Federated Learning (FL) is constrained by the communication and energy limitations of decentralized edge devices. While gradient sparsification via Top-K magnitude pruning effectively reduces the communication payload, it remains inherently energy-agnostic. It assumes all parameter updates incur identical downstream transmission and memory-update costs, ignoring hardware realities. We formalize the pruning process as an energy-constrained projection problem that accounts for the hardware-level disparities between memory-intensive and compute-efficient operations during the post-backpropagation phase. We propose Cost-Weighted Magnitude Pruning (CWMP), a selection rule that prioritizes parameter updates based on their magnitude relative to their physical cost. We demonstrate that CWMP is the optimal greedy solution to this constrained projection and provide a probabilistic analysis of its global energy efficiency. Numerical results on a non-IID CIFAR-10 benchmark show that CWMP consistently establishes a superior performance-energy Pareto frontier compared to the Top-K baseline.
Figures & tables
Fig. 1 : Performance-Energy Pareto Frontier. CWMP is the dominant strategy in the extreme scarcity regime (1%) and maintains a superior accuracy-per-energy profile as the budget increases, avoiding the performance regression observed in Top-K.
Fig. 2 : Convergence Dynamics at 10% Sparsity. CWMP matches the convergence rate of the Top-K baseline while achieving a higher accuracy, demonstrating a more efficient allocation of the fixed communication budget.