Detecting the origin of information or infection spread in networks is a fundamental challenge with applications in misinformation tracking, epidemiology, and beyond. We study the multi-source detection problem: given snapshot observations of node infection status on a graph, estimate the set of source nodes that initiated the propagation. Existing methods either lack statistical guarantees or are limited to specific diffusion models and assumptions. We propose a novel conformal prediction framework that provides statistically valid recall guarantees for source set detection, independent of the underlying diffusion process or data distribution. Our approach introduces principled score functions to quantify the alignment between predicted probabilities and true sources, and leverages a calibration set to construct prediction sets with user-specified recall and coverage levels. The method is applicable to both single- and multi-source scenarios, supports general network diffusion dynamics, and is computationally efficient for large graphs. Empirical results demonstrate that our method achieves rigorous coverage with competitive accuracy, outperforming existing baselines in both reliability and scalability.

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.

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 the FRactional-Order graph Neural Dynamical network (FROND), a new continuous graph neural network (GNN) framework. Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo fractional derivative to leverage the non-local properties of fractional calculus. This approach enables the capture of long-term dependencies in feature updates, moving beyond the Markovian update mechanisms in conventional integer-order models and offering enhanced capabilities in graph representation learning. We offer an interpretation of the node feature updating process in FROND from a non-Markovian random walk perspective when the feature updating is particularly governed by a diffusion process. We demonstrate analytically that oversmoothing can be mitigated in this setting. Experimentally, we validate the FROND framework by comparing the fractional adaptations of various established integer-order continuous GNNs, demonstrating their consistently improved performance and underscoring the framework's potential as an effective extension to enhance traditional continuous GNNs. The code is available at \url{https://github.com/zknus/ICLR2024-FROND}.

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}.