Knowledge graph (KG) embedding methods predict missing links by computing the similarities between entities. The existing embedding methods are designed with either shallow or deep architectures. Shallow methods are scalable to large KGs but are limited in capturing fine-grained semantics. Deep methods can capture rich semantic interactions, but they require numerous model parameters. This study proposes a novel embedding model that effectively combines the strengths of both shallow and deep models. In particular, the proposed model adopts the design principles of shallow models and incorporates an expressive compositional operator inspired by deep models. This approach maintains the scalability while significantly enhancing the expressive capacity of the proposed model. Moreover, the proposed model learns embeddings using the Poincaré ball model of hyperbolic geometry to preserve the hierarchies between entities. The experimental results demonstrated the effectiveness of learning Poincaré embeddings with an expressive compositional operator. Notably, a substantial improvement of 2.4% in the Mean Reciprocal Rank (MRR) and a 1.4% improvement in hit@1 was observed on the CoDEx-m and CoDEx-s datasets, respectively, when compared to the current state-of-the-art methods. The proposed model was implemented using PyTorch 1.8.1, and experiments were conducted on a server with an NVIDIA GeForce RTX 2080 Ti GPU.