FM4WiFi: Flow Matching for Multi-AP Coordination in Dense Deployments of Beyond Wi-Fi 8 Networks

FM4WiFi: Flow Matching for Multi-AP Coordination in Dense Deployments of Beyond Wi-Fi 8 Networks Maksymilian Wojnar, Krzysztof Rusek, Katarzyna Kosek-Szott, and Szymon Szott

arXiv:2608.04050v1 [cs.NI] 4 Aug 2026

AGH University of Krakow, Poland Email: {name.surname}@agh.edu.pl Abstract—Wi-Fi networks are moving beyond random channel access toward tightly coordinated operation across access points (APs), a shift reflected in Wi-Fi 8’s multi-AP coordination (MAPC). However, the current MAPC specification restricts cooperation to AP pairs, fundamentally limiting the gains achievable in dense deployments and calling for scalable, network-wide coordination in beyond Wi-Fi 8 systems. We target coordinated spatial reuse (Co-SR), where APs transmit concurrently at reduced power. Effective Co-SR demands joint selection and configuration of AP–station transmissions, yet existing approaches simply do not scale: they rely on heavy signaling, slow convergence, unrealistic assumptions, and often require computation time that explodes with network size. We introduce FM4WiFi, a generative ML pipeline that addresses these limitations by producing high-quality Co-SR configurations in a single inference step. FM4WiFi integrates (i) an autoencoder that learns compact latent representations of network states, (ii) a flow-matching generative model that synthesizes feasible Co-SR configurations (including rate control, absent from prior work), and (iii) a surrogate rate predictor that allows rapid, largescale Co-SR candidate evaluation without dependence on a live system or digital twin. Across extensive evaluations (including experimental validation), FM4WiFi matches or exceeds state-ofthe-art baselines at medium-to-large scales and scales to 30+ APs with sub-second inference. Extensive ablation studies validate each modeling and optimization choice. Index Terms—flow matching, generative AI, multi-AP coordination, Wi-Fi

I. I NTRODUCTION Wi-Fi networks are undergoing a shift from competitive, randomly distributed channel access to collaborative coordination among access points (APs). This transition is reflected in one of the defining features of the forthcoming Wi-Fi 8 standard: multi-AP coordination (MAPC). However, MAPC’s design limits cooperation to pairs of APs, restricting its potential benefits. Consequently, we expect that future beyond This research was funded by the National Science Centre, Poland (2023/05/Y/ST7/00004). We gratefully acknowledge Polish high-performance computing infrastructure PLGrid (HPC Center: ACK Cyfronet AGH) for providing computer facilities and support within computational grant no. PLG/2025/018718. We gratefully acknowledge the support of the National Research Institute, grant number POIR.04.02.00-00-D008/20-01 on “National Laboratory for Advanced 5G Research” (acronym PL-5G) for providing computing facilities. For the purpose of Open Access, the authors have applied a CC-BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.

(a) In Wi-Fi 8, only two APs can coordinate transmissions.

(b) Beyond Wi-Fi 8, several APs can coordinate transmissions.

Fig. 1: Example topologies and Co-SR scheduling in (a) WiFi 8 and (b) beyond Wi-Fi 8 networks. Triangles denote APs, squares – stations, lines – viable concurrent transmissions, dotted lines – associations.

Wi-Fi 8 systems will need to support scalable, network-wide coordination strategies. We focus on coordinated spatial reuse (Co-SR), an MAPC variant, which is particularly promising for high-density deployments, e.g., industrial warehouses or stadiums. Co-SR scheduling requires selecting (i) AP groups that transmit simultaneously, (ii) stations (STAs) these APs transmit to, and (iii) Wi-Fi parameters (such as modulation and coding scheme (MCS) indices and transmit power levels) [1], [2]. We refer to such a complete assignment as a Co-SR configuration. Fig. 1 provides example topologies for Co-SR in both Wi-Fi 8 and beyond Wi-Fi 8 networks. The scheduling problem in the latter case is compounded by the explosion in the number of possible configurations. Existing Co-SR scheduling solutions are not ready to operate on a network scale due to their signaling overhead, slow convergence times, computational complexity, and idealistic assumptions [3]. Indeed, the four APs shown in Fig. 1 are at the limit for currently available scheduling solutions. To address this challenge, we propose FM4WiFi: a generative pipeline that learns offline from a diverse dataset of network topologies and subsequently generates high-performance

Context

FM

Encoder

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Co-SR candidate configuration generation

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0.1

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Fig. 2: Full FM4WiFi inference pipeline. The central controller encodes recent network observations with the encoder, generates candidate Co-SR configurations with the flow matching (FM) model, scores them using the surrogate predictor, and decodes the top-k candidates into scheduling decisions.

AP 1

Co-SR Invite

SIFS

SIFS

Co-SR Response

AP 2 STA 1 associated with AP 1

Co-SR Trigger

SIFS

missions, which motivates the need for automated methods capable of optimizing such operations in larger, beyond-WiFi 8 networks.

Co-SR Transmission Co-SR Transmission

SIFS

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MUBAR 2

BA 1

STA 2 associated with AP 2

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BA 2

Fig. 3: Co-SR frame exchange sequence [4].

We extensively evaluate FM4WiFi across a wide range of scenarios (including experimental validation), demonstrating improvements over state-of-the-art baselines in data rate with unmatched scalability, and validating key design choices through ablation studies. Our contributions are as follows: FM4WiFi. We propose the first generative pipeline in the literature for Co-SR scheduling, built on a GNN autoencoder with a novel mixture categorical loss for heterogeneous Wi-Fi attributes, a flow matching model for configuration generation, and a surrogate predictor for fast candidate ranking. • Joint scheduling and rate selection. FM4WiFi jointly optimizes Co-SR group formation, station selection, MCS, and transmit power in a single model, eliminating the idealized MCS assumptions of all prior work. • Scalability and speed. FM4WiFi produces schedules in under 1 s and scales to 30+ APs, where the existing analytical and reinforcement learning (RL) Co-SR baselines become intractable. • Dynamic robustness. Event-triggered regeneration enables immediate adaptation to topology changes, station joins, reassociations, and mobility without retraining in contrast to fixed-action-space RL methods. • Full reproducibility. The FM4WiFi pipeline and all code used for dataset generation and model training are available as open source.1 • Experimental testbed. We provide the first open-source experimental testbed on commercial-off-the-shelf devices for evaluating Co-SR.2 •

Co-SR transmission configurations at inference time. Our pipeline incorporates the latest advancements in machine learning (ML): a graph neural network (GNN) autoencoder to learn latent representations of network states, a flow matching (FM) generative model to produce plausible Co-SR configurations, and a surrogate data rate predictor that enables rapid evaluation of Co-SR configuration candidates without the need to access a real network or its digital twin (Fig. 2). During inference, the central controller collects data (received signal strength indicator (RSSI) values and transmission outcomes) from all managed access points through wired connections, both regarding themselves and their associated stations. This allows the controller to understand the current state of the network (context), almost immediately select promising candidates for Co-SR transmissions, and apply the configuration to the Co-SR AP group, as elaborated in Section III-F. To clarify how Co-SR operates at the MAC-layer, Fig. 3 presents the Wi-Fi 8 Co-SR frame-exchange sequence. In this example, two APs perform simultaneous downlink Co-SR transmissions following an initiation exchange. The associated stations then acknowledge both transmissions using block acknowledgment (BA) frames. Additionally, AP 1 configures the acknowledgment (ACK) policy as part of the Co-SR transmission; as a result, the second station’s ACK is explicitly requested by its AP via a multi-user BA request (MU-BAR) frame to avoid potential collisions. This MAC-layer exchange illustrates the practical complexity of configuring Co-SR trans-

1 https://github.com/ml4wifi-devs/fm4wifi 2 https://github.com/ml4wifi-devs/mapc-testbed

Joint MCS opt.

Generalization

Ref.

Real-time

Approach

Low overhead

Our work on developing a Co-SR scheduler able to operate in dense Wi-Fi 8 networks is motivated by the following limitations of existing works. Vulnerability of RSSI-based centralized schemes. Several centralized Co-SR schemes choose AP groups, their transmit power levels, and MCS indices from global RSSI or signalto-interference-plus-noise ratio (SINR) information available at a central controller [5], [6]. Although effective in smallscale scenarios, these architectures add coordination overhead as the network grows and depend on heuristic, parametertuned group formation. In [5], the stations wirelessly report the environment data to the controller, introducing signaling overhead, and MCS selection relies on topology-dependent thresholds. Similarly, [6] uses two key parameters that govern successful grouping, yet their selection is deferred to future work. In dense or mobile environments, RSSI variance can perturb SINR estimates, causing poor Co-SR configuration. Scalability and convergence in probing-based methods. To reduce dependence on unreliable measurements, online learning methods have been introduced [3], [7]. These methods probe different configurations to learn agent policies (i.e., mapping states to actions) without a priori knowledge of the wireless channel. However, the convergence time still increases with the topology size and transmission opportunity (TXOP) duration, and large deployments typically require additional clustering to keep the action space manageable [3]. Rigidity of traditional RL Recent discrete-action RL schedulers [8], [9] select one action from a precomputed catalog of feasible Co-SR groups, i.e., a fixed discrete output space with masking over topology-dependent options. This design does not generate new Co-SR configurations online; it only schedules among configurations prepared in advance. Notably, [9] is specifically concerned with the temporal scheduling of pre-formed configurations to reduce latency, which is a complementary problem to configuration generation and not a direct competitor to our approach. Thus, adaptation to unseen deployments typically requires regenerating the action space and retraining, while convergence may require millions of interaction steps [9]. In contrast, our approach can accept any topology at both input and output, making adaptation to unseen deployments an inherent property of the architecture rather than a separate engineering effort. Model-based optimization restrictions. Model-based approaches fall into two categories: solver-based and optimization-guided RL. Solver-based formulations can provide exact (or upper-bound) configurations [3], [10], but require accurate inputs (e.g., path loss or RSSI measurements) and iterative solving, which is difficult to recompute at strict per-TXOP timescales in fast-varying settings. Meanwhile, optimization-guided RL formulations, such as [8], replace direct combinatorial search with multi-agent deep reinforcement learning (MA-DRL), but still rely on periodic channel-state updates and introduce substantial training complexity. Lack of joint MCS selection. A critical but frequently

TABLE I: Comparison of Co-SR scheduling approaches.

