Since heterogeneity presents a fundamental challenge in graph federated learning, many existing methods are proposed to deal with node feature heterogeneity and structure heterogeneity. However, they overlook the critical homophily heterogeneity, which refers to the substantial variation in homophily levels across graph data from different clients. The homophily level represents the proportion of edges connecting nodes that belong to the same class. Due to adapting to their local homophily, local models capture inconsistent spectral properties across different clients, significantly reducing the effectiveness of collaboration. Specifically, local models trained on graphs with high homophily tend to capture low-frequency information, whereas local models trained on graphs with low homophily tend to capture high-frequency information. To effectively deal with homophily heterophily, we introduce the spectral Graph Neural Network (GNN) and propose a novel Federated learning method by mining Graph Spectral Properties (FedGSP). On one hand, our proposed FedGSP enables clients to share generic spectral properties (i.e., low-frequency information), allowing all clients to benefit through collaboration. On the other hand, inspired by our theoretical findings, our proposed FedGSP allows clients to complement non-generic spectral properties by acquiring the spectral properties they lack (i.e., high-frequency information), thereby obtaining additional information gain. Extensive experiments conducted on six homophilic and five heterophilic graph datasets, across both non-overlapping and overlapping settings, validate the superiority of our method over eleven state-of-the-art methods. Notably, our FedGSP outperforms the second-best method by an average margin of 3.28% on all heterophilic datasets.

Heterogeneity is a fundamental and challenging issue in federated learning, especially for the graph data due to the complex relationships among the graph nodes. To deal with the heterogeneity, lots of existing methods perform the weighted federation based on their calculated similarities between pairwise clients (i.e., subgraphs). However, their inter-subgraph similarities estimated with the outputs of local models are less reliable, because the final outputs of local models may not comprehensively represent the real distribution of subgraph data. In addition, they ignore the critical intra-heterogeneity which usually exists within each subgraph itself. To address these issues, we propose a novel Federated learning method by integrally modeling the Inter-Intra Heterogeneity (FedIIH). For the inter-subgraph relationship, we propose a novel hierarchical variational model to infer the whole distribution of subgraph data in a multi-level form, so that we can accurately characterize the inter-subgraph similarities with the global perspective. For the intra-heterogeneity, we disentangle the subgraph into multiple latent factors and partition the model parameters into multiple parts, where each part corresponds to a single latent factor. Our FedIIH not only properly computes the distribution similarities between subgraphs, but also learns disentangled representations that are robust to irrelevant factors within subgraphs, so that it successfully considers the inter- and intra- heterogeneity simultaneously. Extensive experiments on six homophilic and five heterophilic graph datasets in both non-overlapping and overlapping settings demonstrate the effectiveness of our method when compared with nine state-of-the-art methods. Specifically, FedIIH averagely outperforms the second-best method by a large margin of 5.79% on all heterophilic datasets.

Scientific laws describing natural systems may be more complex than our intuition can handle, and thus how we discover laws must change. Machine learning (ML) models can analyze large quantities of data, but their structure should match the underlying physical constraints to provide useful insight. Here we demonstrate a ML approach that incorporates such physical intuition to infer force laws in dusty plasma experiments. Trained on 3D particle trajectories, the model accounts for inherent symmetries and non-identical particles, accurately learns the effective non-reciprocal forces between particles, and extracts each particle's mass and charge. The model's accuracy (R^2 > 0.99) points to new physics in dusty plasma beyond the resolution of current theories and demonstrates how ML-powered approaches can guide new routes of scientific discovery in many-body systems.

In frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems, downlink channel state information (CSI) needs to be sent back to the base station (BS) by the users, which causes prohibitive feedback overhead. In this paper, we propose a lightweight and flexible deep learning-based CSI feedback approach by capitalizing on deep equilibrium models. Different from existing deep learning-based methods that stack multiple explicit layers, we propose an implicit equilibrium block to mimic the behavior of an infinite-depth neural network. In particular, the implicit equilibrium block is defined by a fixed-point iteration and the trainable parameters in different iterations are shared, which results in a lightweight model. Furthermore, the number of forward iterations can be adjusted according to users' computation capability, enabling a flexible accuracy-efficiency trade-off. Simulation results will show that the proposed design obtains a comparable performance as the benchmarks but with much-reduced complexity and permits an accuracy-efficiency trade-off at runtime.

Terahertz ultra-massive multiple-input multiple-output (THz UM-MIMO) is envisioned as one of the key enablers of 6G wireless systems. Due to the joint effect of its array aperture and small wavelength, the near-field region of THz UM-MIMO is greatly enlarged. The high-dimensional channel of such systems thus consists of a stochastic mixture of far and near fields, which renders channel estimation extremely challenging. Previous works based on uni-field assumptions cannot capture the hybrid far- and near-field features, thus suffering significant performance loss. This motivates us to consider hybrid-field channel estimation. We draw inspirations from fixed point theory to develop an efficient deep learning based channel estimator with adaptive complexity and linear convergence guarantee. Built upon classic orthogonal approximate message passing, we transform each iteration into a contractive mapping, comprising a closed-form linear estimator and a neural network based non-linear estimator. A major algorithmic innovation involves applying fixed point iteration to compute the channel estimate while modeling neural networks with arbitrary depth and adapting to the hybrid-field channel conditions. Simulation results verify our theoretical analysis and show significant performance gains over state-of-the-art approaches in the estimation accuracy and convergence rate.

Recently, Graph Convolutional Network (GCN) has been widely used in Hyperspectral Image (HSI) classification due to its satisfactory performance. However, the number of labeled pixels is very limited in HSI, and thus the available supervision information is usually insufficient, which will inevitably degrade the representation ability of most existing GCN-based methods. To enhance the feature representation ability, in this paper, a GCN model with contrastive learning is proposed to explore the supervision signals contained in both spectral information and spatial relations, which is termed Contrastive Graph Convolutional Network (ConGCN), for HSI classification. First, in order to mine sufficient supervision signals from spectral information, a semi-supervised contrastive loss function is utilized to maximize the agreement between different views of the same node or the nodes from the same land cover category. Second, to extract the precious yet implicit spatial relations in HSI, a graph generative loss function is leveraged to explore supplementary supervision signals contained in the graph topology. In addition, an adaptive graph augmentation technique is designed to flexibly incorporate the spectral-spatial priors of HSI, which helps facilitate the subsequent contrastive representation learning. The extensive experimental results on four typical benchmark datasets firmly demonstrate the effectiveness of the proposed ConGCN in both qualitative and quantitative aspects.