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

An associative memory (AM) enables cue-response recall, and it has recently been recognized as a key mechanism underlying modern neural architectures such as Transformers. In this work, we introduce the concept of distributed dynamic associative memory (DDAM), which extends classical AM to settings with multiple agents and time-varying data streams. In DDAM, each agent maintains a local AM that must not only store its own associations but also selectively memorize information from other agents based on a specified interest matrix. To address this problem, we propose a novel tree-based distributed online gradient descent algorithm, termed DDAM-TOGD, which enables each agent to update its memory on the fly via inter-agent communication over designated routing trees. We derive rigorous performance guarantees for DDAM-TOGD, proving sublinear static regret in stationary environments and a path-length dependent dynamic regret bound in non-stationary environments. These theoretical results provide insights into how communication delays and network structure impact performance. Building on the regret analysis, we further introduce a combinatorial tree design strategy that optimizes the routing trees to minimize communication delays, thereby improving regret bounds. Numerical experiments demonstrate that the proposed DDAM-TOGD framework achieves superior accuracy and robustness compared to representative online learning baselines such as consensus-based distributed optimization, confirming the benefits of the proposed approach in dynamic, distributed environments.

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.

In this paper, we tackle the problem of jointly estimating the system states and partially unknown dynamics within distributed sensor-equipped networks, particularly in scenarios where only partial state observations are available. To address this issue, we propose an observer-based dynamic cooperative learning framework incorporating online distributed Gaussian Process (GP) regression, which enables accurate estimation despite incomplete in measurements and deficient GP models. In addition, a novel data collection strategy is introduced, with theoretical conditions ensuring feasible data acquisition. Moreover, we also derive an error upper bound encompassing state estimation and model estimation, leveraging the deterministic error bounds of GPs. Empirical simulations demonstrate the superiority of our approach compared to existing distributed GP-based methods.