains (Taniguchi et al., 5 Dec 2025).

Clustered OTA wireless FL provides another application-oriented result. Using MNIST and CIFAR-10, CWFL and CWFL-Prox achieve accuracy comparable to central-server-based COTAF and proximal methods while beating single-client training by large margins (Madhan-Sohini et al., 2022). Theoretical convergence to global minima occurs at $$\min_{w} F(w) \triangleq \min_w \sum_{k=1}^K p_k F_k(w),$$9 for each cluster under smooth strongly convex losses (Madhan-Sohini et al., 2022). This is especially relevant for ad hoc systems with mid-tier devices, fog nodes, or stronger peers able to act as local aggregators.

Applications discussed across the surveyed works include edge computing and caching, including infrastructure-less caching on user devices (Niknam et al., 2019); spectrum management and coexistence in decentralized intelligent radio networks (Niknam et al., 2019); vehicular and ITS scenarios (Niknam et al., 2019); smart grids and unmanned mobility in 6G (Bouzinis et al., 2021); low-probability-of-detection communication regions in military-style ad hoc networks (Krishnan et al., 2023); and smart-campus building recognition as a mission-oriented IoT sensor system (Taniguchi et al., 5 Dec 2025). These applications share two properties: local data collection at the edge and a mismatch between infrastructure assumptions and deployment reality.

7. Limitations and open problems

A recurring limitation is the gap between communication models and learning models. The paper “Over-the-Air Federated Learning In Broadband Communication” contains only a high-level conceptual paragraph on federated learning; its technical contribution is actually a Gaussian approximation of MIMO capacity and outage probability in line-of-sight Vandermonde channels with perfect CSI at the receiver and no CSI at the transmitter (Lemieux et al., 2023). It defines channel outage via

$p_k = \frac{|D_k|}{\sum_j |D_j|}$0

and models capacity as

$p_k = \frac{|D_k|}{\sum_j |D_j|}$1

with Gaussian outage approximation

$p_k = \frac{|D_k|}{\sum_j |D_j|}$2

(Lemieux et al., 2023). The paper does not propose an OTA FL aggregation scheme, formal FL objective, or ad hoc topology model (Lemieux et al., 2023). Its WAFL value is therefore as a physical-layer design tool for MIMO link budgeting and outage planning rather than as a learning algorithm (Lemieux et al., 2023). This illustrates a broader open problem: rigorous integration of link-level wireless reliability with end-to-end learning performance.

Synchronization and CSI assumptions are another limitation. OTA FL often requires slot-level or symbol-level synchronization and either explicit CSI or strong structural assumptions. FedCOTA assumes simultaneous transmissions over a WMAC and i.i.d. positive real fading coefficients (Oksuz et al., 2023). Clustered OTA FL assumes synchronous FL rounds and an error-free downlink (Madhan-Sohini et al., 2022). The two-tier AirComp design assumes perfect instantaneous CSI for power control (Guo et al., 2022). The MIMO outage paper assumes perfect CSI at the receiver and does not discuss pilot overhead or timing/frequency synchronization (Lemieux et al., 2023). In practical WAFL with mobility and contention, these assumptions are difficult to sustain.

Scalability and realism remain incomplete. The graph-based LPD work evaluates only 200 synthetic 5-node graphs and assumes a trusted global server for aggregation (Krishnan et al., 2023). The CUBR paper evaluates only 10 nodes and IID data distribution (Taniguchi et al., 5 Dec 2025). The WAFL poisoning analysis uses a static 10-node line topology and a single attacker (Tezuka et al., 2022). The original WAFL benchmark uses a small fully connected network on MNIST rather than modern large models (Ochiai et al., 2022). This suggests that the field still lacks large-scale, realistic system evaluations combining mobility, modern architectures, non-IID data, and communication constraints in one experimental platform.

Theoretical coverage is also fragmented. Some works provide convergence guarantees only for convex or strongly convex objectives, such as FedCOTA (Oksuz et al., 2023), clustered OTA FL (Madhan-Sohini et al., 2022), and analog over-the-air ADMM (Elgabli et al., 2020). Other works provide empirical but not formal convergence analysis under non-convex deep models, including the original WAFL benchmark (Ochiai et al., 2022) and WAFL-ViT (Taniguchi et al., 5 Dec 2025). A plausible implication is that practical WAFL designs will continue to rely on hybrid methodology: theory for simplified convex surrogates and empirical study for realistic deep models.

Open directions appear consistently across the corpus: decentralized secure aggregation and differential privacy with low overhead (Niknam et al., 2019, Bouzinis et al., 2021); topology-aware and channel-aware participant selection (Niknam et al., 2019, Bouzinis et al., 2021); asynchronous schemes that handle unbounded delays and realistic mobility (Bouzinis et al., 2021); hierarchical and cluster-based aggregation with dynamic cluster-head election (Madhan-Sohini et al., 2022, Guo et al., 2022); multi-hop and time-varying graph extensions of random-walk or ADMM-style algorithms (Parsons et al., 2023, Elgabli et al., 2020); adaptive compression and subnetwork scheduling that incorporate end-to-end path costs (Su et al., 2024); and explicit convergence bounds that integrate physical-layer outage terms such as $p_k = \frac{|D_k|}{\sum_j |D_j|}$3 into WAFL learning guarantees (Lemieux et al., 2023).

Wireless Ad Hoc Federated Learning therefore remains best understood as a systems-and-optimization program rather than a single algorithm. The common core is distributed model training over private local data without centralized infrastructure. The main variables are how local models are mixed, when and where aggregation occurs, how wireless superposition or hierarchy is exploited, and how topology, heterogeneity, privacy, and robustness are encoded into the training process.