Title: Two Birds, One Stone: An Equivalent Transformation for Hyper-relational Knowledge Graph Modeling. Abstract: By representing knowledge in a primary triple associated with additional attribute value qualifiers, hyper-relational knowledge graph (HKG) that generalizes triple based knowledge graph (KG) has been attracting research attention recently. Compared with KG, HKG is enriched with the semantic difference between the primary triple and additional qualifiers as well as the structural connection between entities in hyper-relational graph structure. However, to model HKG, existing studies mainly focus on either semantic information or structural information therein, fail to capture both simultaneously. To tackle this issue, in this paper, we propose an equivalent transformation for HKG modeling, referred to as TransEQ. Specifically, the equivalent transformation transforms a HKG to a KG, which considers both semantic and structural characteristics. Then a generalized encoder-decoder framework is developed to bridge the modeling research between KG and HKG. In the encoder part, KG-based graph neural networks are leveraged for structural modeling; while in the decoder part, various HKG-based scoring functions are exploited for semantic modeling. Especially, we design the sharing embedding mechanism in the encoder-decoder framework with semantic relatedness captured. We further theoretically prove that TransEQ preserves complete information in the equivalent transformation, and also achieves full expressivity. Finally, extensive experiments on three benchmarks demonstrate the superior performance of TransEQ in terms of both effectiveness and efficiency. On the largest benchmark WikiPeople, TransEQ significantly improves the state-of-the-art models by 15% on MRR.