Q-LocalAdam: Memory-Efficient Client-Side Adaptive Optimization for Edge Federated Learning

Deploying state-of-the-art deep neural networks (DNNs) at the wireless edge is severely bottlenecked by the strict energy and resource constraints of mobile devices. While federated split learning (FSL) mitigates on-device computation by offloading workloads to an edge server, this may introduce systemic overheads, while the continuous exchange of cut-layer data, and submodels still incurs significant energy consumption (EC). To address this, we propose a green quantized FSL (GQ-FSL) framework that incorporates stochastic quantization for both local collaborative training and wireless transmissions. Notably, GQ-FSL supports asymmetric precision levels for the client- and server-side submodels, effectively decoupling device energy constraints from global convergence degradation. To quantify these tradeoffs, we develop parameterized energy models for the split architecture and derive a theoretical convergence bound under statistically heterogeneous data. Building on that, we formulate a joint optimization problem to configure the DNN split point and precision levels, minimizing the total system EC while satisfying a strict target accuracy constraint. Ultimately, we demonstrate that GQ-FSL enables large-scale DNN deployment on resource-constrained devices, achieving superior energy efficiency compared to quantized federated learning and full-precision FSL.

AdamW is a default optimizer for modern deep learning, but its first and second moment states add roughly two parameter-sized buffers to training memory, increasing the already substantial cost of large-scale pretraining. We propose Gefen, a memory-efficient optimizer that automatically shares second-moment estimates across parameter blocks and quantizes the first moment using a learned codebook, thereby reducing AdamW's memory footprint by ~8x while maintaining the same performance, corresponding to a reduction of 6.5 GiB per billion parameters. The method is motivated by a theoretical result showing that large mixed Hessian entries constrain the ratio of squared gradients toward one, suggesting that Hessian-aligned parameters are natural candidates for sharing second-moment statistics. Since computing Hessians is impractical at scale, Gefen infers block structure from the initial squared gradients, requiring no architecture-specific metadata or hyperparameters beyond AdamW defaults. Gefen learns an exact histogram-based dynamic-programming quantization codebook and reuses the same blocks for first-moment scaling. Across diverse pretraining experiments, Gefen achieves the lowest peak optimizer memory among the compared AdamW-like methods while maintaining AdamW-level performance. In single-machine or distributed training, the reduced memory footprint enables larger microbatches and improves throughput significantly over AdamW, providing a practical drop-in replacement with lower memory usage that can increase throughput and enable training larger models or using larger global batch sizes. We provide the complete Python implementation, including fused CUDA kernels at https://github.com/ndvbd/Gefen

Federated Learning (FL) has become a foundational paradigm for privacy-preserving distributed intelligence, yet its scalability remains fundamentally constrained by communication bottlenecks, device heterogeneity, and the challenges of training under statistically non-IID data. Quantization is one of the most effective mechanisms for mitigating these limitations, reducing both uplink/downlink payloads and on-device computation. This paper provides the first FL-centric systematic review of quantization, introducing a novel taxonomy organized around FL-specific dimensions, including client heterogeneity, aggregation consistency, communication-scheduling adaptation, non-IID robustness, privacy/security integration, and hardware/energy co-optimization. Beyond cataloging existing methods, we analyze how quantization interacts with core FL behaviors such as client drift, partial participation, convergence stability, secure aggregation, and differential privacy. We further identify cross-method insights, open research gaps, and design guidelines for practitioners deploying quantized FL on mobile, IoT, and edge platforms. This survey thus establishes quantization not merely as a compression technique, but as a fundamental systems component shaping the performance, robustness, and practicality of modern FL.