Adjacency-Based Spectral Proxy Control of Mobile Communication Agents

We consider a heterogeneous mobile-agent network composed of uncontrolled task agents and controllable communication agents. The objective is to reposition communication agents online as task agents move. Since throughput-based objectives are generally unsuitable for real-time control, spectral graph metrics such as algebraic connectivity are commonly adopted as surrogate objectives. However, controlling algebraic connectivity relies on the eigenvector corresponding to the second-smallest eigenvalue of a graph's Laplacian matrix (i.e., the Fiedler vector), whose distributed estimation requires an unbounded number of communication rounds to converge. In this work, we identify a structural decomposition of this Fiedler-gradient controller into a local interaction rule and a graph embedding component, suggesting the use of alternative embeddings that are easier to estimate distributively than the Fiedler vector. As a particular instance, we propose A-Fiedler, which replaces the Fiedler embedding with the dominant eigenvector of the adjacency matrix, commonly used as a graph embedding of nodes into a latent geometry. This representation is more naturally suited for distributed implementation under local communication constraints. We evaluate A-Fiedler against the classical Fiedler-gradient controller. Results show comparable network performance in the absence of communication constraints and improved robustness under distributed estimation. For instance, under the same number of communication rounds, the Fielder-gradient may even converge to disconnected configurations whereas our proposition maintains performance. We believe our contribution provides a simpler path toward distributed network control.

Learning to Distributedly Estimate under Partially Known Dynamics: A Covariance-Agnostic Neural Kalman Consensus Filter

Online latent state estimation constitutes a fundamental challenge within the artificial intelligence field, serving as a foundational tool for diverse applications, including sequential decision making, anomaly and change-point detection. In this paper, a novel online distributed sensing framework, where agents collaborate and exchange information to perform latent state estimation, is presented. The proposed estimator combines available partial domain knowledge with the representation capabilities of deep neural networks. In particular, the designed sensing framework incorporates prior estimates, optimized consensus weights, and Kalman-like recursive updates to perform decentralized inference, without relying on knowledge of noise statistics. Extensive experiments on linear, chaotic (Lorenz), and practical wireless tracking environments reveal that the proposed Covariance-Agnostic Neural Kalman Consensus Filter (CA-NKCF) outperforms traditional distributed Kalman and particle filters as well as purely model-free deep neural networks, exhibiting robustness even when the underlying motion and observation models are misspecified. It is also demonstrated that CA-NKCF's performance advantage remains stable across varying noise levels, random communication topologies, latent state dimensions, and observation clutter densities induced by scattering objects in wireless systems.

A Gated Graph Neural Network Approach to Fast-Convergent Dynamic Average Estimation

Dynamic average estimation is a critical problem in multi-agent systems, enabling agents to collaboratively estimate time-varying signals using only local information exchange. Traditional model-based approaches often face challenges related to convergence speed and sensitivity to network topology changes. This paper introduces a novel learning-based solution leveraging Gated Graph Neural Networks (GGNNs) for fast-convergent dynamic average estimation in a fully distributed manner. Taking advantage of the inherent structure of GGNNs, the proposed method models the estimation process as a distributed autoregressor, ensuring rapid convergence while maintaining stability. We incorporate a regularization term during training to enforce convergence guarantees and introduce an encoding-decoding mechanism to reduce communication overhead without sacrificing accuracy compared to standard GGNNs. Extensive numerical experiments demonstrate that our approach significantly outperforms conventional model-based estimators in terms of both convergence speed and precision, making it a promising alternative for multi-agent applications that require dynamic average estimation.

Information-Theoretic Bounds for Sparse Covariance Estimation in the Vertical-Split Distributed Model

We study the minimax estimation error for distributed covariance matrix estimation in the vertical-split (feature-split) setting, where two agents each observe different coordinates of $m$ i.i.d. sub-Gaussian samples and communicate a limited number of bits to a central server. While Rahmani et al. [2025] established nearly tight bounds for dense (unstructured) cross-covariance matrices, we investigate whether imposing elementwise $s$-sparsity on the cross-covariance $C_{21}$ can reduce the required communication and sample complexity. In contrast to the horizontal-split setting, where Braverman et al. [2016] showed that sparsity does not reduce communication cost for mean estimation, we prove that sparsity does help for cross-covariance estimation in the vertical split. Specifically, we establish minimax lower bounds showing that the communication budget per agent scales as $B_k = Ω(σ^4 d_k\, s' \log(d_1 d_2/s')/\varepsilon^2)$ and the sample complexity for cross-covariance estimation as $m = Ω(σ^4\, s' \log(d_1 d_2/s')/\varepsilon^2)$, where $s' = s \wedge d_{\min}$. For the $1$-sparse case, this yields an exponential improvement from $d_1 d_2$ to $\log(d_1 d_2)$ compared to the dense rate. Our lower bounds are established via Fano's method with an explicit sparse packing using a Varshamov--Gilbert-type argument for signed partial permutation matrices combined with the Conditional Strong Data Processing Inequality of Rahmani et al. [2025]. We show the bounds are tight with a matching achievable scheme, based on covering-net quantization and entry-wise hard thresholding, that attains the $s$-sparse lower bound up to polylogarithmic factors.