Federated learning (FL), as an emerging edge artificial intelligence paradigm, enables many devices to collaboratively train a global model without sharing their private data. To enhance the training efficiency of FL, various algorithms have been proposed, ranging from first-order second-order methods. However, these cannot be applied in scenarios where gradient information is not available, e....

Classical geometric mechanics, including the study of symmetries, Lagrangian and Hamiltonian Hamilton-Jacobi theory, are founded on structures such as jets, symplectic contact ones. In this paper, we shall use a partly forgotten framework second-order (or stochastic) differential geometry, developed originally by L. Schwartz P.-A. Meyer, to construct counterparts those classical structures. The...