Ergodic Trajectory Design by Learned Pushforward Maps: Provable Coverage via Conditional Flow Matching

Designing continuous trajectories whose time-averaged occupancy provably matches a prescribed spatial density (the \emph{ergodic coverage} problem) is central to UAV-assisted data collection and sensing, robotic exploration, and mobile monitoring. For flying agents in particular, this challenge is acute: trajectories must balance coverage fidelity against tight energy budgets, no-fly zones, and acceleration limits. Existing methods either re-optimize each trajectory online (with cost growing in the horizon and re-running for every target, agent, and realization) or rely on bespoke analytical constructions that must be re-derived for each new constraint. We propose a \emph{epushforward} framework that decouples ergodicity from density matching: an analytic latent trajectory provides exact uniform ergodicity on a simple annular domain, and a single map, learned offline by optimal-transport conditional flow matching, transports this latent occupancy onto the prescribed target density. The composed trajectory is then asymptotically ergodic with respect to the learned pushforward distribution, with deviation from the target controlled by the flow-matching training loss. Once trained for a given target density and constraint set, the map serves an unbounded number of trajectories and a multi-agent fleet without per-agent retraining, and many differentiable operational constraints (no-fly zones, acceleration ceilings, or fairness penalties) enter as additive soft penalties in the training loss without re-deriving the design. We prove three results (an acceleration-energy bound, an $O(1/\sqrt{K})$ ergodic convergence rate in the number of trajectory cycles $K$, and an approximation-error bound) that combine into an end-to-end coverage bound estimable from CFM training diagnostics (certified given an architectural Lipschitz bound on $v_θ$).

Tiny Graph Neural Networks for Radio Resource Management

The surge in demand for efficient radio resource management has necessitated the development of sophisticated yet compact neural network architectures. In this paper, we introduce a novel approach to Graph Neural Networks (GNNs) tailored for radio resource management by presenting a new architecture: the Low Rank Message Passing Graph Neural Network (LR-MPGNN). The cornerstone of LR-MPGNN is the implementation of a low-rank approximation technique that substitutes the conventional linear layers with their low-rank counterparts. This innovative design significantly reduces the model size and the number of parameters. We evaluate the performance of the proposed LR-MPGNN model based on several key metrics: model size, number of parameters, weighted sum rate of the communication system, and the distribution of eigenvalues of weight matrices. Our extensive evaluations demonstrate that the LR-MPGNN model achieves a sixtyfold decrease in model size, and the number of model parameters can be reduced by up to 98%. Performance-wise, the LR-MPGNN demonstrates robustness with a marginal 2% reduction in the best-case scenario in the normalized weighted sum rate compared to the original MPGNN model. Additionally, the distribution of eigenvalues of the weight matrices in the LR-MPGNN model is more uniform and spans a wider range, suggesting a strategic redistribution of weights.

Adversarial Attacks on Graph Neural Networks based Spatial Resource Management in P2P Wireless Communications

This paper introduces adversarial attacks targeting a Graph Neural Network (GNN) based radio resource management system in point to point (P2P) communications. Our focus lies on perturbing the trained GNN model during the test phase, specifically targeting its vertices and edges. To achieve this, four distinct adversarial attacks are proposed, each accounting for different constraints, and aiming to manipulate the behavior of the system. The proposed adversarial attacks are formulated as optimization problems, aiming to minimize the system's communication quality. The efficacy of these attacks is investigated against the number of users, signal-to-noise ratio (SNR), and adversary power budget. Furthermore, we address the detection of such attacks from the perspective of the Central Processing Unit (CPU) of the system. To this end, we formulate an optimization problem that involves analyzing the distribution of channel eigenvalues before and after the attacks are applied. This formulation results in a Min-Max optimization problem, allowing us to detect the presence of attacks. Through extensive simulations, we observe that in the absence of adversarial attacks, the eigenvalues conform to Johnson's SU distribution. However, the attacks significantly alter the characteristics of the eigenvalue distribution, and in the most effective attack, they even change the type of the eigenvalue distribution.