Decimated Hypergraph Framelets Based on Spline Wavelets Basis.

Hypergraph Neural Networks (HGNNs) can effectively model high-order relational data but lack robust multi-scale analysis tools and struggle with heterophilic hypergraphs. To address these issues, this paper proposes SWDHFN, a novel Spline-Wavelet-based Decimated Hypergraph Framelets Neural Network. Inspired by Haar wavelets and spline theory, SWDHFN embeds hypergraph structures into spline function spaces to encode multi-entity interactions. SWDHFN leverages the smoothness of spline bases into hypergraph modeling. This ensures the continuity and smooth transition of feature encoding and avoids noise interference during neighborhood information aggregation. We also propose the fast framelet transforms for the spline-Wavelet-based decimated hypergraph framelets, with computational complexity 𝒪(Nlog N) . Experimental results on benchmark datasets show that SWDHFN achieves state-of-the-art (SOTA) performance on both homophilic and heterophilic hypergraphs, outperforming traditional HGNNs and framelet-based models. Its sparse matrix optimization ensures superior computational scalability.