Abstract: Hypergraph Neural Networks (HGNNs) have recently attracted much attention and exhibited satisfactory performance due to their superiority in high-order correlation modeling. However, it is noticed that the high-order modeling capability of hypergraph also brings increased computation complexity, which hinders its practical industrial deployment.In practice, we find that one key barrier to the efficient deployment of HGNNs is the high-order structural dependencies during inference.In this paper, we propose to bridge the gap between the HGNNs and inference-efficient Multi-Layer Perceptron (MLPs) to eliminate the hypergraph dependency of HGNNs and thus reduce computational complexity as well as improve inference speed. Specifically, we introduce LightHGNN and LightHGNN$^+$ for fast inference with low complexity. LightHGNN directly distills the knowledge from teacher HGNNs to student MLPs via soft labels, and LightHGNN$^+$ further explicitly injects reliable high-order correlations into the student MLPs to achieve topology-aware distillation and resistance to over-smoothing.Experiments on eight hypergraph datasets demonstrate that even without hypergraph dependency, the proposed LightHGNNs can still achieve competitive or even better performance than HGNNs and outperform vanilla MLPs by $16.3$ on average. Extensive experiments on three graph datasets further show the average best performance of our LightHGNNs compared with all other methods.Experiments on synthetic hypergraphs with 5.5w vertices indicate LightHGNNs can run $100\times$ faster than HGNNs, showcasing their ability for latency-sensitive deployments.