🤖 AI Summary
This paper addresses the joint optimization of computation, communication, and model accuracy in multi-user–multi-server distributed computing and inference. We propose GMUDC, a unified framework supporting personalized objective optimization over arbitrary network topologies and heterogeneous task allocations. Methodologically, we introduce spectral-covering duality—establishing, for the first time, a theoretical link between network topology and generalization capability. Leveraging reproducing kernel Hilbert spaces and translation-invariant kernels, we integrate quenched–annealed two-phase analysis to achieve topology-aware distributed optimization under resource constraints. We theoretically prove GMUDC’s verifiable efficiency under given computational and communication budgets. Our framework provides a foundational information–energy co-design principle for federated learning and edge intelligence.
📝 Abstract
This work develops a unified {learning- and information-theoretic} framework for distributed computation and inference across multiple users and servers. The proposed emph{General Multi-User Distributed Computing (GMUDC)} model characterizes how computation, communication, and accuracy can be jointly optimized when users demand heterogeneous target functions that are arbitrary transformations of shared real-valued subfunctions. Without any separability assumption, and requiring only that each target function lies in a reproducing-kernel Hilbert space associated with a shift-invariant kernel, the framework remains valid for arbitrary connectivity and task-assignment topologies. A dual analysis is introduced: the emph{quenched design} considers fixed assignments of subfunctions and network topology, while the emph{annealed design} captures the averaged performance when assignments and links are drawn uniformly at random from a given ensemble. These formulations reveal the fundamental limits governing the trade-offs among computing load, communication load, and reconstruction distortion under computational and communication budgets~$Γ$ and~$Δ$. The analysis establishes a spectral--coverage duality linking generalization capability with network topology and resource allocation, leading to provably efficient and topology-aware distributed designs. The resulting principles provide an emph{information--energy foundation} for scalable and resource-optimal distributed and federated learning systems, with direct applications to aeronautical, satellite, and edge-intelligent networks where energy and data efficiency are critical.