分层多阈值随机压缩，显著降低联邦学习通信开销

Personalized federated learning (PFL) is a promising paradigm for collaborative learning over distributed devices, where edge nodes collaboratively train personalized models without sharing raw data. Although PFL addresses data heterogeneity by learning client-specific models, it still suffers from substantial uplink and downlink communication costs when exchanging high-dimensional parameters in bandwidth-constrained systems. Recent one-bit methods achieve extreme compression, but they usually rely on a single thresholding rule applied to the whole model. This design has two limitations. First, it overlooks layer-wise differences in parameter distributions and quantization sensitivities. Second, a single threshold provides only coarse binary information and cannot capture fine-grained variations in parameter distributions. To address these issues, we propose a communication-efficient PFL framework via layer-wise multi-threshold random sketching. In the proposed method, each layer is assigned its own set of quantization thresholds, so that the compressed representation can adapt to layer-specific statistics while using multiple intervals to provide a finer low-bit description of sketched parameters. The proposed method supports bidirectional communication using compact low-bit sketches and improves the communication-accuracy tradeoff compared with existing one-bit compression approaches.