please polish this ABSTRACT:Federated Learning aims to train a shared model collaboratively in a privacy-preserving manner that is effective for all clients. However, the main challenge it faces is dealing with heterogeneous data distribution from different sources. Existing solutions either focus on regularization to reduce differences in optimization objectives among clients or design rules to optimize the aggregation mechanism. Nonetheless, the inconsistency of feature spaces makes it difficult to train a model that fits the data from all clients. To address this issue, this paper proposes a method called cross-silo prototypical calibration (FedCSPC). Its main idea is to relearn the mapping to align features from heterogeneous spaces. Specifically, FedCSPC explores the common and individual patterns of sample features and uses the representation distribution modeling (RDM) module to generate class-aware prototypes that simulate real features. This approach helps with model calibration without compromising privacy. The cross-silo prototypical calibration (CSPC) module then focuses on learning the mapping that can effectively project cross-source features into a consistent space while maintaining clear decision boundaries to enhance the generalization of the model. Notably, the CSPC module generates an anchor for each class, which could be used as a knowledge base to reduce prediction errors. Moreover, the CSPC module’s ease of implementation and plug-and-play characteristics make it even more remarkable. The 