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

arXiv:2608.29207v1 Announce Type: cross Abstract: 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.

Abstract: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.

Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

arXiv:2608.29207 [cs.AI]

(or arXiv:2608.29207v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2608.29207 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

aiqbench analysis

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

Related coverage