Scalable

II. M OTIVATION

× × × × ×

× ✓ ✓ × ×

✓ ✓ ✓ ✓ ✓ × ✓ × × × ✓ ✓/× ✓ × ×

RSSI-based Probing-based Fixed action-space RL Optimization (solver-based) Optimization (RL-assisted)

[5], [6] [3], [7] [9] [3], [10] [8]

Generative model (ours)

This paper ✓ ✓ ✓ ✓

✓

simplified dimension of Co-SR scheduling is the selection of appropriate MCS. Many methods decouple this step or use a fixed MCS to maintain model simplicity or tractability [3], [7], [8], [10]. This simplification fails to capture the interplay between interference management and feasible data rates, often leading to higher packet error rates or the reliance on unrealistic ideal MCS selection. Generative approach. We identify a common limitation across state-of-the-art approaches: they treat Co-SR scheduling as either a search over a fixed set of groups or a discrete classification problem. This limits their ability to both generalize to arbitrary, non-grid topologies and provide fast and accurate joint optimization. In contrast, we treat Co-SR group formation as a conditional generation task. As summarized in Table I, our framework is designed to provide the signaling efficiency, flexibility, and generalization needed for next-generation WiFi coordination schemes. III. S YSTEM D ESIGN We propose a generative pipeline that learns offline from a diverse dataset of network topologies and subsequently generates high-performance Co-SR configurations at inference time. The pipeline consists of three components: (i) an autoencoder that learns latent representations of Wi-Fi network states, (ii) an FM generative model that produces plausible Co-SR configurations conditioned on recent network history, and (iii) a surrogate data rate predictor that enables rapid evaluation of Co-SR configuration candidates without the need for timeconsuming simulation. The design of these components is grounded in a Bayesian view of the coordination problem, which we formalize next. A. Inductive Bias Co-SR scheduling can be viewed as a joint process of inference and optimization. A coordination agent must deploy a configuration c to maximize observed network throughput T . If the agent possessed complete environmental knowledge, i.e., exact station positions and propagation conditions, collectively denoted Θ, this would reduce to a deterministic optimization problem [3]. In practice, Θ is latent; only empirical observations D (packet outcomes, RSSI) are available.

Scheduling decisions: – selected ∈ {True, False, N/A}: indicates whether the AP–STA pair is chosen for transmission, – mcs ∈ {0, 1, . . . , 13, N/A}: MCS index3 , – tx_power ∈ {1, 2, 3, 4, N/A}: transmission power level (Table II). • Outcome: – success ∈ [0, 1]: ratio of aggregated MAC protocol data units (A-MPDUs) successfully received at the destination STA.

• rssi : 0.23 link_type : AP-STA active : True selected : True mcs : 7 tx_power : 3 success : 0.92

Fig. 4: Example graph of a Wi-Fi network with four APs and eight STAs. Green dash-dotted edges represent AP–AP interference links; black edges represent AP–STA transmission links (solid if selected, dotted if inactive). The legend shows the seven-attribute feature vector carried by each edge. We formalize this as a Bayesian problem. The agent maintains a prior p(Θ) and uses D to form a posterior p(Θ|D). The optimal configuration is then:   (1) c∗ = arg max EΘ∼p(Θ|D) T (c, Θ) . c

Both the inference and optimization steps are analytically intractable for real-world deployments, motivating learned approximations. The FM model serves as the inference step: drawing diverse candidate configurations conditioned on recent observations in a single forward pass. This mirrors the role of Markov chain Monte Carlo (MCMC) in Bayesian statistics, where a Markov chain converges to the posterior as its stationary distribution; FM provides a tractable surrogate for this process. The surrogate data-rate predictor serves as the optimization step: acting as a learned digital twin of the network, it scores each candidate and replaces costly real-network evaluation, approximating the expectation under the posterior. B. Graph Representation of Wi-Fi Networks We model the Wi-Fi network as an undirected graph G = (V, E), where the vertex set V = A ∪ S comprises APs A and STAs S. The edge set E contains two types of edges: AP–STA transmission links (one per each associated AP– STA pair, representing the downlink channel) and AP–AP interference edges (between APs whose mutual RSSI exceeds the clear channel assessment (CCA) threshold of −82 dBm). An example of such a graph is shown in Fig. 4. Edges are undirected (i.e., a symmetric channel is assumed) and carry a feature vector defined by a seven-attribute tuple, which we group by their roles: • Channel/topology: – rssi ∈ R: received signal strength, standardized as r̃s = (rs − µRSSI )/σRSSI with µRSSI = −51.6 dBm, σRSSI = 14.3 dB (computed from a training set), – link_type ∈ {AP-AP, AP-STA, N/A}: edge type, – active ∈ {True, False, N/A}: indicates whether the AP–STA pair can be used in a Co-SR configuration.

C. Autoencoder GNNs [11] extend deep learning to graph-structured data by iteratively passing learned messages between neighboring elements. We adopt the graph network framework of [12], in which each layer maintains three levels of representation – edges, nodes, and a global summary vector – and updates each of them by aggregating information from local neighborhoods through dedicated neural networks. After L such layers, each element’s representation captures information from its Lhop neighborhood. This makes GNNs a natural fit for WiFi networks, where interference and scheduling decisions are governed by spatial proximity and local topology. Importantly, the formulation is permutation-equivariant and handles graphs of varying size, allowing a single trained model to generalize across different network deployments. The GNN autoencoder learns a latent representation of Wi-Fi network graphs, jointly encoding both fixed channel/topology attributes and variable scheduling decisions into a latent space so that the FM model can generate configurations that are consistent with current channel conditions. The architecture follows a variational autoencoder (VAE) [13] adapted to graph-structured data using the message-passing neural network (MPNN) framework [11]. The latent space is defined per edge, i.e., each edge e is mapped to a vector ze ∈ Rdz , preserving the graph topology and allowing the FM model to operate on graphs of varying size. A diagram of the autoencoder is provided in Fig. 14 (Appendix C). 1) Architecture: The encoder first projects the flattened edge features into an intermediate embedding space via a linear layer. The embedded graph is then processed by messagepassing layers, each implemented as a graph network [12] parameterized by residual multi-layer perceptrons (MLPs) with layer normalization and Gaussian error linear unit (GELU) activations [14]. Messages are aggregated via mean pooling. The encoder projects each edge representation to two vectors µe and log σ 2e of dimension dz , defining an approximate posterior q(ze |G) = N (µe , diag(σ 2e )), where µe is the mean vector and diag(σ 2e ) is the diagonal of the covariance matrix. The decoder takes a latent graph with edge features ze ∼ q(ze |G) (sampled via the reparameterization trick of [13]) and processes it through message-passing layers with the same architecture as the encoder. The final edge representations are 3 Since the final version of the IEEE 802.11bn standard is not released yet, IEEE 802.11be MCS indices are assumed.

passed through attribute-specific fully-connected output heads that reconstruct the original attributes. 2) Loss Function: For categorical attributes with N/A support, the decoder outputs C logits l ∈ RC , where l1:C−1 are the valid-class logits and lC is the N/A logit. These parametrize a mixture: a Bernoulli gate decides whether the attribute is N/A, and a categorical over the C−1 valid classes covers the remaining cases. The negative log-likelihood (NLL) of this mixture (derived in Appendix B) gives the N/A-gated categorical loss: Lmix (l, y) = LBCE (lC , yC ) + (1 − yC ) LCE (l1:C−1 , y1:C−1 ), (2) where LBCE is the binary cross-entropy and LCE is the categorical cross-entropy. When yC = 1, only the gate is trained; when yC = 0, both the gate and the valid-class head contribute. For continuous rssi and success attributes, mean squared error (MSE) and sigmoid binary cross-entropy losses are used, respectively. Each attribute-specific loss is thus a proper NLL loss under the respective decoder marginal distribution pθ (xk |z). The total loss is a weighted negative evidence lower bound (ELBO), where the weights per-attribute account for the different scales and importance of the seven attributes: L=

7 X

Lk + λKL DKL (qϕ (z|G)∥N (0, I)) ,

(3)

k=1

where Lk are per-attribute loss functions and λKL controls the Kullback-Leibler (KL) regularization strength [13]. D. Flow Matching Generative Model The FM model learns to generate Co-SR configurations using continuous flow matching [15], a state-of-the-art generative approach that produces high-quality samples in very few steps, training a velocity field that defines a continuous-time flow in the latent space of the autoencoder. 1) Problem Formulation: Given a context of n recent network observations obtained by executing random Co-SR configurations and recording the resulting network state, the goal is to generate a new configuration that is consistent with the observed network conditions. Random (rather than optimized) context configurations are used so that the model does not depend on a particular scheduling policy and can generalize from policy-free probing of the environment. Let h = (h1 , . . . , hn ) denote the encoded context, x ∈ R|E|×dz the target latent configuration, and z ∼ N (0, I) a noise sample. We define the linear interpolation path xt = (1 − t) z + t x,

t ∈ [0, 1),

(4)

with the corresponding target velocity field vt = x − z. The model vθ is trained to predict this velocity conditioned on the context by minimizing h i 2 LFM = Et,z,x ∥vθ (xt , t, h) − vt ∥ , (5) where t ∼ U(0, 1).

