  Personalized federated learning (PFL) has been widely investigated to address
the challenge of data heterogeneity, especially when a single generic model is
inadequate in satisfying the diverse performance requirements of local clients
simultaneously. Existing PFL methods are inherently based on the idea that the
relations between the generic global and personalized local models are captured
by the similarity of model weights. Such a similarity is primarily based on
either partitioning the model architecture into generic versus personalized
components, or modeling client relationships via model weights. To better
capture similar (yet distinct) generic versus personalized model
representations, we propose \textit{spectral distillation}, a novel
distillation method based on model spectrum information. Building upon spectral
distillation, we also introduce a co-distillation framework that establishes a
two-way bridge between generic and personalized model training. Moreover, to
utilize the local idle time in conventional PFL, we propose a wait-free local
training protocol. Through extensive experiments on multiple datasets over
diverse heterogeneous data settings, we demonstrate the outperformance and
efficacy of our proposed spectral co-distillation method, as well as our
wait-free training protocol.
