Personalized federated learning (PFL) plays a pivotal role in ensuring efficient privacy preservation and secure collaborative learning. However, PFL faces significant challenges due to data heterogeneity and device diversity. To enhance personalization and robustness in PFL, we propose a novel model called FedNODE, which leverages hierarchical embeddings. FedNODE incorporates personalized, pseudo-generic, and fusion embeddings to facilitate hierarchical information representation. We utilize a hypernetwork based on neural ordinary differential equations (ODEs) within the server to generate backbone parameters for different clients, enabling the creation of personalized embeddings. Additionally, we introduce a pseudo-generic embedding based on a learnable vector to balance personalized and generic information. A neural ODE-based network follows the backbone module for each client, integrating personalized and pseudo-generic embeddings. To validate the efficacy of FedNODE, we conduct extensive evaluations across various classification datasets, encompassing diverse statistically heterogeneous settings and noisy scenarios. The results demonstrate that FedNODE achieves state-of-the-art performance.

Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamic systems with nonlocal characteristics. Recent progress at the intersection of FDEs and deep learning has catalyzed a new wave of innovative models, demonstrating the potential to address challenges such as graph representation learning. However, training neural FDEs has primarily relied on direct differentiation through forward-pass operations in FDE numerical solvers, leading to increased memory usage and computational complexity, particularly in large-scale applications. To address these challenges, we propose a scalable adjoint backpropagation method for training neural FDEs by solving an augmented FDE backward in time, which substantially reduces memory requirements. This approach provides a practical neural FDE toolbox and holds considerable promise for diverse applications. We demonstrate the effectiveness of our method in several tasks, achieving performance comparable to baseline models while significantly reducing computational overhead.

Graph-structured data is prevalent in many applications. In subgraph federated learning (FL), this data is distributed across clients, each with a local subgraph. Personalized subgraph FL aims to develop a customized model for each client to handle diverse data distributions. However, performance variation across clients remains a key issue due to the heterogeneity of local subgraphs. To overcome the challenge, we propose FedSheafHN, a novel framework built on a sheaf collaboration mechanism to unify enhanced client descriptors with efficient personalized model generation. Specifically, FedSheafHN embeds each client’s local subgraph into a server-constructed collaboration graph by leveraging graph-level embeddings and employing sheaf diffusion within the collaboration graph to enrich client representations. Subsequently, FedSheafHN generates customized client models via a server-optimized hypernetwork. Empirical evaluations demonstrate that FedSheafHN outperforms existing personalized subgraph FL methods on various graph datasets. Additionally, it exhibits fast model convergence and effectively generalizes to new clients.

We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we quantify signal localization across these domains, revealing a trade-off between them. This framework allows us to identify a class of signals with maximal energy concentration in both domains, forming the fundamental atoms for a new joint vertex-time dictionary. This dictionary enhances signal reconstruction under practical constraints, such as intermittent data, commonly encountered in sensor and social networks. Numerical experiments on real-world datasets demonstrate the effectiveness of the proposed approach, showing improved reconstruction accuracy and noise robustness compared to existing methods.

Many works on graph neural networks (GNNs) focus on graph topologies and analyze graph-related operations to enhance performance on tasks such as node classification. In this paper, we propose to understand GNNs based on a feature-centric approach. Our main idea is to treat the features of nodes from each label class as a whole, from which we can identify the centroid. The convex hull of these centroids forms a simplex called the feature centroid simplex, where a simplex is a high-dimensional generalization of a triangle. We borrow ideas from coarse geometry to analyze the geometric properties of the feature centroid simplex by comparing them with basic geometric models, such as regular simplexes and degenerate simplexes. Such a simplex provides a simple platform to understand graph-based feature aggregation, including phenomena such as heterophily, oversmoothing, and feature re-shuffling. Based on the theory, we also identify simple and useful tricks for the node classification task.