We maintain an exponential moving average (EMA) of the model parameters with a decay rate βEMA = 0.999, and use the EMA parameters for inference and validation. The training procedure is illustrated in Fig. 15 (Appendix C). 2) Architecture: The n context configurations are encoded by the frozen GNN encoder into latent vectors and stacked along a temporal axis. During training, the target configuration is appended as the last slice and the result is flattened into a single vector of dimension (n + 1)dz per edge. The velocity network vθ employs MPNN with transformer blocks [16]. A sinusoidal time embedding [17] of the timestep t is calculated and added to the edge features. Within each transformer, attention is masked so that features belonging to different graphs do not attend to each other. A final linear projection maps the edge features back to the latent dimension dz . 3) Sampling via Euler’s Method: The samples are generated by initializing x0 = z ∼ N (0, I) and solving the ordinary differential equation (ODE) dx/dt = vθ (xt , t, h) from t = 0 (noise) to t = 1 (data) using the Euler method. Given a step size ∆t = 1/S, the update at each step is: xt+∆t = xt + vθ (xt , t, h) ∆t.

(6)

The Euler method requires only one model evaluation per step, enabling fast generation. Empirical results are consistent with a smooth velocity field: first-order integration with S=6 steps achieves high-quality results (Appendix D-B). E. Surrogate Data Rate Predictor During inference, a digital twin of the real network is generally unavailable, so candidate configurations cannot be evaluated by simulation. The surrogate model addresses this by providing a data rate predictor, trained offline on simulated data, enabling fast candidate evaluation without access to the real network or its digital twin. The surrogate architecture is shown in Fig. 16 (Appendix C). 1) Architecture: The surrogate model takes the embedded graph representation as input and predicts the expected effective data rate. The architecture mirrors the backbone of the FM model, and the final global features are projected to the parameters of a Gaussian mixture model following the mixture density network (MDN) [18] framework. 2) Mixture Density Network: The output layer produces 3m values per graph, where m is the number of mixture components. These are split into mixture logits α ∈ Rm , means µ ∈ Rm , and scales σ ∈ Rm + . The weights of the mixture are obtained as wk = softmax(α) k . The target is P the aggregate data rate, defined as e∈Esel re · se where Esel is the set of selected edges, re is the PHY-layer data rate of edge e, and se is the observed success probability. For the sake of training stability, the data rate is standardized as r̃e = (re − µrate )/σrate with µrate = 657.2 Mb/s and σrate = 462.2 Mb/s, resulting from a training set. The model is trained by minimizing the NLL of the standardized data rate under the predicted mixture [18]: m X LMDN = − log wk · fN (r̃e | µk , σk2 ). (7) k=1

During inference, the pipeline components are combined as illustrated in Fig. 2: 1) Context encoding. Given the current scenario and n recent random network observations, each observation is converted to a graph and encoded by the frozen GNN encoder. 2) Candidate generation. The encoded context is batched into Ncand copies, each paired with an independent noise sample, and the FM model generates Ncand candidate configurations in parallel by solving ODE with the Euler method. 3) Evaluation and selection. All Ncand candidates are scored by the surrogate model, and the top-k configurations with the highest expected data rate are retained. 4) Decoding. Latent vectors of the top-k candidates are decoded by the decoder and the attributes are extracted to obtain a valid scheduling decision (i.e., exactly one STA per active AP), with MCS index and transmission power level sampled from categorical distributions to maintain diversity across Co-SR configuration candidates. 5) Execution. The selected configurations are applied to the network for the next TXOPs. Drawing multiple Co-SR configuration candidates in parallel is motivated by the analysis in [19]. For a generative model that has learned the underlying solution distribution, the probability of at least one of Ncand independent samples falling within of the optimal solution increases as  an ϵ-neighborhood  D Ncand 1 − 1 − (1 − ϵ) , where D is the dimensionality of the solution space. This probability approaches 1 for sufficiently large Ncand , so even when individual samples are suboptimal, parallel sampling combined with surrogate scoring enables the pipeline to approximate the optimum with high probability. Because channel conditions and associations change much slower than individual TXOPs, a well-chosen Co-SR configuration can be reused across many consecutive TXOPs before recalculation is needed. Therefore, the proposed pipeline produces a set of Co-SR configurations that is reused in consecutive TXOPs until conditions change (e.g., new associations or significant performance degradation). The Co-SR configuration candidates can be applied in a round-robin fashion or scheduled with an external algorithm, e.g., [9], providing temporal diversity or reducing latency. IV. I MPLEMENTATION All experiments use mapc_sim [7], an open-source JAXbased IEEE 802.11 Co-SR simulator; simulation parameters are given in Table II and the full software stack in Appendix C.

Parameter

Value

Band PHY Channel width Spatial streams MCS values Transmission power levels Path loss model Multipath fading Noise floor CCA threshold Frame size TXOP limit Traffic

5 GHz IEEE 802.11be 80 MHz 1, SISO {0, 1, . . . , 13} {16, 13, 10, 7} dBm TGax enterprise [20] Additive white Gaussian noise −94 dBm −82 dBm 1500 B 5.484 ms Full buffer, downlink

Y [m]

F. Full Inference Pipeline

TABLE II: Simulation parameters used in all experiments.

Y [m]

3) Candidate Selection: The mixture density output is used for candidate selection. Given the predicted mixture weights w Pk and component parameters, the expected data rate is r̄e = k wk µk . Candidates are ranked by their expected data rate, and the top-scoring configurations are retained.

X [m]

(a) Residential topology

X [m]

(b) Enterprise topology

Fig. 5: Example topologies of the scenarios: (a) residential (structured room layout with walls), (b) enterprise (regular AP grid without walls; dashed lines indicate room boundaries).

A. Training Scenarios Network topologies are drawn from a set of parameterized scenarios that can be instantiated with varying AP/STA counts, spatial layouts, and radio parameters. Moreover, different baseline models are used to generate Co-SR configurations for training and validation datasets. To train models that generalize across diverse network deployments, we use many parameterized scenario types that span a wide range of topologies. These include (i) small topologies (2 APs with variable inter-AP distances of 1–50 m), (ii) structured residential scenarios from [20] (rooms arranged in grids from 2x2 to 5x2 square rooms with 1 AP and 1– 6 STAs per room, 5–20 m room width, with walls providing additional attenuation), (iii) open-space random deployments (2–10 APs, 1–5 STAs per AP, in square areas with a width of 20–100 m), (iv) dense co-located deployments (2–10 APs, 1– 5 associations each), (v) indoor small basic service sets (BSSs) scenarios from [20], and (vi) challenging interference patterns (hidden node and flow-in-the-middle topologies). Network sizes range from 2 APs with 2 STAs to 10 APs with up to 50 STAs. During dataset generation, scenarios are sampled with a probability proportional to the number of their configurable parameters, ensuring that scenarios with larger parameter spaces (which exhibit greater variability and thus require more samples for adequate coverage) contribute proportionally more

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Fig. 6: FM4WiFi sample count scaling for residential scenarios: solid curves (left axis) show effective data rate; dashed curves (right axis) – inference time. training data. For each sampled scenario type, a realization is drawn by uniformly sampling all parameters within their respective ranges. B. Baseline Configuration Algorithms For each scenario realization, Co-SR configurations are generated using four complementary algorithms: • Random: uniform random sampling of AP–STA pairs, transmission power levels, and MCS index values. • H-MAB: hierarchical multi-armed bandits (H-MABs) proposed in [3]. Three levels of agents sequentially select active APs, recipient STAs, and transmission power, while MCS values are selected by an oracle. • F-Optimal: max-min fairness upper bound solver, following the formulation in [3]. • T-Optimal: maximum aggregate data rate upper bound solver, optimized for total throughput [3]. This mixture ensures that the training data covers both optimal configurations (F-Optimal, T-Optimal) and the broader configuration landscape (Random, H-MAB), allowing the generative model to learn the underlying structure of viable Co-SR configurations. No deep reinforcement learning (DRL) baseline is included: the only directly relevant DRL scheme for Co-SR configuration generation, SAIOC [8], does not provide a public implementation, and we found no other reproducible DRL baseline addressing the same problem. Additionally, we do not compare directly against legacy IEEE 802.11 operation because it is consistently outperformed by H-MAB in Co-SR scenarios [3]. Finally, we note that only FM4WiFi provides MCS selection, while the other baselines assume perfect MCS values. Therefore, to isolate scheduling quality, we also report FM4WiFi with the same oracle MCS to enable a more direct and fair comparison with the state-of-the-art baselines. C. Dataset Composition For each baseline algorithm, we generate a training set (1,000 scenario realizations) and a validation set (200 realizations). Each realization contributes 5–50 Co-SR configurations

