A Theoretical Framework for Energy-Aware Gradient Pruning in Federated Learning

Federated learning on heterogeneous edge devices requires personalized compression while preserving aggregation compatibility and stable convergence. We present Curvature-Aware Heterogeneous Federated Pruning (CA-HFP), a practical framework that enables each client perform structured, device-specific pruning guided by a curvature-informed significance score, and subsequently maps its compact submodel back into a common global parameter space via a lightweight reconstruction. We derive a convergence bound for federated optimization with multiple local SGD steps that explicitly accounts for local computation, data heterogeneity, and pruning-induced perturbations; from which a principled loss-based pruning criterion is derived. Extensive experiments on FMNIST, CIFAR-10, and CIFAR-100 using VGG and ResNet architectures under varying degrees of data heterogeneity demonstrate that CA-HFP preserves model accuracy while significantly reducing per-client computation and communication costs, outperforming standard federated training and existing pruning-based baselines.

Federated Learning (FL) enables collaborative model training across distributed clients without sharing raw data, thereby preserving privacy. However, FL often suffers from significant communication and computational overhead, limiting its scalability and sustainability. In this work, we introduce a Full Compression Pipeline (FCP) for FL in communication-constrained environments. FCP integrates three complementary deep compression techniques (pruning, quantization, and Huffman encoding) into a unified end-to-end framework. By compressing local models and communication payloads, FCP substantially reduces transmission costs and resource consumption while maintaining competitive accuracy. To quantify its impact, we develop an evaluation framework that captures both communication and computation overheads as a unified model cost, allowing a holistic assessment of efficiency trade-offs. The pipeline is evaluated in an independent and identically distributed (IID) and non-IID data setting. In one representative scenario, training a ResNet-12 model on the CIFAR-10 dataset with ten clients and a 2 Mbps bandwidth, the FCP achieves more than 11$\times$ reduction in model size, with only a 2% drop in accuracy compared to the uncompressed baseline. This results in an FL training that is more than 60% faster.

Federated Learning (FL) faces major challenges in real-world deployments due to statistical heterogeneity across clients and system heterogeneity arising from resource-constrained devices. While clustering-based approaches mitigate statistical heterogeneity and pruning techniques improve memory and communication efficiency, these strategies are typically studied in isolation. We propose CA-AFP, a unified framework that jointly addresses both challenges by performing cluster-specific model pruning. In CA-AFP, clients are first grouped into clusters, and a separate model for each cluster is adaptively pruned during training. The framework introduces two key innovations: (1) a cluster-aware importance scoring mechanism that combines weight magnitude, intra-cluster coherence, and gradient consistency to identify parameters for pruning, and (2) an iterative pruning schedule that progressively removes parameters while enabling model self-healing through weight regrowth. We evaluate CA-AFP on two widely used human activity recognition benchmarks, UCI HAR and WISDM, under natural user-based federated partitions. Experimental results demonstrate that CA-AFP achieves a favorable balance between predictive accuracy, inter-client fairness, and communication efficiency. Compared to pruning-based baselines, CA-AFP consistently improves accuracy and lower performance disparity across clients with limited fine-tuning, while requiring substantially less communication than dense clustering-based methods. It also shows robustness to different Non-IID levels of data. Finally, ablation studies analyze the impact of clustering, pruning schedules and scoring mechanism offering practical insights into the design of efficient and adaptive FL systems.