A complete structure-preserving learning scheme for single-input/single-output (SISO) linear port-Hamiltonian systems is proposed. The construction is based on the solution, when possible, of the unique identification problem for these systems, in ways that reveal fundamental relationships between classical notions in control theory and crucial properties in the machine learning context, like structure-preservation and expressive power. In the canonical case, it is shown that, {up to initializations,} the set of uniquely identified systems can be explicitly characterized as a smooth manifold endowed with global Euclidean coordinates, which allows concluding that the parameter complexity necessary for the replication of the dynamics is only $\mathcal{O}(n)$ and not $\mathcal{O}(n^2)$, as suggested by the standard parametrization of these systems. Furthermore, it is shown that linear port-Hamiltonian systems can be learned while remaining agnostic about the dimension of the underlying data-generating system. Numerical experiments show that this methodology can be used to efficiently estimate linear port-Hamiltonian systems out of input-output realizations, making the contributions in this paper the first example of a structure-preserving machine learning paradigm for linear port-Hamiltonian systems based on explicit representations of this model category.

Federated learning is a privacy-preserving machine learning technique that learns a shared model across decentralized clients. It can alleviate privacy concerns of personal re-identification, an important computer vision task. In this work, we implement federated learning to person re-identification (FedReID) and optimize its performance affected by statistical heterogeneity in the real-world scenario. We first construct a new benchmark to investigate the performance of FedReID. This benchmark consists of (1) nine datasets with different volumes sourced from different domains to simulate the heterogeneous situation in reality, (2) two federated scenarios, and (3) an enhanced federated algorithm for FedReID. The benchmark analysis shows that the client-edge-cloud architecture, represented by the federated-by-dataset scenario, has better performance than client-server architecture in FedReID. It also reveals the bottlenecks of FedReID under the real-world scenario, including poor performance of large datasets caused by unbalanced weights in model aggregation and challenges in convergence. Then we propose two optimization methods: (1) To address the unbalanced weight problem, we propose a new method to dynamically change the weights according to the scale of model changes in clients in each training round; (2) To facilitate convergence, we adopt knowledge distillation to refine the server model with knowledge generated from client models on a public dataset. Experiment results demonstrate that our strategies can achieve much better convergence with superior performance on all datasets. We believe that our work will inspire the community to further explore the implementation of federated learning on more computer vision tasks in real-world scenarios.