2,000 2x2

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Fig. 7: FM4WiFi top-k selection scaling for residential scenarios with 128 generated candidates: solid curves (left axis) show effective data rate, and dashed curves (right axis) show Jain’s fairness index.

depending on the algorithm (5 for T-Optimal, 30 for Random and F-Optimal, 50 for H-MAB), yielding ∼ 138,000 examples in total. The random dataset is excluded from FM training because it contains degraded configurations that would bias the generative model. The autoencoder is trained on all four baseline datasets, including the random Co-SR configurations. The surrogate model is trained separately on configurations generated by the trained FM model and evaluated in the simulator to obtain ground-truth data rates. V. E VALUATION We first characterize the evaluated scenario families and inference-time design choices, then benchmark FM4WiFi against established static-scenario baselines, and analyze periodic regeneration under mobility. Fig. 5 illustrates the scenario families used throughout this section. Residential topologies [20] make it straightforward to build realistic large-scale indoor deployments with structured propagation constraints (i.e., walls). In contrast, enterprise topologies arrange APs on a regular grid with stations randomly placed within each cell, but without walls. We additionally evaluate the proposed approach on open-space topologies, in which APs are placed randomly within a 75 m × 75 m area without walls, and station positions are drawn from a normal distribution centered at their associated AP with variable standard deviation. Each open-space topology has 2– 5 APs and 3–5 stations per AP. Halfway through each openspace simulation, all station positions are redrawn to introduce a sudden topology change. A. Scalability and Number of Samples Fig. 6 evaluates the effect of candidate-set size under a fixed top-1 selection policy. To isolate the effectiveness of FM sampling, generated candidates are evaluated directly in the simulator rather than through the surrogate model. Each data point is averaged over three realizations of each scenario type with different random node placements. Effective data

Effective data rate [Mbit/s]

4,000

T-Optimal FM4WiFi (oracle MCS)

F-Optimal FM4WiFi

H-MAB

T-Optimal F-Optimal

Resource limit for analytical models Resource limit for H-MAB

H-MAB

3,000

FM4WiFi (oracle MCS) FM4WiFi

2,000

0

1,000

1,500

2,000

Effective data rate [Mbit/s]

1,000 H-MAB stage [%]

0

500

0

50

2x2 2x3 3x3 3x4 4x4 4x5 5x5 Number of APs in scenario

100

Fig. 9: Effective data rate distribution across open-space scenarios with 2–5 APs.

5x6

Fig. 8: Effective data rate across scenario sizes. Curves are shown for visual guidance. Dashed H-MAB curves show intermediate convergence stages; vertical dashed lines – tractability limits for H-MAB and analytical baselines, respectively.

rate grows roughly linearly with the number of samples, reaching diminishing returns beyond 128 candidates for small networks. The reported GPU time covers only the compiled inference pipeline; input graph construction on the CPU is excluded as it is negligible relative to GPU overhead. GPU time scales quadratically with the number of samples and the network size, staying below 50 ms for 64 candidates in the 2x2 scenario and approximately 1 s for the 4x4 scenario. The quadratic scaling stems from the transformer’s self-attention mechanism. Notably, generating all candidates in a single large batch is suboptimal: since graphs within a batch are masked from one another to keep their computations independent, the joint attention matrix becomes highly sparse, wasting compute. Generating candidates in smaller batches is therefore more efficient in practice. We adopt 128 samples as the default operating point, balancing throughput gains against GPU latency. Next, we analyze the effect of selecting the top-k candidates instead of the single highest-ranked one (Fig. 7). Since not all stations are involved in a single Co-SR candidate, top1 selection can over-focus on a subset of stations. Keeping the top-k provides a practical fairness–data rate trade-off: data rate decreases moderately while Jain’s fairness index improves substantially (e.g., from 0.15 to 0.73 for the 2x2 scenario). We set k = 8 as the default since it typically covers all stations while preserving a strong data rate. B. Static Scenarios All static experiments use residential scenarios with room widths of 10 m, 1 AP and 4 STAs per room with random placement and topologies ranging from 2x2 to 5x6 apartments. For FM4WiFi, the full inference pipeline (128 candidates, top 8 selected) is executed 32 times per scenario; for each run,

the reported value is the mean over 5 simulator evaluations of the selected configurations, and the final result is the mean across all runs. T-Optimal and F-Optimal are deterministic and computed once per scenario. For H-MAB, the reported value is the mean over the last 20% of the run, after convergence or upon reaching the computation budget; analytical baselines (TOptimal, F-Optimal) are granted up to 12 hours per scenario, while H-MAB is additionally limited by memory: at larger scales, agent initialization exceeds available RAM and the method cannot run at all. Fig. 8 compares FM4WiFi (with and without oracle MCS) with H-MAB, F-Optimal, and T-Optimal. T-Optimal achieves the highest data rate but imposes no fairness constraints, starving all but a few selected stations. F-Optimal enforces equal per-station rates and serves as a more practical upper bound. At small scales (2x2–3x3), H-MAB outperforms FM4WiFi even with oracle MCS, benefiting from online adaptation to a single topology. As the network grows, H-MAB’s data rate degrades and it fails to converge within the time budget, while FM4WiFi with oracle MCS overtakes it at 12 APs (3x4), staying within 7% of F-Optimal at larger scales. Beyond 16 APs (4x4), H-MAB becomes intractable, and beyond 20 APs (4x5) so do the analytical baselines, while FM4WiFi scales to 30 APs (5x6) and beyond. Wall-clock cost follows the same ordering: in the 4x4 scenario, FM4WiFi generates and scores 128 candidates in 0.62 s, whereas T-Optimal requires 29.7 s, FOptimal nearly 50 minutes, and H-MAB does not converge at all (Table IX). Fig. 9 further evaluates small open-space networks (2– 5 APs), using 24 scenario realizations evaluated twice (i.e., before and after the mid-simulation position is redrawn), producing 48 data points in total. When comparing under equal conditions (oracle MCS), FM4WiFi matches H-MAB – the medians are 542 Mbit/s and 505 Mbit/s, respectively, with near-identical distributions. Both methods exhibit high variability across scenario instances, reflecting the diversity of random topologies rather than instability of the algorithms. C. Dynamic Scenarios FM4WiFi is designed for static snapshots: given the current network state, it outputs a Co-SR configuration for that

800 400

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Fig. 11: Effective data rate for the 3x3 enterprise scenario. Stations move freely and may reassociate; 10 new stations join every 4 s (right axis). Vertical lines mark reassociations.

400

MCS) cyclic [0.5 s] outperforms the no-regeneration baseline by roughly 25%, at the cost of higher throughput variability. H-MAB converges even more slowly in this larger topology, 0 0 5 10 15 20 staying well below all FM4WiFi (oracle MCS) curves while achieving only slightly better performance than FM4WiFi with Time [s] its own MCS selection. Individual per-seed traces for this (b) Room size 20 m, without walls. scenario are provided in Appendix F. Finally, Fig. 11 evaluates the most demanding enterprise Fig. 10: Effective data rate over time for the 4x4 residential scenario with mobility. Dashed lines show FM4WiFi with its scenario representing managed venues where APs are centrally own MCS selection; solid lines – FM4WiFi with oracle MCS. coordinated and the number of connected stations grows over time. This highly demanding and strongly dynamic setup reflects realistic enterprise deployments. The scenario starts moment. Therefore, for dynamic operation, we recommend with 46 stations; every 4 s, 10 new stations join, reaching periodic recomputation. All dynamic results are averaged over 86 by the end. Stations also move freely throughout the area, five independent runs; instantaneous throughput is reported as triggering reassociations when a closer AP is found; each a 0.2 s moving average. Stations follow a random waypoint such event is marked by a vertical line. FM4WiFi responds to mobility model (with a speed sampled from U [0.3, 1.5] m/s each join or reassociation by immediately running inference and a pause – from U [0, 5] s) in a 4x4 residential layout. We on the updated network state. Despite continuous disruptions, compare a one-shot configuration with cyclic regeneration of FM4WiFi with oracle MCS maintains a stable throughput the Co-SR configuration at intervals of 0.5, 1, and 2 s. Fig. 10a around 680 Mbit/s to 760 Mbit/s, recovering quickly after shows results for a room width of 10 m (with walls), while each event. H-MAB, by contrast, maintains a static action Fig. 10b presents results with walls removed and a room width space tied to the current set of associated stations: any join of 20 m. or reassociation requires complete reset and relearning from In Fig. 10a, stations move within their rooms to avoid scratch. Faced with continuous disruptions, H-MAB never reassociation. This is the simplest of the dynamic scenarios: converges and stays flat around 400 Mbit/s to 480 Mbit/s walls partition the interference structure, so the link conditions throughout the run, well below both FM4WiFi variants. This remain largely stable despite mobility. FM4WiFi (oracle MCS) challenging scenario demonstrates that FM4WiFi, even withachieves a data rate around 1100 Mbit/s to 1400 Mbit/s, out an MCS oracle, can outperform a state-of-the-art solution confirming that a single generated configuration is sufficient (H-MAB) operating with perfect MCS selection. under these conditions. H-MAB starts well below FM4WiFi (oracle MCS) and is still visibly converging at t = 20 s. D. Experimental Validation FM4WiFi, despite the decreased performance due to MCS For experimental validation, we use an indoor testbed selection, maintains consistency over time. with six APs, eight stations, and an FM4WiFi controller In Fig. 10b, stations also stay within the initial room (Fig. 12). We use FM4WiFi sampling 128 candidates and boundaries. However, with walls removed, the propagation top-4 selection. The model is not retrained, so it operates environment changes more as stations move, leading to often zero-shot on a previously unseen topology and, for the first radical changes in interference patterns. Consequently, peri- time, in a real-world environment. The APs are laptops with odic regeneration yields significant gains: for FM4WiFi (oracle Atheros AR9271 cards running Modwifi [21] for low-level 200

