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

• URL: http://arxiv.org/abs/2608.29207v2
• Date: Tue, 01 Sep 2026 05:39:16 GMT
• Title: Hyper-Fold: Exploring the Expressive Limit of Sequence-Geometry Learning for Proteins via Hypergraph Modeling
• Abstract summary: We show that the complete bilinear operator over content-geometry outer products--the sufficient statistic of all second-order interactions--is the expressive ceiling.<n>We then introduce Hyper-Fold, a rank-K separable convolutional backbone approaching this ceiling at message-passing cost.
• Score: 55.36837305276515
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• MeshWeaver: Sparse-Voxel-Guided Surface Weaving for Autoregressive Mesh Generation [53.06620176910962]
  MeshWeaver is an autoregressive framework that treats mesh generation as a surface weaving process.<n>MeshWeaver achieves a state-of-the-art compression ratio of 18%, can generate meshes with up to 16K faces, and significantly improves geometric fidelity over prior approaches.
  arXiv  Detail & Related papers  (2026-06-03T10:15:43Z)
• Contrastive Multi-Modal Hypergraph Reasoning for 3D Crowd Mesh Recovery [12.116457701406047]
  Multi-person 3D reconstruction is pivotal for real-world interaction analysis.<n>Current approaches rely on single-modality inputs, which inherently lack geometric guidance.<n>We propose Contrastive Multi-modal Hypergraph Reasoning to synergize semantic, geometric, and pose cues for crowd reconstruction.
  arXiv  Detail & Related papers  (2026-04-01T09:39:01Z)
• Protein Structure Tokenization via Geometric Byte Pair Encoding [36.39587248348813]
  We introduce GeoBPE, a principled protein structure tokenizers (PSTs)<n>GeoBPE transforms continuous, noisy, multi-scale backbone conformations into discrete sentences'' of geometry while enforcing global constraints.<n>It offers compression ($>$10x reduction in bits-per-residue at similar distortion rate), data efficiency ($>$10x less training data), and generalization.
  arXiv  Detail & Related papers  (2025-11-13T22:53:29Z)
• Consistent line clustering using geometric hypergraphs [0.6749750044497732]
  We show how a 3-uniform hypergraph can be used to group lines in a Euclidean space.<n>In contrast to classical block models, latent geometric constraints in this construction introduce significant dependencies between hyperedges.<n>We derive information-theoretic thresholds for exact and almost exact recovery for data generated from intersecting lines on a plane with additive noise.
  arXiv  Detail & Related papers  (2025-05-30T17:59:17Z)
• EquiCPI: SE(3)-Equivariant Geometric Deep Learning for Structure-Aware Prediction of Compound-Protein Interactions [0.0]
  EquiCPI is an end-to-end geometric deep learning framework that synergizes first-principles structural modeling with SE(3)-equivariant neural networks.<n>At its core, EquiCPI employs SE(3)-equivariant message passing over atomic point clouds, preserving symmetry under rotations, translations, and reflections.<n>The proposed model is evaluated on BindingDB (affinity prediction) and DUD-E (virtual screening), EquiCPI performance on par with or exceeding the state-of-the-art deep learning competitors.
  arXiv  Detail & Related papers  (2025-04-07T00:57:08Z)
• Geometric Algebra Planes: Convex Implicit Neural Volumes [70.12234371845445]
  We show that GA-Planes is equivalent to a sparse low-rank factor plus low-resolution matrix. We also show that GA-Planes can be adapted for many existing representations.
  arXiv  Detail & Related papers  (2024-11-20T18:21:58Z)
• Tensorized Hypergraph Neural Networks [69.65385474777031]
  We propose a novel adjacency-tensor-based textbfTensorized textbfHypergraph textbfNeural textbfNetwork (THNN) THNN is faithful hypergraph modeling framework through high-order outer product feature passing message. Results from experiments on two widely used hypergraph datasets for 3-D visual object classification show the model's promising performance.
  arXiv  Detail & Related papers  (2023-06-05T03:26:06Z)
• Data Topology-Dependent Upper Bounds of Neural Network Widths [52.58441144171022]
  We first show that a three-layer neural network can be designed to approximate an indicator function over a compact set. This is then extended to a simplicial complex, deriving width upper bounds based on its topological structure. We prove the universal approximation property of three-layer ReLU networks using our topological approach.
  arXiv  Detail & Related papers  (2023-05-25T14:17:15Z)
• Tensor Representations for Action Recognition [54.710267354274194]
  Human actions in sequences are characterized by the complex interplay between spatial features and their temporal dynamics. We propose novel tensor representations for capturing higher-order relationships between visual features for the task of action recognition. We use higher-order tensors and so-called Eigenvalue Power Normalization (NEP) which have been long speculated to perform spectral detection of higher-order occurrences.
  arXiv  Detail & Related papers  (2020-12-28T17:27:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.