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.

翻译：联邦学习（FL）在去中心化边缘设备的通信与能量限制下运行。尽管基于Top-K幅度剪枝的梯度稀疏化能有效降低通信负载，但其本质上是能量无关的——该方法假设所有参数更新产生相同的下游传输与内存更新代价，忽略了硬件现实。我们将剪枝过程形式化为一个能量约束的投影问题，该问题计及反向传播后阶段中内存密集型与计算高效型操作间的硬件层差异。我们提出代价加权幅度剪枝（CWMP），这是一种基于参数更新幅度与其物理成本相对比值进行优先排序的选择规则。我们证明CWMP是该约束投影下的最优贪心解，并对其全局能量效率进行概率分析。在非独立同分布CIFAR-10基准测试上的数值结果显示，与Top-K基线相比，CWMP持续建立了更优的性能-能量帕累托前沿。