Accelerating Differentially Private Federated Learning via Adaptive Extrapolation

The federated learning (FL) framework enables multiple clients to collaboratively train machine learning models without sharing their raw data, but it remains vulnerable to privacy attacks. One promising approach is to incorporate differential privacy (DP)-a formal notion of privacy-into the FL framework. DP-FedAvg is one of the most popular algorithms for DP-FL, but it is known to suffer from the slow convergence in the presence of heterogeneity among clients' data. Most of the existing methods to accelerate DP-FL require 1) additional hyperparameters or 2) additional computational cost for clients, which is not desirable since 1) hyperparameter tuning is computationally expensive and data-dependent choice of hyperparameters raises the risk of privacy leakage, and 2) clients are often resource-constrained. To address this issue, we propose DP-FedEXP, which adaptively selects the global step size based on the diversity of the local updates without requiring any additional hyperparameters or client computational cost. We show that DP-FedEXP provably accelerates the convergence of DP-FedAvg and it empirically outperforms existing methods tailored for DP-FL.

Mean-field Analysis on Two-layer Neural Networks from a Kernel Perspective

In this paper, we study the feature learning ability of two-layer neural networks in the mean-field regime through the lens of kernel methods. To focus on the dynamics of the kernel induced by the first layer, we utilize a two-timescale limit, where the second layer moves much faster than the first layer. In this limit, the learning problem is reduced to the minimization problem over the intrinsic kernel. Then, we show the global convergence of the mean-field Langevin dynamics and derive time and particle discretization error. We also demonstrate that two-layer neural networks can learn a union of multiple reproducing kernel Hilbert spaces more efficiently than any kernel methods, and neural networks acquire data-dependent kernel which aligns with the target function. In addition, we develop a label noise procedure, which converges to the global optimum and show that the degrees of freedom appears as an implicit regularization.

Approximation and Estimation Ability of Transformers for Sequence-to-Sequence Functions with Infinite Dimensional Input

Despite the great success of Transformer networks in various applications such as natural language processing and computer vision, their theoretical aspects are not well understood. In this paper, we study the approximation and estimation ability of Transformers as sequence-to-sequence functions with infinite dimensional inputs. Although inputs and outputs are both infinite dimensional, we show that when the target function has anisotropic smoothness, Transformers can avoid the curse of dimensionality due to their feature extraction ability and parameter sharing property. In addition, we show that even if the smoothness changes depending on each input, Transformers can estimate the importance of features for each input and extract important features dynamically. Then, we proved that Transformers achieve similar convergence rate as in the case of the fixed smoothness. Our theoretical results support the practical success of Transformers for high dimensional data.