PHL: Persistent Hyperdigraph Learning for Protein-Protein Binding Affinity Prediction

Persistent homology and persistent Laplacians have become effective descriptors of large molecular binding interactions, the latter encoding multiscale geometry and spectral information beyond the harmonic subspace. Both, however, are built on undirected graphs and pairwise contracts, while the interactions that determine binding are often directional and involve more than two atoms at once. We introduce persistent hyperdigraph learning (PHL), which represents these directed, many-body interactions directly. Because hyperdigraph Laplacian spectra become costly to compute at higher topological orders, we further use stochastic trace estimation to develop a matrix-free formulation(MFPHL) that estimates Laplacian trace statistics from probe-based quadratic forms evaluated through sparse boundary operators, without assembling or diagonalizing. The number of probes required for a target relative accuracy of the trace estimate is independent of matrix dimension, and per-probe cost scales with operator sparsity. On protein-protein binding affinity benchmarks, MFPHL reduces feature-generation time by roughly two orders of magnitude relative to the eigenvalue-based pipeline. Its predictive accuracy matches that of spectral PHL on the P2P wild-type set within training-seed variability but is lower on the two larger datasets. This dataset-dependent trade-off brings higher-order hyperdigraph features within practical reach.

Source: arXiv:2609.33122v1 - http://arxiv.org/abs/2609.33122v1 PDF: https://arxiv.org/pdf/2609.33122v1 Original Link: http://arxiv.org/abs/2609.33122v1