Machine-learning methods in biochemistry commonly represent molecules as graphs of pairwise intermolecular interactions for property and structure predictions. Most methods operate on a single graph, typically the minimal free energy (MFE) structure, for low-energy ensembles (conformations) representative of structures at thermodynamic equilibrium. We introduce a thermodynamically parameterized exponential-family random graph (ERGM) embedding that models molecules as Boltzmann-weighted ensembles of interaction graphs. We evaluate this embedding on SELEX datasets, where experimental biases (e.g., PCR amplification or sequencing noise) can obscure true aptamer-ligand affinity, producing anomalous candidates whose observed abundance diverges from their actual binding strength. We show that the proposed embedding enables robust community detection and subgraph-level explanations for aptamer ligand affinity, even in the presence of biased observations. This approach may be used to identify low-abundance aptamer candidates for further experimental evaluation.
@article{arxiv.2510.21980,
title = {Boltzmann Graph Ensemble Embeddings for Aptamer Libraries},
author = {Starlika Bauskar and Jade Jiao and Narayanan Kannan and Alexander Kimm and Justin M. Baker and Matthew J. Tyler and Andrea L. Bertozzi and Anne M. Andrews},
journal= {arXiv preprint arXiv:2510.21980},
year = {2025}
}