Synthetic aperture radar (SAR) image change detection is of great importance for many applications but is significantly hampered by the presence of speckle noise. Recent learning-based methods have suppressed speckle noise by exploiting deep feature representations in both spatial and frequency domains. However, these methods are not interpretable while also imposing a high computational burden. Here, an interpretable and efficient spatial-frequency network is presented, which extracts noise-robust features in both spatial and frequency domains simultaneously. Spatially, noise-robust features are generated based on the neighborhood-based ratio (NR) and fed into an extreme learning machine (ELM) as a classifier for its efficiency and effectiveness. In the frequency domain, a shallow broad wavelet scattering network (SWSN) is proposed, which is an adaptation of the deep scattering network (DSN) that offers interpretable and noise-resilient feature representation with reduced depth. Instead of the sequential, layer-by-layer feature extraction approach of the DSN, the SWSN parallelly extracts frequency information, which significantly enhances computational efficiency. The proposed joint spatial-frequency framework provides robustness against speckle noise and obtains state-of-the-art performance as well as high computational efficiency in unsupervised SAR image change detection. Experimental results on two real SAR image datasets demonstrate the effectiveness of the proposed method.

In this work, we rigorously investigate the robustness of graph neural fractional-order differential equation (FDE) models. This framework extends beyond traditional graph neural (integer-order) ordinary differential equation (ODE) models by implementing the time-fractional Caputo derivative. Utilizing fractional calculus allows our model to consider long-term memory during the feature updating process, diverging from the memoryless Markovian updates seen in traditional graph neural ODE models. The superiority of graph neural FDE models over graph neural ODE models has been established in environments free from attacks or perturbations. While traditional graph neural ODE models have been verified to possess a degree of stability and resilience in the presence of adversarial attacks in existing literature, the robustness of graph neural FDE models, especially under adversarial conditions, remains largely unexplored. This paper undertakes a detailed assessment of the robustness of graph neural FDE models. We establish a theoretical foundation outlining the robustness characteristics of graph neural FDE models, highlighting that they maintain more stringent output perturbation bounds in the face of input and graph topology disturbances, compared to their integer-order counterparts. Our empirical evaluations further confirm the enhanced robustness of graph neural FDE models, highlighting their potential in adversarially robust applications.

We introduce the Distributed-order fRActional Graph Operating Network (DRAGON), a novel continuous Graph Neural Network (GNN) framework that incorporates distributed-order fractional calculus. Unlike traditional continuous GNNs that utilize integer-order or single fractional-order differential equations, DRAGON uses a learnable probability distribution over a range of real numbers for the derivative orders. By allowing a flexible and learnable superposition of multiple derivative orders, our framework captures complex graph feature updating dynamics beyond the reach of conventional models. We provide a comprehensive interpretation of our framework's capability to capture intricate dynamics through the lens of a non-Markovian graph random walk with node feature updating driven by an anomalous diffusion process over the graph. Furthermore, to highlight the versatility of the DRAGON framework, we conduct empirical evaluations across a range of graph learning tasks. The results consistently demonstrate superior performance when compared to traditional continuous GNN models. The implementation code is available at \url{https://github.com/zknus/NeurIPS-2024-DRAGON}.

In recent years, algorithm unrolling has emerged as a powerful technique for designing interpretable neural networks based on iterative algorithms. Imaging inverse problems have particularly benefited from unrolling based deep network design since many traditional model-based approaches rely on iterative optimization. Despite exciting progress, typical unrolling approaches heuristically design layer-specific convolution weights to improve performance. Crucially, convergence properties of the underlying iterative algorithm are lost once layer specific parameters are learned from training data. In this paper, we propose a neural network architecture that breaks the trade-off between retaining algorithm properties while simultaneously enhancing performance. We focus on non-blind image deblurring problem and unroll the widely-applied Half-Quadratic Splitting (HQS) algorithm. We develop a new parameterization scheme that enforces the layer-specific parameters to asymptotically approach certain fixed points, a new result that we analytically establish. Experimental results show that our approach outperforms many state of the art non-blind deblurring techniques on benchmark datasets, while enabling convergence and interpretability.

Recently, synthetic aperture radar (SAR) image change detection has become an interesting yet challenging direction due to the presence of speckle noise. Although both traditional and modern learning-driven methods attempted to overcome this challenge, deep convolutional neural networks (DCNNs)-based methods are still hindered by the lack of interpretability and the requirement of large computation power. To overcome this drawback, wavelet scattering network (WSN) and Fourier scattering network (FSN) are proposed. Combining respective merits of WSN and FSN, we propose Stockwell scattering network (SSN) based on Stockwell transform (ST), which is widely applied against noisy signals and shows advantageous characteristics in speckle reduction. The proposed SSN provides noise-resilient feature representation and obtains state-of-the-art performance in SAR image change detection as well as high computational efficiency. Experimental results on three real SAR image datasets demonstrate the effectiveness of the proposed method.