Toward more effective bag-of-functions architectures: Exploring initialization and sparse parameter representation

Time series datasets often present complex temporal patterns that challenge both feature extraction and interpretability. The Bag-of-Functions (BoF) architecture has emerged as a promising approach to model such data by capturing diverse dynamics through functional components. However, its effectiveness is constrained by limitations in both interpretability and training stability. In this work, we address these challenges by introducing two complementary contributions: a regularization strategy that promotes sparse and interpretable parameter representations, and a tailored initialization scheme based on the Kaiming method adapted to the properties of BoF models. Our proposed initialization ensures improved convergence behavior and training stability, while the regularization enhances the clarity and semantic interpretability of the learned components. Evaluations on synthetic and real-world time series datasets demonstrate that these improvements preserve model performance and generalize well across varying signal complexities. Together, these strategies provide a more robust and interpretable foundation for Bag-of-Functions architectures in time series decomposition tasks.