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Hyper-Fold: Exploring the Expressive Limit of Sequence-Geometry Learning for Proteins via Hypergraph Modeling

arXiv · AI, language, vision and robotics · article · Aug 29, 2026 · UTC

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 cei

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