  Message passing on hypergraphs has been a standard framework for learning
higher-order correlations between hypernodes. Recently-proposed hypergraph
neural networks (HGNNs) can be categorized into spatial and spectral methods
based on their design choices. In this work, we analyze the impact of change in
hypergraph topology on the suboptimal performance of HGNNs and propose DPHGNN,
a novel dual-perspective HGNN that introduces equivariant operator learning to
capture lower-order semantics by inducing topology-aware spatial and spectral
inductive biases. DPHGNN employs a unified framework to dynamically fuse
lower-order explicit feature representations from the underlying graph into the
super-imposed hypergraph structure. We benchmark DPHGNN over eight benchmark
hypergraph datasets for the semi-supervised hypernode classification task and
obtain superior performance compared to seven state-of-the-art baselines. We
also provide a theoretical framework and a synthetic hypergraph isomorphism
test to express the power of spatial HGNNs and quantify the expressivity of
DPHGNN beyond the Generalized Weisfeiler Leman (1-GWL) test. Finally, DPHGNN
was deployed by our partner e-commerce company for the Return-to-Origin (RTO)
prediction task, which shows ~7% higher macro F1-Score than the best baseline.
