Multi-modal Knowledge Graph Completion (KGC), which aims to enrich knowledge graph embeddings by incorporating images and text as supplementary information alongside triplets, is an significant task in learning KGs. Existing multi-modal KGC methods mainly focus on modalitylevel fusion, neglecting the importance of modeling the complex structures, such as hierarchical and circular patterns. To address this, we propose a Mixed-Curvature multi-modal Knowledge Graph Completion method (MCKGC) that embeds the information into three single-curvature spaces, including hyperbolic space, hyperspherical space, and Euclidean space, and incorporates multi-modal information into a mixed space. Specifically, MCKGC consists of Modality Information Mixed-Curvature Module (MIMCM) and Progressive Fusion Module (PFM). To improve the expressive ability for different modalities, MIMCM introduces multi-modal information into three single-curvature spaces for interaction. Then, to extract useful information from different modalities and capture the complex structure from the geometric information, PFM implements a progressive fusion strategy by utilizing modality-level and space-level gates to adaptively incorporate the information from different spaces. Extensive experiments on three widely used benchmarks demonstrate the effectiveness of our method.

Blockchain serves as a replicated transactional processing system in a trustless distributed environment. Existing blockchain systems all rely on an explicit ordering step to determine the global order of transactions that are collected from multiple peers. The ordering consensus can be the bottleneck since it must be Byzantine-fault tolerant and can scarcely benefit from parallel execution. In this paper, we propose an ordering-free architecture that makes ordering implicit through deterministic execution. Based on this novel architecture, we develop a permissioned blockchain system NeuChain. A number of key optimizations such as asynchronous block generation and pipelining are leveraged for high throughput and low latency. Several security mechanisms are also designed to make our system robust to malicious attacks. Our geo-distributed experimental results show that NeuChain can achieve 47.2--64.1X throughput improvement over HyperLedger Fabric and 1.6--12.2X throughput improvement over the state-of-the-art high performance blockchains.