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Fig. 12: Experimental topology (indoor office). 250 Maximum Mean with 95% CI

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Fig. 13: Throughput of FM4WiFi and the baselines in the testbed: 20 MHz channels, fixed MCS 6. Numbers above the bars give the mean simultaneous transmissions (± std. dev.). The gradient on the H-MAB bar marks its convergence period. The trends match the 2x3 AP simulation results in Fig. 8.

control over frame transmissions; the stations are Raspberry Pi 3B+ boards running Nexmon [22] for monitor-mode access to raw IEEE 802.11 frames. To enable simultaneous transmissions, carrier sensing and random backoff are disabled, and a lightweight scheduler in the AR9271 firmware releases frames at absolute timestamps based on the local timing synchronization function (TSF) timer, with a median timing error below 2 µs. Results show that FM4WiFi on average outperforms simple baseline schedulers: single-transmission round-robin and simultaneous transmissions by all APs. H-MAB gives higher throughput, but only after convergence. Altogether, these results confirm that FM4WiFi can be used in practical deployments. VI. D ISCUSSION FM4WiFi combines features that no previous approach has, namely scalability, speed, and topology independence, but in its current form it remains a starting point. We discuss the key trade-offs and open directions below. Because learning is performed offline, FM4WiFi cannot fine-tune to a specific deployment over time. Online methods such as H-MAB learn the exact interference structure of a

fixed topology, which is why they can outperform FM4WiFi on small scales. The offline approach is most advantageous when deployment diversity is high; a static long-term deployment could benefit from continual online adaptation on top of the pretrained model. FM4WiFi primarily optimizes the aggregate effective data rate rather than per-station fairness. Co-SR inherently favors stations selected for concurrent transmissions, so some stations may experience longer access delays. The current top-k selection partially mitigates this, but a richer strategy maximizing coverage diversity across the sample set could better balance throughput, fairness, and latency. The proposed deployment has two hard requirements: a central controller with wired backhaul to all APs, and a hardware accelerator for sub-second inference. Furthermore, as a stochastic method, FM4WiFi provides no deterministic throughput or latency guarantees. In particular, individual samples may be suboptimal, and the surrogate predictor adds approximation error. Deployments with hard quality of service requirements would need additional safeguards. Finally, because the surrogate is trained on FM-generated configurations, it may not generalize well to configurations outside the FM model’s support; retraining on a broader simulated distribution is a natural mitigation. Due to the absence of baselines with joint MCS selection, the non-oracle results of FM4WiFi lack a direct point of comparison and require further validation as such baselines emerge. Beyond addressing these limitations, future work includes extending FM4WiFi to uplink Co-SR (not planned for Wi-Fi 8, yet easy to add in our method) and mixed-traffic scenarios, exploring continual adaptation to specific deployments, and systematically quantifying how approximation errors compound across the autoencoder, FM, and surrogate stages. VII. C ONCLUSIONS The complexity of Co-SR scheduling is a fundamental barrier to coordinated Wi-Fi at scale: existing heuristic, solverbased, and RL-driven approaches all share one failure mode, their cost or convergence time grows with network size. We address this by reframing Co-SR scheduling as a conditional generation problem. FM4WiFi learns the distribution of high-quality Co-SR configurations offline and, conditioned on the current network state, samples from it in under one second regardless of network size. This shift from search to generation unlocks Co-SR scalability: FM4WiFi handles 30+ APs with sub-second inference and jointly optimizes group formation, station selection, MCS, and transmission power. The method is both fast and effective, matching or exceeding baselines at medium and large scales and maintaining high throughput under continuous topology changes. Crucially, this is not a simulation-only result: on a six-AP testbed built from commercial off-the-shelf hardware, FM4WiFi operated zeroshot on a previously unseen topology and outperformed the random, round-robin, and all-AP baselines. An ablation study (Appendix D) confirms that each component contributes to

FM4WiFi’s performance. More broadly, for MAC-layer problems whose action space is too large to enumerate and whose environments are too diverse for per-deployment learning, our results suggest that offline generative models, following a learn-once, deploy-anywhere paradigm, are a promising way forward. R EFERENCES [1] W. Ning, F. Tang, M. Zhao, and N. Kato, “A Survey on IEEE 802.11bn Wi-Fi 8: Advantages of Ultra High Reliability for Next-Generation Wireless LANs,” IEEE Communications Surveys & Tutorials, vol. 28, pp. 4215–4247, 2025. [2] I. Val, D. López-Pérez, A. Kijanka, S. Schelstraete, L. Muñoz, D. Arlandis, and M. Martínez, “Wi-Fi 8 unveiled: Key features, multiAP coordination, and the role of C-TDMA,” IEEE Communications Magazine, 2025. [3] M. Wojnar, W. Ci˛eżobka, A. Tomaszewski, P. Chołda, K. Rusek, K. Kosek-Szott, J. Haxhibeqiri, J. Hoebeke, B. Bellalta, A. Zubow, F. Dressler, and S. Szott, “Coordinated Spatial Reuse Scheduling With Machine Learning in IEEE 802.11 MAPC Networks,” IEEE Journal on Selected Areas in Communications, vol. 43, no. 11, pp. 3666–3682, 2025. [4] J. Y. G. et al., “LB291 CR for Co-BF and CoSR MISC Part 2,” 2026, accessed on March 2, 2026. [Online]. Available: https://mentor.ieee.org/802.11/dcn/26/ 11-26-0287-01-00bn-lb291-cr-for-co-bf-and-co-sr-misc-part-2.docx [5] J. Haxhibeqiri, X. Jiao, X. Shen, C. Pan, X. Jiang, J. Hoebeke, and I. Moerman, “Coordinated Spatial Reuse for WiFi Networks: A Centralized Approach,” in 2024 IEEE 20th International Conference on Factory Communication Systems (WFCS), 2024, pp. 1–8. [6] D. Nunez, M. Smith, and B. Bellalta, “Multi-AP Coordinated Spatial Reuse for Wi-Fi 8: Group Creation and Scheduling,” in 2023 21st Mediterranean Communication and Computer Networking Conference (MedComNet), 2023, pp. 203–208. [7] M. Wojnar, W. Ciezobka, K. Kosek-Szott, K. Rusek, S. Szott, D. Nunez, and B. Bellalta, “IEEE 802.11bn Multi-AP Coordinated Spatial Reuse With Hierarchical Multi-Armed Bandits,” IEEE Communications Letters, vol. 29, no. 3, pp. 428–432, 2025. [8] J. Jung, G. Lee, and J.-M. Chung, “Coordinated Spatial Reuse With Shared AP Index Optimization for IEEE 802.11be WLAN Enhancement,” IEEE Transactions on Network Science and Engineering, vol. 13, pp. 930–947, 2026. [9] D. Nunez, F. Wilhelmi, M. Wojnar, K. Kosek-Szott, S. Szott, and B. Bellalta, “Deep Reinforcement Learning-Based Scheduling for Wi-Fi Multi-Access Point Coordination,” 2025. [10] D. Zhu, L. Wang, G. Pan, and S. Luan, “Two enhanced schemes for coordinated spatial reuse in IEEE 802.11be: Adaptive and distributed approaches,” Computer Networks, vol. 258, p. 111060, 2025. [Online]. Available: https://www.sciencedirect.com/science/article/pii/ S1389128625000283 [11] J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals, and G. E. Dahl, “Neural message passing for quantum chemistry,” in Proceedings of the 34th International Conference on Machine Learning - Volume 70, ser. ICML’17. JMLR.org, 2017, pp. 1263–1272. [12] P. W. Battaglia, J. B. Hamrick, V. Bapst, A. Sanchez-Gonzalez, V. F. Zambaldi, M. Malinowski, A. Tacchetti, D. Raposo, A. Santoro, R. Faulkner, Ç. Gülçehre, H. F. Song, A. J. Ballard, J. Gilmer, G. E. Dahl, A. Vaswani, K. R. Allen, C. Nash, V. Langston, C. Dyer, N. Heess, D. Wierstra, P. Kohli, M. M. Botvinick, O. Vinyals, Y. Li, and R. Pascanu, “Relational inductive biases, deep learning, and graph networks,” CoRR, vol. abs/1806.01261, 2018. [13] D. P. Kingma and M. Welling, “Auto-Encoding Variational Bayes,” 2014. [14] D. Hendrycks and K. Gimpel, “Bridging nonlinearities and stochastic regularizers with gaussian error linear units,” CoRR, vol. abs/1606.08415, 2016. [15] Y. Lipman, R. T. Q. Chen, H. Ben-Hamu, M. Nickel, and M. Le, “Flow matching for generative modeling,” 2023. [16] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. u. Kaiser, and I. Polosukhin, “Attention is all you need,” in Advances in Neural Information Processing Systems, I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus,

