Huiyuan Wang

Yiming Huang, Huiyuan Wang, Yuxuan Du et al.

Quantum neural networks (QNNs) and quantum kernels stand as prominent figures in the realm of quantum machine learning, poised to leverage the nascent capabilities of near-term quantum computers to surmount classical machine learning challenges. Nonetheless, the training efficiency challenge poses a limitation on both QNNs and quantum kernels, curbing their efficacy when applied to extensive datasets. To confront this concern, we present a unified approach: coreset selection, aimed at expediting the training of QNNs and quantum kernels by distilling a judicious subset from the original training dataset. Furthermore, we analyze the generalization error bounds of QNNs and quantum kernels when trained on such coresets, unveiling the comparable performance with those training on the complete original dataset. Through systematic numerical simulations, we illuminate the potential of coreset selection in expediting tasks encompassing synthetic data classification, identification of quantum correlations, and quantum compiling. Our work offers a useful way to improve diverse quantum machine learning models with a theoretical guarantee while reducing the training cost.

Huiyuan Wang, Xuyang Zhao, Wei Lin

Federated learning, where algorithms are trained across multiple decentralized devices without sharing local data, is increasingly popular in distributed machine learning practice. Typically, a graph structure $G$ exists behind local devices for communication. In this work, we consider parameter estimation in federated learning with data distribution and communication heterogeneity, as well as limited computational capacity of local devices. We encode the distribution heterogeneity by parametrizing distributions on local devices with a set of distinct $p$-dimensional vectors. We then propose to jointly estimate parameters of all devices under the $M$-estimation framework with the fused Lasso regularization, encouraging an equal estimate of parameters on connected devices in $G$. We provide a general result for our estimator depending on $G$, which can be further calibrated to obtain convergence rates for various specific problem setups. Surprisingly, our estimator attains the optimal rate under certain graph fidelity condition on $G$, as if we could aggregate all samples sharing the same distribution. If the graph fidelity condition is not met, we propose an edge selection procedure via multiple testing to ensure the optimality. To ease the burden of local computation, a decentralized stochastic version of ADMM is provided, with convergence rate $O(T^{-1}\log T)$ where $T$ denotes the number of iterations. We highlight that, our algorithm transmits only parameters along edges of $G$ at each iteration, without requiring a central machine, which preserves privacy. We further extend it to the case where devices are randomly inaccessible during the training process, with a similar algorithmic convergence guarantee. The computational and statistical efficiency of our method is evidenced by simulation experiments and the 2020 US presidential election data set.

Huiyuan Wang, Wei Lin

Large neural networks have proved remarkably effective in modern deep learning practice, even in the overparametrized regime where the number of active parameters is large relative to the sample size. This contradicts the classical perspective that a machine learning model must trade off bias and variance for optimal generalization. To resolve this conflict, we present a nonasymptotic generalization theory for two-layer neural networks with ReLU activation function by incorporating scaled variation regularization. Interestingly, the regularizer is equivalent to ridge regression from the angle of gradient-based optimization, but plays a similar role to the group lasso in controlling the model complexity. By exploiting this "ridge-lasso duality," we obtain new prediction bounds for all network widths, which reproduce the double descent phenomenon. Moreover, the overparametrized minimum risk is lower than its underparametrized counterpart when the signal is strong, and is nearly minimax optimal over a suitable class of functions. By contrast, we show that overparametrized random feature models suffer from the curse of dimensionality and thus are suboptimal.