  The exploration of computational and communication efficiency within
Federated Learning (FL) has emerged as a prominent and crucial field of study.
While most existing efforts to enhance these efficiencies have focused on
Horizontal FL, the distinct processes and model structures of Vertical FL
preclude the direct application of Horizontal FL-based techniques. In response,
we introduce the concept of Lightweight Vertical Federated Learning (LVFL),
targeting both computational and communication efficiencies. This approach
involves separate lightweighting strategies for the feature model, to improve
computational efficiency, and for feature embedding, to enhance communication
efficiency. Moreover, we establish a convergence bound for our LVFL algorithm,
which accounts for both communication and computational lightweighting ratios.
Our evaluation of the algorithm on a image classification dataset reveals that
LVFL significantly alleviates computational and communication demands while
preserving robust learning performance. This work effectively addresses the
gaps in communication and computational efficiency within Vertical FL.