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A PPENDIX A R ELATED W ORK The IEEE 802.11bn task group has defined a common framework for MAPC coordination (including Co-SR) and procedures for discovery and negotiation [23]. The expected adoption of MAPC in future Wi-Fi networks [1] has motivated research on optimizing Co-SR, yet existing approaches struggle to balance decision quality with strict real-time MAC constraints. a) Analytical and heuristic models: Early continuous time Markov chain (CTMC)-based studies show up to 59% throughput gains [24] but rely on saturated traffic assumptions. Practical systems typically use centralized controllers driven by periodic RSSI reports [5], [6], which introduce a latency loop that degrades performance under mobility. Distributed schemes using convex optimization [10] or coordinated time division multiple access (Co-TDMA) [25] reduce signaling but remain intractable at scale due to the combinatorial groupformation space. b) RL in MAPC: To overcome the rigidity of heuristics, RL has been widely adopted. Multi-armed bandit (MAB) formulations provide robust adaptation without a priori knowledge of the channel [3], [7]. Deep RL (DRL) approaches offer joint interference detection and power control, often using multi-agent frameworks to decentralize execution [8], [26]. Recent work [9] has demonstrated improved latency by scheduling pre-formed Co-SR configurations. Schemes such as SAIOC [8] require more than 20,000 training episodes to converge and no public implementation is available. In general, a fundamental limitation identified by surveys is that DRL agents often exhibit high sensitivity to reward function design and lack of robustness to dynamic distribution shifts in network state [27], [28]. c) Generative AI for wireless optimization: Beyond RL, recent research has explored generative artificial intelligence (AI) as a means to model the complex underlying distributions of feasible network states [27], [29]. Although early efforts used generative adversarial networks (GANs) for channel estimation and resource allocation, surveys highlight their inherent training instability and the tendency toward mode collapse in high-dimensional wireless data [28]. This has led to an emerging preference for generative diffusion models (GDMs), which offer superior stability and the ability to capture multimodal action distributions [28], [30]. Nevertheless, GDMs suffer from an iterative “denoising bottleneck” that restricts their application to static or slow-varying snapshots. Simultaneously, agentic AI frameworks utilizing large language models (LLMs) have been proposed for multi-AP negotiation [31], although their multi-second inference latency remains orders of magnitude too slow for MAC-layer scheduling. A PPENDIX B N/A-G ATED C ATEGORICAL L OSS D ERIVATION The decoder outputs C logits l ∈ RC , interpreted as a mixture via pN/A = σ(lC ),

π = softmax(l1:C−1 ).

(8)

The mixture assigns probability pN/A when yC = 1 (attribute is N/A), and probability (1−pN/A ) Pcat (y1:C−1 ) when yQC = 0 (attribute takes a valid class), where Pcat (y1:C−1 ) = C−1 yi i=1 πi . Using yC as an indicator to unify both cases: h i1−yC yC . (9) · (1 − pN/A ) Pcat (y1:C−1 ) P (y) = pN/A Taking the negative logarithm of (9) and expanding: − log P (y) = −yC log pN/A − (1 − yC ) log(1 − pN/A ) − (1 − yC ) log Pcat (y1:C−1 ).

(10)

Substituting pN/A = σ(lC ) and log Pcat (y1:C−1 ) = PC−1 i=1 yi log πi into (10), each term is recognized as a standard loss:
− log P (y) = −yC log σ(lC ) − (1 − yC ) log 1 − σ(lC ) {z } | LBCE (lC , yC )

" + (1 − yC ) −

C−1 X

# yi log πi .

(11)

i=1

|

{z

}

(1−yC ) LCE (l1:C−1 , y1:C−1 )

This gives the final form (2): Lmix (l, y) = LBCE (lC , yC ) + (1 − yC ) LCE (l1:C−1 , y1:C−1 ). A PPENDIX C A RCHITECTURE AND T RAINING D ETAILS Figures 14–16 illustrate the training-time operation of the three pipeline components. The inference pipeline, which combines these components, is shown in Fig. 2 in the main text. Table III summarizes the architecture and training hyperparameters. The entire pipeline is implemented in JAX [32] with GNN primitives provided by Jraph [33] and neural network modules defined using Flax [34]. Optimization is handled by Optax [35], checkpointing by Orbax [36], and data loading by Grain [37]. Hydra [38] manages configuration files and the Weights & Biases [39] platform tracks training experiments. We use mapc_sim [7], an open-source JAX-based IEEE 802.11 simulator that models MAPC operation, including Co-SR frame exchanges. It computes per-link data rates based on SINR, taking into account interference from concurrent transmissions. A. More Training Details All three FM4WiFi models (i.e., autoencoder, FM, and surrogate) are trained using the AdamW optimizer [40] with gradient clipping (global norm ≤ 1.0). The autoencoder and FM use (β1 , β2 ) = (0.95, 0.95) following [41]; the surrogate uses the standard values (0.9, 0.999) for training stability. The autoencoder and FM models use a constant learning rate, while the surrogate model uses a cosine learning rate schedule to improve convergence in the last phase of training. Graphs are batched and padded to power-of-two sizes for efficient GPU compilation. All models use float64 precision to ensure numerical stability. Table III (Appendix C) summarizes the

TABLE III: AdamW optimizer and training hyperparameters for each model family. Within each family, all settings except the learning rate are shared across sizes; the learning rate is tuned independently per size. Model Family Autoencoder Flow matching Surrogate

β1 0.95 0.95 0.9

β2

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LR (Small)

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−4

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−5

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Fig. 14: GNN autoencoder: the encoder maps edge attributes to per-edge latent vectors ze ; the decoder reconstructs the original attributes from the latent graph. Context encoding

Denoising

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+z Encoder

Fig. 15: Flow matching training: a velocity network learns to transport noise toward the data distribution, conditioned on encoded context configurations.

architecture and training hyperparameters for each model. For performance tests, we use a server with NVIDIA GH200, 118 GB of RAM, and Rocky Linux 9. 1) Autoencoder: We set the KL divergence weight λKL = 0.01 to balance two competing goals: the FM model assumes a Gaussian source distribution p(z) = N (0, I) when generating samples from noise, so the aggregate posterior should approximate this prior; at the same time, too large a λKL risks posterior collapse, where qϕ (z|G) ignores the input and the decoder loses reconstruction fidelity. We verify this setting in Section D-A. During inference, only the mean µe is used (no sampling), ensuring deterministic encoding. Following the graph network framework, information is stored at three levels: nodes represent individual APs and STAs (initialized without features, they accumulate information through message

Fig. 16: Surrogate data rate predictor: the model takes an encoded graph and outputs the parameters of a Gaussian mixture predicting the effective data rate.

passing), edges carry per-link attributes, and a global vector (initially empty) summarizes the entire network state. 2) Flow Matching: The FM model loads the frozen encoder from a trained autoencoder checkpoint. During data preparation, each training example is augmented with n context configurations (ablated in Section D-B; we find n = 1 to be optimal) generated by running random transmissions through the simulator and encoding the resulting graphs. The time variable t is sampled uniformly from [0, 0.99). Both standard and EMA parameters are tracked, with EMA parameters used for validation and inference. 3) Surrogate: The surrogate is trained on configurations generated by the FM model and evaluated in the simulator, rather than on the original baseline dataset. This ensures that the surrogate learns to score the kinds of configurations actually produced at inference time. Like the FM model, the surrogate operates on latent representations of the network. The number of components in the mixture is fixed at m = 4 as a practical quality–complexity trade-off (Section D-C), while larger mixtures can slightly reduce validation NLL. We ensure that the scales σ remain positive by applying softplus activation. A PPENDIX D A BLATION S TUDIES We perform ablation studies to isolate the impact of key modeling and optimization choices. Because the full pipeline has inter-model dependencies, each model is ablated independently and evaluated with model-specific metrics to avoid confounding effects across stages; consequently, this section does not report end-to-end metrics. We vary one factor at a time and keep other settings unchanged to make comparisons attributable to the modified component; when a new setting is

TABLE IV: Effect of KL regularization strength β on GNN autoencoder reconstruction accuracy and latent-space regularity. β=0 yields near-perfect reconstruction but an unstructured latent space; β=0.01 preserves high accuracy while substantially reducing KL divergence. Model Size

β

MCS Accuracy [%] ↑

TX Power Accuracy [%] ↑

RSSI Accuracy [%] ↑

KL Divergence ↓

0.0 0.01 1.0

98.7 96.2 26.2

99.6 99.3 31.8

97.6 72.1 17.1

61.806 1.028 0.174

0.0 0.01 1.0

100.0 99.9 71.9

100.0 100.0 86.3

98.8 88.4 27.2

14.568 0.325 0.027

0.0 Medium 0.01 1.0

100.0 100.0 91.4

100.0 100.0 94.8

99.4 92.2 30.3

6.735 0.183 0.019

0.0 0.01 1.0

100.0 100.0 97.1

100.0 100.0 97.8

99.7 91.8 34.5

5.226 0.110 0.013

Tiny

Small

Large

found to be beneficial, we adopt it for all subsequent ablations and main experiments. For each model family (autoencoder, flow matching, surrogate) and each size (tiny, small, medium, large), we tune the learning rate. Model sizes correspond to approximately 10k (tiny), 100k (small), 1M (medium), and 10M (large) trainable parameters, excluding time embeddings. Due to the large number of configurations explored, each ablation is a single run; the main evaluation results in the preceding sections use multiple seeds with statistical analysis. All ablation experiments use a 20 MHz channel bandwidth; while absolute data rates are lower than in the main evaluation, the relative comparisons remain qualitatively valid. In all tables, the best value per group is shown in bold; when a second-best result is within the rounding precision, it is also in bold. A. Autoencoder a) KL regularization strength.: As shown in Table IV, with β = 0, the autoencoder reaches a near-perfect reconstruction but produces an unregularized latent space (high KL divergence). In contrast, strong regularization (β = 1) damages reconstruction, especially for RSSI. In our setting, β = 0.01 provides the best balance: it preserves nearperfect MCS/transmission power accuracy4 while substantially reducing the KL term, suggesting a more structured latent representation without sacrificing fidelity. From this point on, we set β = 0.01 and use it for all subsequent ablation studies and experiments. b) N/A-gated categorical loss.: We compare our proposed N/A-gated categorical loss against a classic softmax baseline. Table V reports the five metrics with the most significant differences in accuracy, which occur predominantly for 4 For categorical attributes, N/A accuracy measures correct N/A vs. nonN/A classification; prediction accuracy measures correct class prediction among non-N/A edges. For continuous attributes, prediction accuracy counts edges with an absolute error below 0.1.

