Link prediction with knowledge graphs has been thoroughly studied in graph machine learning, leading to a rich landscape of graph neural network architectures with successful applications. Nonetheless, it remains challenging to transfer the success of these architectures to link prediction with relational hypergraphs. The presence of relational hyperedges makes link prediction a task between $k$ nodes for varying choices of $k$, which is substantially harder than link prediction with knowledge graphs, where every relation is binary ($k=2$). In this paper, we propose two frameworks for link prediction with relational hypergraphs and conduct a thorough analysis of the expressive power of the resulting model architectures via corresponding relational Weisfeiler-Leman algorithms, and also via some natural logical formalisms. Through extensive empirical analysis, we validate the power of the proposed model architectures on various relational hypergraph benchmarks. The resulting model architectures substantially outperform every baseline for inductive link prediction, and lead to state-of-the-art results for transductive link prediction. Our study therefore unlocks applications of graph neural networks to fully relational structures.

New findings in natural language processing (NLP) demonstrate that the strong memorization capability contributes a lot to the success of Large Language Models (LLM). This inspires us to explicitly bring an independent memory mechanism into CTR ranking model to learn and memorize cross features' representations. In this paper, we propose multi-Hash Codebook NETwork (HCNet) as the memory mechanism for efficiently learning and memorizing representations of cross features in CTR tasks. HCNet uses a multi-hash codebook as the main memory place and the whole memory procedure consists of three phases: multi-hash addressing, memory restoring, and feature shrinking. We also propose a new CTR model named MemoNet which combines HCNet with a DNN backbone. Extensive experimental results on three public datasets and online test show that MemoNet reaches superior performance over state-of-the-art approaches. Besides, MemoNet shows scaling law of large language model in NLP, which means we can enlarge the size of the codebook in HCNet to sustainably obtain performance gains. Our work demonstrates the importance and feasibility of learning and memorizing representations of cross features, which sheds light on a new promising research direction.