Federated learning is a distributed machine learning paradigm, which aims to train a model using the local data of many distributed clients. A key challenge in federated learning is that the data samples across the clients may not be identically distributed. To address this challenge, personalized federated learning with the goal of tailoring the learned model to the data distribution of every individual client has been proposed. In this paper, we focus on this problem and propose a novel personalized Federated Learning scheme based on Optimal Transport (FedOT) as a learning algorithm that learns the optimal transport maps for transferring data points to a common distribution as well as the prediction model under the applied transport map. To formulate the FedOT problem, we extend the standard optimal transport task between two probability distributions to multi-marginal optimal transport problems with the goal of transporting samples from multiple distributions to a common probability domain. We then leverage the results on multi-marginal optimal transport problems to formulate FedOT as a min-max optimization problem and analyze its generalization and optimization properties. We discuss the results of several numerical experiments to evaluate the performance of FedOT under heterogeneous data distributions in federated learning problems.

Existing works focus on fixed-size layout pattern generation, while the more practical free-size pattern generation receives limited attention. In this paper, we propose ChatPattern, a novel Large-Language-Model (LLM) powered framework for flexible pattern customization. ChatPattern utilizes a two-part system featuring an expert LLM agent and a highly controllable layout pattern generator. The LLM agent can interpret natural language requirements and operate design tools to meet specified needs, while the generator excels in conditional layout generation, pattern modification, and memory-friendly patterns extension. Experiments on challenging pattern generation setting shows the ability of ChatPattern to synthesize high-quality large-scale patterns.

The success of deep neural networks stems from their ability to generalize well on real data; however, Zhang et al. zhang2016understanding have observed that neural networks can easily overfit randomly-generated labels. This observation highlights the following question: why do gradient methods succeed in finding generalizable solutions for neural networks while there exist solutions with poor generalization behavior? In this work, we use a Fourier-based approach to study the generalization properties of gradient-based methods over 2-layer neural networks with band-limited activation functions. Our results indicate that in such settings if the underlying distribution of data enjoys nice Fourier properties including bandlimitedness and bounded Fourier norm, then the gradient descent method can converge to local minima with nice generalization behavior. We also establish a Fourier-based generalization error bound for band-limited function spaces, applicable to 2-layer neural networks with general activation functions. This generalization bound motivates a grouped version of path norms for measuring the complexity of 2-layer neural networks with ReLU-type activation functions. We empirically demonstrate that regularization of the group path norms results in neural network solutions that can fit true labels without losing test accuracy while not overfitting random labels.

This study addresses the critical challenge of detecting out-of-distribution (OOD) chest X-rays, where subtle view differences between lateral and frontal radiographs can lead to diagnostic errors. We develop a GAN-based framework that learns the inherent feature distribution of frontal views from the MIMIC-CXR dataset through latent space optimization and Kolmogorov–Smirnov statistical testing. Our approach generates similarity scores to reliably identify OOD cases, achieving exceptional performance with 100% precision, and 97.5% accuracy in detecting lateral views. The method demonstrates consistent reliability across operating conditions, maintaining accuracy above 92.5% and precision exceeding 93% under varying detection thresholds. These results provide both theoretical insights and practical solutions for OOD detection in medical imaging, demonstrating how GANs can establish feature representations for identifying distributional shifts. By significantly improving model reliability when encountering view-based anomalies, our framework enhances the clinical applicability of deep learning systems, ultimately contributing to improved diagnostic safety and patient outcomes.

Human activity recognition (HAR) is a prominent research direction in ubiquitous computing. Current state-of-the-art HAR models achieve great success by learning the correlations between the regions of the body parts by using the attached sensing devices for feature extraction. However, explicitly computing the correlations between whole body parts and whole sub-body parts, which is crucial for extracting discriminatory features for some activities, has not been investigated due to the lack of sensing devices that capture the movements of the whole (sub-)body parts. This study proposes an effective yet lightweight VirtualHAR framework, which automatically models correlations between the whole body parts, whole sub-body parts, and regions based on the concept of virtual sensing devices. The VirtualHAR framework mainly encompasses three modules. The backbone feature extraction (BEF) module extracts the features from a physical sensing device, based on which the Multipurpose Correlations Learning module constructs virtual sensing devices for body parts and sub-body parts and then exploits the explicit correlations between body parts, sub-body parts as well as in regions by using their attached physical sensing devices. Finally, the global aggregation (GA) module learns the GA representation for each physical sensing device by collecting the learned correlated representation from each virtual sensing device and physical sensing device. Comprehensive experiments on benchmark HAR datasets and a resource-constrained device confirm that VirtualHAR outperforms SOTA models in recognition performance and computational complexity. Through thorough quantitative and qualitative analysis, we validate the proposed VirtualHAR framework’s effectiveness and efficiency.

Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and empirical challenges. GANs trained using first-order optimization methods commonly fail to converge to a stable solution where the players cannot improve their objective, i.e., the Nash equilibrium of the underlying game. Such issues raise the question of the existence of Nash equilibrium solutions in the GAN zero-sum game. In this work, we show through several theoretical and numerical results that indeed GAN zero-sum games may not have any local Nash equilibria. To characterize an equilibrium notion applicable to GANs, we consider the equilibrium of a new zero-sum game with an objective function given by a proximal operator applied to the original objective, a solution we call the proximal equilibrium. Unlike the Nash equilibrium, the proximal equilibrium captures the sequential nature of GANs, in which the generator moves first followed by the discriminator. We prove that the optimal generative model in Wasserstein GAN problems provides a proximal equilibrium. Inspired by these results, we propose a new approach, which we call proximal training, for solving GAN problems. We discuss several numerical experiments demonstrating the existence of proximal equilibrium solutions in GAN minimax problems.