TABLE V: Five largest accuracy deltas when replacing our proposed N/A-gated categorical loss (2) with standard softmax cross-entropy (negative values indicate softmax is worse). Feature

Model Size

N/A-gated Accuracy [%]

Softmax Accuracy [%]

Difference [%]

Selected (N/A) MCS (pred.) Selected (N/A) Active (N/A) Transmission power (pred.)

Small Tiny Tiny Medium

100.00 96.19 99.99 100.00

87.13 94.14 98.07 98.22

-12.87 -2.13 -1.91 -1.78

Tiny

99.25

98.07

-1.19

TABLE VI: PCA characterization of the learned latent space for four autoencoder sizes (β=0.01). The number of principal components required to explain 90%, 95%, and 99% of variance grows sub-linearly with dimensionality, suggesting an intrinsic dimensionality of roughly 10–17. Metric

Tiny

Small

Medium

Large

Latent dim PCA dims (90% var.) PCA dims (95% var.) PCA dims (99% var.) Top-1 PCA explained var.

6 4 5 6 47%

16 7 8 10 38%

32 9 11 18 34%

64 13 17 34 33%

the tiny and small models. This concentration indicates that our proposed loss function is particularly important for preserving performance at smaller scales. The largest regression appears for Selected (N/A) in the small model (absolute drop of 12.87 pp.), indicating that softmax substantially degrades the link-selection decision in this setting. For the remaining metrics, the gap is comparatively small (about 1 % to 2 % absolute), suggesting that softmax preserves prediction accuracy (e.g., MCS and transmission power values) but struggles with the higher-level objectives. c) Dimensionality.: Table VI summarizes the principal component analysis (PCA) structure of the learned latent spaces depending on the dimension dz ∈ {6, 16, 32, 64}. Effective utilization grows sub-linearly with dz : 95% of variance is explained by 5 out of 6 dimensions for tiny but only 17 out of 64 for large. The variance also becomes more evenly spread: the first principal component accounts for 47% of variance in the tiny model and only 33% in large. These observations suggest that the Wi-Fi configuration space has a latent dimensionality of roughly 10–17, so that 32 latent dimensions are sufficient for high-fidelity encoding, while 64 dimensions add redundancy without clear benefit. Therefore, we use the medium-sized model for all experiments. d) Interpolation quality.: To assess whether interpolated latent vectors remain realistic, we use the maximum mean discrepancy (MMD), a kernel-based distance between probability distributions. Fig. 17 reports MMD between interpolants and the training distribution at ratios α ∈ {0, 0.1, . . . , 1}. All models exhibit a gentle, midpoint peak (maximum near α ≈ 0.4), yet the absolute increase is small (< 0.01 MMD). Crucially, all interpolants remain far below the random noise

100

Loss MMD

Metric value ↓

Latent MMD ↓

0.19 0.18 0.17 Tiny Small

0.16 0

0.2

Loss (EMA) MMD (EMA)

10−1

Medium Large

0.4 0.6 0.8 Interpolation parameter α

1

Fig. 17: MMD between linearly interpolated latent vectors and the training distribution as a function of the interpolation ratio α. All models show a gentle midpoint peak at α ≈ 0.4, yet remain far below the random-noise baselines (tiny: 0.43, small: 0.73, medium: 0.76, large: 0.76), confirming that interpolants stay on the learned manifold.

baselines: tiny’s baseline is 0.43 (lower due to the compact 6dim space), while the baselines for other sizes are 0.73–0.76 (not shown in the figure). This confirms that interpolated latent vectors stay within the learned manifold rather than drifting into unstructured regions. B. Flow Matching We ablate the key design choices of the FM model: latentspace formulation and denoising scope, model scaling, EMA of parameters, timestep sampling schedule, number of context observations, and ODE solver configuration. Unless stated otherwise, ablations use the medium-sized model with n = 7 context observations and the Euler solver with 10 integration steps. When a better configuration is identified, it is adopted for all subsequent ablations and main experiments; the final configuration is n = 1 with 6 Euler steps. a) Formulation.: Table VII compares three FM variants: (i) continuous FM denoising only edge features (edges only), (ii) continuous FM denoising edges, nodes, and the global vector jointly (full graph), and (iii) a discrete FM operating on raw integer attribute indices rather than latent vectors. Continuous edges-only FM achieves the highest MCS accuracy (up to 25.2 % for the large model) and transmission power accuracy (up to 26.3 % for the large model), while maintaining comparable selected and success accuracy. Denoising the full graph yields no benefit, as node and global features carry no scheduling information beyond what the graph structure already encodes. The discrete formulation performs substantially worse on scheduling-decision metrics (i.e., MCS and transmission power). This gap is expected for two reasons: first, continuous FM relies on continuous interpolation paths (4), and the latent space of the autoencoder provides a smooth manifold where such paths are well-defined, unlike the raw combinatorial attribute space; second, the continuous variants receive a pre-trained graph representation from the autoencoder, whereas the discrete model must learn its own internal

Tiny

Small

Medium

Large

Model size

Fig. 18: Validation loss and MMD for FM models of varying size, with and without EMA of parameters. Solid lines: standard parameters; dashed lines: EMA parameters. EMA halves the MMD at medium scale and reduces it by ≈40% for the large model, while having negligible effect on smaller models.

representation from scratch within the same parameter and training budget. We therefore adopt continuous edges-only FM for all subsequent experiments. b) Model scaling.: Fig. 18 (solid lines) shows the validation loss and MMD as a function of the model size. Both metrics improve steadily from tiny to medium, but the large model does not improve over medium (loss: 0.098 vs. 0.087; MMD: 0.076 vs. 0.071). As with the surrogate (Section D-C), all sizes are trained for the same number of optimization steps (Table III), so the large model likely requires a longer training budget to fully converge. Since medium achieves the best quality–cost tradeoff, we use it for all subsequent FM experiments. c) Exponential moving average.: Fig. 18 (dashed lines) shows that EMA with decay β = 0.999 slightly improves MMD for medium and large models, with the largest gain at medium size where MMD is halved from 0.071 to 0.035. For tiny and small models, the effect is negligible. Since EMA adds negligible computational overhead but improves distributional quality at the scales we deploy, we use EMA parameters for all validation and inference. d) Timestep sampling schedule.: We compare five distributions for sampling the training timestep t: uniform U(0, 1), log-normal (sigmoid of a standard normal), and three Beta distributions – Beta(2, 1), Beta(1, 2), and Beta(2, 2) – which, respectively, bias training toward t ≈ 1 (near data), t ≈ 0 (near noise), or the midpoint. All schedules yield nearly identical loss and MMD, with differences below 0.005 in both metrics. This insensitivity is consistent with a low-curvature velocity field: when the flow is close to a straight-line interpolation, all regions are roughly equally easy to fit and no schedule can substantially outperform uniform sampling. We retain the uniform schedule for simplicity. e) Number of context observations.: We evaluate the effect of providing n ∈ {1, 3, 5, 7} random context observations to the FM model. Both loss and MMD increase monotonically with n, though the differences are small: loss grows from

TABLE VII: Per-attribute prediction accuracy of generated Co-SR configurations for three FM formulations across four model sizes. Continuous edges-only achieves the best scheduling-decision accuracy (MCS, TX power), while the discrete variant performs substantially worse despite comparable structural accuracy (selected, success). Size

Type

MCS Acc. [%] ↑

TX Power Acc. [%] ↑

Selected Acc. [%] ↑

Success Acc [%] ↑

Tiny

Cont. FM (edges only) Cont. FM Discrete FM

21.2 21.1 3.3

25.7 25.8 4.7

85.9 82.3 82.2

92.4 89.4 89.7

Small

Cont. FM (edges only) Cont. FM Discrete FM

22.8 22.4 5.7

24.8 25.5 6.7

83.1 81.1 81.0

90.5 88.8 88.8

Medium

Cont. FM (edges only) Cont. FM Discrete FM

25.0 24.0 7.6

26.0 25.9 7.8

80.7 79.9 80.7

88.7 88.1 88.7

Large

Cont. FM (edges only) Cont. FM Discrete FM

25.2 23.6 7.3

26.3 25.8 7.2

80.6 80.2 81.1

88.8 88.2 89.0

C. Surrogate Model a) Number of mixture components.: Fig. 20 shows the validation NLL of the surrogate as a function of the number of components of the mixture m. This ablation uses the non-embedded MDN variant (graph input, without autoencoder pre-encoding). Across all model sizes, using mixtures (m ≥ 2) substantially improves NLL over a single Gaussian, and performance generally keeps improving with larger m: the best results are at m = 8 for the tiny model and at m = 16 for the small, medium, and large models. The medium model still achieves lower NLL than the large model despite having fewer parameters, which suggests the large model may require a longer training budget to fully converge (Table III). The effective-component analysis (Fig. 21) shows increasing component utilization with larger mixtures: for m = 16, the

