The fundamental gap of a kind of two dimensional sub-elliptic operator

This paper is concerned at the minimization fundamental gap problem for a class of two-dimensional degenerate sub-elliptic operators. We establish existence results for weak solutions, Sobolev embedding theorem and spectral theory of sub-elliptic operators. We provide the existence and characterization theorems for extremizing potentials $V(x)$ when $V(x)$ is subject to $L^\infty$ norm constraint

Efficient Semi-Supervised Federated Learning for Heterogeneous Participants

Federated Learning (FL) has emerged to allow multiple clients to collaboratively train machine learning models on their private data. However, training and deploying large-scale models on resource-constrained clients is challenging. Fortunately, Split Federated Learning (SFL) offers a feasible solution by alleviating the computation and/or communication burden on clients. However, existing SFL works often assume sufficient labeled data on clients, which is usually impractical. Besides, data non-IIDness across clients poses another challenge to ensure efficient model training. To our best knowledge, the above two issues have not been simultaneously addressed in SFL. Herein, we propose a novel Semi-SFL system, which incorporates clustering regularization to perform SFL under the more practical scenario with unlabeled and non-IID client data. Moreover, our theoretical and experimental investigations into model convergence reveal that the inconsistent training processes on labeled and unlabeled data have an influence on the effectiveness of clustering regularization. To this end, we develop a control algorithm for dynamically adjusting the global updating frequency, so as to mitigate the training inconsistency and improve training performance. Extensive experiments on benchmark models and datasets show that our system provides a 3.0x speed-up in training time and reduces the communication cost by about 70.3% while reaching the target accuracy, and achieves up to 5.1% improvement in accuracy under non-IID scenarios compared to the state-of-the-art baselines.Comment: 16 pages, 12 figures, conferenc

MergeSFL: Split Federated Learning with Feature Merging and Batch Size Regulation

Recently, federated learning (FL) has emerged as a popular technique for edge AI to mine valuable knowledge in edge computing (EC) systems. To mitigate the computing/communication burden on resource-constrained workers and protect model privacy, split federated learning (SFL) has been released by integrating both data and model parallelism. Despite resource limitations, SFL still faces two other critical challenges in EC, i.e., statistical heterogeneity and system heterogeneity. To address these challenges, we propose a novel SFL framework, termed MergeSFL, by incorporating feature merging and batch size regulation in SFL. Concretely, feature merging aims to merge the features from workers into a mixed feature sequence, which is approximately equivalent to the features derived from IID data and is employed to promote model accuracy. While batch size regulation aims to assign diverse and suitable batch sizes for heterogeneous workers to improve training efficiency. Moreover, MergeSFL explores to jointly optimize these two strategies upon their coupled relationship to better enhance the performance of SFL. Extensive experiments are conducted on a physical platform with 80 NVIDIA Jetson edge devices, and the experimental results show that MergeSFL can improve the final model accuracy by 5.82% to 26.22%, with a speedup by about 1.74x to 4.14x, compared to the baselines