Protein structure modeling rests on a single computational primitive: the interaction between what a residue is (sequence content) and where it sits (three-dimensional geometry). What is the expressive limit of this layer class? We show that the complete bilinear operator over content-geometry outer products--the sufficient statistic of all second-order interactions--is the expressive ceiling, while the additive message passing of mainstream geometric GNNs is provably blind to content-geometry binding. We then introduce Hyper-Fold, a rank-K separable convolutional backbone approaching this ceiling at message-passing cost: each radius neighborhood is organized into a sequence hyperedge and a contact hyperedge, modulated by an edge-conditioned matrix-valued operator factorized into K learned basis operators with geometry-generated coefficients. Across enzyme function prediction, fold classification, and ligand binding site detection, Hyper-Fold and its hierarchical variant Hyper-Fold-Deep achieve the best results among protein-specific structure encoders; Hyper-Fold-Pocket, an anchored set-prediction head, surpasses UniSite-3D on UniSite-DS and two zero-shot benchmarks with no sequence language model features, 68x fewer parameters, and 4.8x lower latency--suggesting that a sufficiently expressive 3D backbone recovers information that fusion architectures previously borrowed from evolution-scale pretraining.
Yifan Feng, Guang Cheng, Shihui Ying et al.· 0 citations
Protein structure modeling rests on a single computational primitive: the interaction between what a residue is (sequence content) and where it sits (three-dimensional geometry). What is the expressive limit of this layer class? We show that the complete bilinear operator over content-geometry outer products--the sufficient statistic of all second-order interactions--is the expressive ceiling, while the additive message passing of mainstream geometric GNNs is provably blind to content-geometry binding. We then introduce Hyper-Fold, a rank-K separable convolutional backbone approaching this ceiling at message-passing cost: each radius neighborhood is organized into a sequence hyperedge and a contact hyperedge, modulated by an edge-conditioned matrix-valued operator factorized into K learned basis operators with geometry-generated coefficients. Across enzyme function prediction, fold classification, and ligand binding site detection, Hyper-Fold and its hierarchical variant Hyper-Fold-Deep achieve the best results among protein-specific structure encoders; Hyper-Fold-Pocket, an anchored set-prediction head, surpasses UniSite-3D on UniSite-DS and two zero-shot benchmarks with no sequence language model features, 68x fewer parameters, and 4.8x lower latency--suggesting that a sufficiently expressive 3D backbone recovers information that fusion architectures previously borrowed from evolution-scale pretraining.
Yifan Feng, Guang Cheng, Shihui Ying et al.· 0 citations
Isomorphism recognition is crucial for analyzing complex network structures. Traditional methods like Weisfeiler-Lehman (WL) kernels and various GNNs often overlook higher-order interactions essential for practical applications. Besides, hypergraph WL kernels struggle to distinguish uniform-regular hypergraphs due to their focus on neighborhood connectivity without effectively capturing unique higher-order structures. To overcome these issues, we introduce the Hypergraph Identity-Aware Subtree (IA Subtree) Kernel, which distinguishes uniform-regular hypergraphs by considering both neighborhood connectivity and connection density. This kernel detects subtle differences in hypergraph structures via variations in Closed Paths of different lengths. Additionally, we develop two Hypergraph Neural Networks: Hypergraph Isomorphism Networks (HGIN) and Identity-Aware Hypergraph Isomorphism Networks (IA-HGIN). These models combine the strengths of the Hypergraph WL subtree kernel with advanced neural architectures, improving classification by integrating features from closed-path distributions. We also provide the first comprehensive theoretical comparison of expressive power between kernel-based methods and neural networks, confirming IA-HGIN's superior performance. Experimental results on eight synthetic and eight real hypergraph datasets validate the effectiveness of our methods over existing State-of-the-Art approaches.
Yifan Feng, Rizhuo Huang, Yifan Zhang et al.· IEEE Transactions on Pattern...· 0 citations