Heun

Euler

0.2 MMD ↓

0.075 (n = 1) to 0.080 (n = 7), while MMD increases from 0.026 to 0.035. We attribute this to two factors: (i) the context is generated by random transmissions, so additional observations are redundant given the first and primarily add noise to the conditioning signal, and (ii) more context slots enlarge the input dimensionality per edge from 2dz to (n+1)dz , increasing the effective learning difficulty. We therefore set n = 1 for all main experiments. f) ODE solver and integration steps.: Fig. 19 compares the first-order Euler and second-order Heun solvers across the 1–20 integration steps. Euler reaches MMD of 0.033 at 6 steps and converges to ≈0.032 beyond 10 steps, while Heun at 14 steps (MMD = 0.034) still does not match Euler’s asymptote. Although counterintuitive given Heun’s higher theoretical order, Euler consistently achieves lower MMD at every step count tested. The results are consistent with a low-curvature velocity field, where first-order steps already trace the flow accurately; the Heun corrector term may introduce noise from querying the network slightly off the learned manifold. Since Euler also requires only one model evaluation per step (vs. two for Heun), it is faster and more accurate in this setting. We select the Euler solver with 6 steps for all experiments.

0.1

0

5

10 15 Number of solver steps

20

Fig. 19: Comparison of Heun and Euler ODE solvers for FM generation as a function of integration steps. Euler achieves lower MMD at every step count and converges in ≈6 steps, while Heun requires ≈14 steps without matching Euler’s asymptote.

median effective component count is roughly 6.6–8.1 across model sizes. We retain m = 4 in the main pipeline as a practical quality–complexity trade-off. b) MDN vs. MSE prediction.: Table VIII reports the prediction quality of the two MDN variants. The best result is R2 = 0.600 (large, non-embedded MDN), with correlations up to 0.774 and biases in a relatively narrow range (−9.7 Mbit/s to 8.4 Mbit/s). We also evaluate MSE-trained point-estimate baselines (with and without autoencoder pre-encoding). They strongly overfit the training data and produce unreliable predictions on out-of-distribution inputs encountered during inference. We therefore adopt the MDN formulation, which provides calibrated uncertainty estimates and more robust generalization. c) Autoencoder pre-encoding.: For the MDN variants, pre-encoding improves tiny/small (R2 : 0.331 → 0.450, 0.485 → 0.528) but is neutral to slightly negative at medium/large (0.552 → 0.551, 0.600 → 0.593). Overall, latent pre-encoding helps low-to-mid capacity models more

TABLE VIII: Surrogate prediction quality on the validation set. MDN uses m=4 mixture components on non-embedded graph input, and MDN+autoencoder (AE) applies GNN autoencoder pre-encoding before the MDN head. P90/P95/P99 denote absolute prediction error at the respective percentiles. Type

R2 ↑

MAE [Mbit/s] ↓

Corr. ↑

Bias [Mbit/s]

P90 [Mbit/s] ↓

P95 [Mbit/s] ↓

P99 [Mbit/s] ↓

Tiny

MDN+AE MDN

0.450 0.331

177.9 201.0

0.674 0.582

−9.7 −8.0

408.0 442.6

499.2 538.2

646.8 697.0

Small

MDN+AE MDN

0.528 0.485

157.9 169.9

0.727 0.698

−0.1 −5.0

371.9 393.1

466.0 480.9

674.2 643.6

Medium

MDN+AE MDN

0.551 0.552

150.2 152.2

0.743 0.743

+8.4 −2.4

365.6 367.0

453.5 460.0

684.8 638.7

Large

MDN+AE MDN

0.593 0.600

142.9 139.9

0.771 0.774

+7.6 +3.0

349.2 349.4

439.2 437.8

617.2 609.3

Tiny Small

NLL ↓

1

Medium Large

0.5 0 −0.5 1

2 4 8 Number of components

16

Effective no. of components

Fig. 20: Validation NLL of the surrogate model as a function of the number of MDN mixture components m for four model sizes. Note the logarithmic scale on the X axis. 16 Tiny Small Medium Large

8 4 2 1 2

4 8 Number of components

16

Fig. 21: Distribution of the effective number of active mixture components (entropy-based) for varying m and model size. Note the logarithmic scale on both axes.

consistently than the largest ones. Since the main pipeline already uses the frozen GNN encoder for the FM model, we retain pre-encoding for the surrogate (MDN+AE) as it adds no extra cost and benefits smaller models. d) Scaling and tail errors.: Taking the best MDN model per size, R2 rises from 0.450 (tiny) to 0.600 (large), indicating consistent improvement with model capacity. Table VIII also

Effective data rate [Mbit/s] ↑

Size

1,500

Optimal

1,200 900 600 Random

300 0

0

0.5

1

1.5

2 λ

2.5

3

3.5

4

Fig. 22: Effect of the risk factor λ on mean effective data rate. Dashed line: best configuration for the scenario (1350.1 Mbit/s); dotted line: random selection (479.5 Mbit/s).

reports absolute-error tails at the 90th, 95th, and 99th percentiles. Tail errors decrease consistently with model size: the P90 error drops from 408 Mbit/s (tiny) to 349 Mbit/s (large), while the P99 error remains in the 609 Mbit/s to 697 Mbit/s range across all configurations. The two MDN variants exhibit similar tail behavior at medium and large scales, whereas MDN+AE has noticeably tighter tails at tiny and small sizes, consistent with the pre-encoding benefit observed in pointprediction metrics. e) Risk-averse candidate selection.: Since the MDN surrogate provides predictive uncertainty via the mixture variance P 2 2 2 σ̄e2 = k wk (σk + µk ) − r̄e , we test whether penalizing uncertain predictions improves candidate selection. We score candidates by s = r̄e − λ · σ̄e , where λ ≥ 0 controls the degree of risk aversion, and evaluate the effect on the effective data rate (Fig. 22). Risk-neutral selection (λ = 0) yields 1136.4 Mbit/s, while the best risk-averse setting (λ = 0.5) achieves 1139.1 Mbit/s – an improvement of only 0.24 %. For λ ≥ 1.5, performance drops sharply as the criterion becomes overly conservative. Given the negligible benefit, we use riskneutral selection (λ = 0) in all main experiments.

Method

4 APs (2x2)

9 APs (3x3)

16 APs (4x4)

T-Optimal F-Optimal H-MAB FM4WiFi

0.34 s 1.24 s 3.78 s 0.13 s

2.58 s 279.2 s 78.97 s 0.24 s

29.7 s 2956 s inf 0.62 s

Effective data rate [Mbit/s]

TABLE IX: Time to produce a Co-SR schedule in the residential scenario (room size 10 m). For FM4WiFi and analytical baselines, this is a one-shot inference time; for H-MAB, it is the online convergence time (inf = did not converge within the time budget).

600 450 300 150 0

0

5

A PPENDIX E C OMPUTATIONAL OVERHEAD

20

600 450 300 150 0

0

5

A PPENDIX F A DDITIONAL R ESULTS

10 Time [s]

15

20

Fig. 24: Per-seed effective data rate for FM4WiFi with cyclic regeneration every 1 s, 4x4 residential scenario (room size 20 m, without walls).

Effective data rate [Mbit/s]

Figures 23–25 show per-seed throughput traces for the wall-free residential scenario (Fig. 10b in the main text), decomposing the averaged curves into the 5 individual runs. All runs share the same topology and mobility pattern, so the observed variance reflects algorithmic stochasticity. FM4WiFi (with MCS selection) (Figures 23 and 24) shows significant variance both between and within runs, as its probabilistic sampling produces different Co-SR configurations each time. H-MAB (Fig. 25) is the most stable across runs – not because it converges well, but because it barely converges at all in this large scenario, maintaining a roughly constant throughput.

15

Fig. 23: Per-seed effective data rate for FM4WiFi without regeneration, 4x4 residential scenario (room size 20 m, without walls).

Effective data rate [Mbit/s]

Table IX compares the time required to produce a Co-SR schedule across methods and scales. FM4WiFi has no online convergence phase: all learning is performed offline, and the online cost is limited to preparing batched inputs and running the compiled inference pipeline (128 candidates in 4 sequential batches of 32, as discussed in Section V-A). This results in sub-second latency at all tested scales, growing only from 0.13 s at 2x2 to 0.62 s at 4x4. In contrast, the other methods exhibit exponential scaling. T-Optimal reaches 29.7 s at 4x4 – too slow for practical use. F-Optimal takes nearly 50 minutes on the same scale, and H-MAB does not converge within any practical budget. FM4WiFi is therefore the only method that remains tractable on all evaluated scales, and its constant-time character with respect to topology changes makes it directly suitable for the event-triggered deployment demonstrated in Fig. 11.

10 Time [s]

600 450 300 150 0

0

5

10 Time [s]

15

20

Fig. 25: Per-seed effective data rate for H-MAB, 4x4 residential scenario (room size 20 m, without walls).

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