A Framework for Hybrid Collective Inference in Distributed Sensor Networks

The increasing heterogeneity of multi-agent systems poses significant challenges for jointly training a global model across agents. At the same time, cooperative inference between agents has long been recognized as a powerful mechanism for distributed decision making over networks. Motivated by these observations, we propose a collaboration framework for distributed binary classification over multi-agent networks, where a set of independently trained agents, potentially differing in architecture, feature space, or modality, coordinate their actions during test time to form collective predictions. This coordination is achieved by exchanging local decision statistics through a distributed learning protocol. We develop a theoretical and experimental study of this independent training and cooperative inference paradigm, and examine its performance under different communication budgets and distributed learning rules. We establish classification error guarantees under sufficient, finite-round, and finite-precision communication, together with PAC-style generalization bounds. These results capture the influence of model heterogeneity, network topology, combination policy, and communication constraints on prediction accuracy. Taken together with the experimental results, they reveal both the price of independent training and the benefit of collective prediction for the proposed distributed decision making framework with models learned from data.

Edge-cloud hybrid inference offloads difficult inputs to a powerful remote model, but the uplink channel imposes hard per-request constraints on the number of bits that can be transmitted. We show that selecting transmitted content based solely on attention-based importance, the standard approach in collaborative inference, is inherently limited under hard budgets. Two findings support this claim. First, replacing high-importance units with low-importance but complementary ones improves server accuracy. This shows that what matters is not individual importance but how well the transmitted set covers diverse aspects of the input. Second, spatially uniform selection without any content information achieves competitive accuracy at moderate budgets. This confirms that spatial coverage alone carries independent value. Based on this analysis, we propose SAGE (Semantic Attention-Guided Evidence), a principled, training-free method that combines importance filtering with embedding-diversity sampling. SAGE achieves 93% of the server ceiling in offloaded accuracy while transmitting fewer than half of the available evidence units on ImageNet-1K, substantially outperforming importance-only composition.

In decentralized decision-making, several agents connected according to a network graph aim at solving a classification problem by collecting streaming observations. Due to decentralization, they run an iterative algorithm where, at each iteration, they can only exchange information locally with their neighbors. While decentralized estimation solutions have been shown to match the performance of optimal centralized systems, we show here that surprisingly this conclusion does not hold for decentralized decision-making. Specifically, we prove that the error probability for the best decentralized decision strategy exhibits an irreducible loss with respect to the optimal centralized classifier. This result establishes a fundamental limit for the performance of any decentralized decision strategy. We obtain an analytical relation showing that this limit is related to the interplay between decentralization and classification. The first aspect appears through the distances between the nodes in the graph, while the second aspect plays through the moment generating functions of the likelihood ratios that describe the decision problem. By applying the derived closed-form relation to different network topologies and inference problems, we observe some interesting and perhaps unexpected behavior emerging. In particular, we characterize the scaling law (with the network size) for the loss over popular network topologies, showing that the error probabilities might differ by orders of magnitude; and we examine how performance is affected by the relative distance between informative and uninformative agents over the graph.