Discrete Ricci Curvature on Protein Contact Graphs for Lightweight Fold Classification

Classifying protein topology is essential for deciphering biological function, but progress is held back by the lack of large-scale benchmarks that avoid duplicates and by models that do not scale well. We introduce TEDBench, a large-scale, non-redundant benchmark for protein fold classification constructed from the Encyclopedia of Domains (TED) and Foldseek-clustered AlphaFold structures. We show that on TEDBench, current protein representation learning methods either require very large models or fail to deliver strong performance. To address this challenge, we propose Masked Invariant Autoencoders (MiAE), a self-supervised framework for protein structure representation learning. MiAE uses an extremely high masking ratio of up to 90% with an $\mathrm{SE(3)}$-invariant encoder and a lightweight decoder that reconstructs backbone coordinates from the latent representation and mask tokens. MiAE scales well and outperforms supervised counterparts and state-of-the-art baselines on TEDBench, establishing a strong recipe for protein fold classification. To test transfer beyond AlphaFold structures, we further benchmark on a curated dataset from experimental structures of CATH v4.4. TEDBench is available at https://github.com/BorgwardtLab/TEDBench.

Protein language models such as ESM-2 learn rich residue representations that achieve strong performance on protein function prediction, but their features remain difficult to interpret as structural $\&$ evolutionary signals are encoded in dense latent spaces. We propose a plug-$\&$-play framework that projects ESM-2 representations onto protein contact graphs $\&$ applies $\textbf{SoftBlobGIN}$, a lightweight Graph Isomorphism Network with differentiable Gumbel-softmax substructure pooling, to perform structure-aware message passing $\&$ learn coarse functional substructures for downstream prediction tasks. Across enzyme classification, SoftBlobGIN achieves 92.8% accuracy $\&$ 0.898 macro-F1. Unlike post hoc analysis of protein language models alone, our method produces directly auditable structural explanations: GNNExplainer recovers biologically meaningful active-site residues, spatially localized functional clusters, $\&$ catalytic contact patterns. On binding-site detection, SoftBlobGIN improves residue AUROC from $0.885$ using an ESM-2 linear probe to $0.983$, indicating that these structural explanations are not recoverable from language-model features alone. Learned blob partitions provide an additional layer of interpretability by automatically grouping residues into functional substructures, with blobs containing annotated active-site residues showing $1.85\times$ higher importance than other blobs ($ρ{=}0.339$, $p{=}0.009$), without any active-site supervision. Our framework requires no retraining of the language model, adds only $\sim$1.1M parameters, $\&$ generalises across ProteinShake tasks, achieving $F_{\max}$ of $0.733$ on Gene Ontology prediction $\&$ AUROC of $0.969$ on binding-site detection. We position this as an interpretable structural companion to protein language models that makes their predictions more transparent $\&$ auditable.

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.