Determining the similarity between dynamical systems remains a long-standing challenge in both machine learning and neuroscience. Recent works based on Koopman operator theory have proven effective in analyzing dynamical similarity by examining discrepancies in the Koopman spectrum. Nevertheless, existing similarity metrics can be severely constrained when systems exhibit complex nonlinear behaviors across multiple temporal scales. In this work, we propose KoopSTD, a dynamical similarity measurement framework that precisely characterizes the underlying dynamics by approximating the Koopman spectrum with explicit timescale decoupling and spectral residual control. We show that KoopSTD maintains invariance under several common representation-space transformations, which ensures robust measurements across different coordinate systems. Our extensive experiments on physical and neural systems validate the effectiveness, scalability, and robustness of KoopSTD compared to existing similarity metrics. We also apply KoopSTD to explore two open-ended research questions in neuroscience and large language models, highlighting its potential to facilitate future scientific and engineering discoveries. Code is available at link.

Hypergraphs play a pivotal role in the modelling of data featuring higher-order relations involving more than two entities. Hypergraph neural networks emerge as a powerful tool for processing hypergraph-structured data, delivering remarkable performance across various tasks, e.g., hypergraph node classification. However, these models struggle to capture global structural information due to their reliance on local message passing. To address this challenge, we propose a novel hypergraph learning framework, HyperGraph Transformer (HyperGT). HyperGT uses a Transformer-based neural network architecture to effectively consider global correlations among all nodes and hyperedges. To incorporate local structural information, HyperGT has two distinct designs: i) a positional encoding based on the hypergraph incidence matrix, offering valuable insights into node-node and hyperedge-hyperedge interactions; and ii) a hypergraph structure regularization in the loss function, capturing connectivities between nodes and hyperedges. Through these designs, HyperGT achieves comprehensive hypergraph representation learning by effectively incorporating global interactions while preserving local connectivity patterns. Extensive experiments conducted on real-world hypergraph node classification tasks showcase that HyperGT consistently outperforms existing methods, establishing new state-of-the-art benchmarks. Ablation studies affirm the effectiveness of the individual designs of our model.

Mobile Edge Computing (MEC) is emerging as a promising computing scheme to support AI-enabled applications in vehicular networks, via offloading some tasks to edge servers deployed on Road Side Units (RSUs) that approximates to vehicles. In this work, we consider a general vehicular edge network (VEN), where each vehicle can offload tasks to edge servers or cloud server via a vehicle-to-infrastructure (V2I) transmission link, or to other vehicles via a vehicle-to-vehicle (V2V) transmission link. To characterize different task flows in different transmission links or computing servers, we introduce a V2V transmission queue, a V2V transmission queue, and a local computation queue for each vehicle, and an edge computation queue for each edge server. In such a queue-based VEN, we focus on the joint task offloading and scheduling problem for vehicles, which consists of (i) offloading problem, i.e., whether to offload tasks, and (ii) scheduling problem, i.e., where and how to offload tasks. The problem is challenging due to the online and asynchronous offloading and scheduling decisions for each task. We propose a Multi-layer Deep Reinforcement Learning (DRL) approach, where each vehicle trains three neural networks (called agents) to make different layers' decisions: (i) offloading agent, determining whether to offload each task when tasks arrive, and (ii) V2I and V2V scheduling agents, determining where and how to offloading each task in V2I and V2V transmission queues, respectively. We provide the detailed algorithm design of each agent by using the Double Deep Q-Network (DDQN) approach. Simulation results show that our proposed multi-layer DRL approach outperforms the existing baseline approaches in terms of both the cost performance and the convergence speed.

Post-hoc explanation techniques on graph neural networks (GNNs) provide economical solutions for opening the black-box graph models without model retraining. Many GNN explanation variants have achieved state-of-the-art explaining results on a diverse set of benchmarks, while they rarely provide theoretical analysis for their inherent properties and explanatory capability. In this work, we propose $\underline{\text{S}}$tructure-$\underline{\text{A}}$ware Shapley-based $\underline{\text{M}}$ultipiece $\underline{\text{E}}$xplanation (SAME) method to address the structure-aware feature interactions challenges for GNNs explanation. Specifically, SAME leverages an expansion-based Monte Carlo tree search to explore the multi-grained structure-aware connected substructure. Afterward, the explanation results are encouraged to be informative of the graph properties by optimizing the combination of distinct single substructures. With the consideration of fair feature interactions in the process of investigating multiple connected important substructures, the explanation provided by SAME has the potential to be as explainable as the theoretically optimal explanation obtained by the Shapley value within polynomial time. Extensive experiments on real-world and synthetic benchmarks show that SAME improves the previous state-of-the-art fidelity performance by 12.9\% on BBBP, 7.01\% on MUTAG, 42.3\% on Graph-SST2, 38.9\% on Graph-SST5, 11.3\% on BA-2Motifs and 18.2\% on BA-Shapes under the same testing condition. Code is available at https://github.com/same2023neurips/same.

Nonunion is one of the challenges faced by orthopedics clinics for the technical difficulties and high costs in photographing interosseous capillaries. Segmenting vessels and filling capillaries are critical in understanding the obstacles encountered in capillary growth. However, existing datasets for blood vessel segmentation mainly focus on the large blood vessels of the body, and the lack of labeled capillary image datasets greatly limits the methodological development and applications of vessel segmentation and capillary filling. Here, we present a benchmark dataset, named IFCIS-155, consisting of 155 2D capillary images with segmentation boundaries and vessel fillings annotated by biomedical experts, and 19 large-scale, high-resolution 3D capillary images. To obtain better images of interosseous capillaries, we leverage state-of-the-art immunofluorescence imaging techniques to highlight the rich vascular morphology of interosseous capillaries. We conduct comprehensive experiments to verify the effectiveness of the dataset and the benchmarking deep learning models (e.g. UNet/UNet++ and the modified UNet/UNet++). Our work offers a benchmark dataset for training deep learning models for capillary image segmentation and provides a potential tool for future capillary research. The IFCIS-155 dataset and code are all publicly available at https://github.com/ncclabsustech/IFCIS-55.

Memetic algorithm (MA) is widely applied to optimize routing problems as it provides one way to combine local search with global search. However, the local search in MA needs to be carefully designed according to the problem’s characteristics. In this article, we consider a real-world large-scale waste collection problem with multiple depots, multiple disposal facilities, multiple trips, and working time constraints. Vehicles with a limited capacity and working time can start from different depots, collect waste at different sites, and make multiple trips to different disposal facilities to empty the waste and return to its origin. While the existing work considered problems with multiple trips and time constraints, none have tackled problems with multiple depots, multiple disposal facilities, multiple trips, as well as working time constraints. The change from “single-depot” to “multidepot” not only reflects better the situation in real life but also leads to a qualitative different and more complex problem. In this article, we first model this complex problem mathematically. Then, a novel region-focused MA is proposed to tackle this new challenge. Compared to classic MA, this region-focused one is enhanced by two major components: 1) a new heuristic-assisted solution initialization algorithm and 2) a region-focused local search with novel heuristics. Comprehensive computational studies show that our proposed approaches significantly outperform several state-of-the-arts on our real problem of thousands of tasks. The new local search procedure and solution initialization method significantly improve the search ability in combination with global search ability of MA.