Capsule Networks (CapsNets) show exceptional graph representation capacity via dynamic routing and vectorized hierarchical representations, but they model the complex geometries of real-world graphs (e.g., hierarchies, clusters, cycles) poorly by fixed-curvature space due to the inherent geodesical disconnectedness issues, leading to suboptimal performance. Recent works find that non-Euclidean pseudo-Riemannian manifolds provide specific inductive biases for embedding graph data, but how to leverage them to improve CapsNets is still underexplored. Here, we extend the Euclidean capsule routing into geodesically disconnected pseudo-Riemannian manifolds and derive a Pseudo-Riemannian Capsule Network (PR-CapsNet), which models data in pseudo-Riemannian manifolds of adaptive curvature, for graph representation learning. Specifically, PR-CapsNet enhances the CapsNet with Adaptive Pseudo-Riemannian Tangent Space Routing by utilizing pseudo-Riemannian geometry. Unlike single-curvature or subspace-partitioning methods, PR-CapsNet concurrently models hierarchical and cluster/cyclic graph structures via its versatile pseudo-Riemannian metric. It first deploys Pseudo-Riemannian Tangent Space Routing to decompose capsule states into spherical-temporal and Euclidean-spatial subspaces with diffeomorphic transformations. Then, an Adaptive Curvature Routing is developed to adaptively fuse features from different curvature spaces for complex graphs via a learnable curvature tensor with geometric attention from local manifold properties. Finally, a geometric properties-preserved Pseudo-Riemannian Capsule Classifier is developed to project capsule embeddings to tangent spaces and use curvature-weighted softmax for classification. Extensive experiments on node and graph classification benchmarks show PR-CapsNet outperforms state-of-the-art models, validating PR-CapsNet's strong representation power for complex graph structures.

As a core module of web search, query understanding aims to bridge the semantic gap between user queries and web page documents, thereby enhancing the ability to deliver more relevant results.Recently, Large Language Models (LLMs) have achieved significant breakthroughs that have fundamentally altered the workflow of existing search ranking tasks.However, few researchers have explored the integration of LLMs into the field of query understanding.In this paper, we investigate the potential of LLMs in query understanding by conducting a comprehensive evaluation across three dimensions: term, structure, and topic.This evaluation includes several representative tasks such as segmentation, term weighting, error correction, query expansion, and intent recognition.The experimental results reveal that LLMs are particularly effective in query expansion and intent recognition but show limited improvement in other areas.This limitation may be attributed to LLMs' primary focus on modeling the semantic knowledge of entire queries, while lacking the capability to capture token-level information with finer granularity.Additionally, we explore potential practical applications of LLMs in query understanding, such as integrating the evaluation and training capabilities of smaller models with LLMs and constructing unsupervised samples.Based on comprehensive empirical results, collaborative training emerges as a promising approach to leverage LLMs for query understanding.We hope this research will advance the practical application of LLMs in query understanding and contribute to the development of this field.

Network-layer security threats have become increasingly sophisticated, exposing significant vulnerabilities in the current Internet architecture. Despite various proposed solutions, the field faces fundamental challenges in balancing user privacy with network security and achieving practical deployment. This paper presents a novel approach called PIPE (Privacy-preserving Identity and Path Enhancement), which leverages a distributed infrastructure of Key Distribution Servers (KDS) to integrate Decentralized Identity (DID) with source and path verification. Our solution binds user identity, address, path, and data while maintaining privacy through encryption and per-hop address transformation. By embedding DID information in address and implementing encrypted path verification, we achieve enhanced network accountability without compromising privacy. Experimental results demonstrate PIPE’s practicality and advantages over existing approaches in terms of deployment flexibility and security guarantees. Our work contributes to the evolution of secure network architectures by balancing accountability requirements with privacy protection while ensuring practical deployability.

Orchestrating the intertwined computing and network resources at the foundational fabric level of Computing Power Networks (CPNs) remains a critical challenge. Current network architectures often lead to resource fragmentation and performance bottlenecks because routing decisions are decoupled from the dynamic, intrinsic processing loads of network nodes. This fundamental disconnect creates inefficiencies and security risks that undermine the entire CPN substrate. To address this, we introduce GAT-GRPO, a Deep Reinforcement Learning (DRL) framework designed for the fine-grained Joint Routing and in-Network Processing Placement (JR-PP) task. GAT-GRPO features a novel dual-path Graph Attention Network (GAT) that explicitly models the distinct heterogeneity of link states and nodal capacity. To master the complex combinatorial action space, we are the first to leverage Group Relative Policy Optimization (GRPO)—a stable, critic-free algorithm—for network resource orchestration. Extensive evaluations show GAT-GRPO boosts network revenue by 3.7%-5.3% over latest baselines. Mininet emulations further validate its superiority, with a 6.7% reduction in peak queue length and a 6% decrease in peak link utilization against the latest DRL agent. Our work delivers a practical, high-performance solution for foundational resource orchestration in CPNs, enabling a more intelligent and resilient networking substrate for higher-level services.