Aug 29, 2026 · cs.AIJ/K move · Enter open · S save
Yifan Feng, Guanjie Cheng, Shihui Ying, Shaoyi Du+1
1{School of Software, BNRist, THUIBCS}, Tsinghua University, Beijing 100084, China · School of Software Technology, Zhejiang University, Ningbo 315100, China · 3Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China · 4State Key Laboratory of Human-Machine Hybrid Augmented Intelligence, Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, Xi’an 710049, China
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.