Weisfeiler-Lehman subtree encoding for Bayesian optimization of atomic configurations
Abstract
The efficiency of Bayesian optimization (BO) of atomic configurations depends strongly on how configurations are encoded. We introduce the Weisfeiler-Lehman (WL) subtree kernel, which views configurations as element-labeled graphs and measures their similarity by how many local structural patterns they share, into Bayesian-optimization-based configuration search. Because this kernel is reproduced as the plain inner product of explicit features (L2-normalized histograms of local topological patterns), introducing it reduces to introducing the corresponding features: the encoding enters existing BO frameworks as an ordinary descriptor. In a benchmark ground-state configuration search of cubic BC2N evaluated with a universal machine-learning interatomic potential, the WL encoding reached the ground state almost immediately after a shared random initialization of 100 samples in every one of five independent rounds (108±5 evaluations on average), whereas the one-hot baseline required 280±122 evaluations; the WL-driven sampler first exhausted the degenerate ground-state group and then discovered the metastable degenerate groups from the bottom up, in order of increasing energy.
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BibTeX
@misc{kusaba2026weisfeilerlehman,
title = {{Weisfeiler-Lehman subtree encoding for Bayesian optimization of atomic configurations}},
author = {Akira Kusaba and Tatoshi Yonemori and Tetsuji Kuboyama and Yoshihiro Kangawa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.00953},
eprint = {2609.00953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00953},
}
RIS
TY - UNPB
TI - Weisfeiler-Lehman subtree encoding for Bayesian optimization of atomic configurations
AU - Akira Kusaba
AU - Tatoshi Yonemori
AU - Tetsuji Kuboyama
AU - Yoshihiro Kangawa
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2609.00953
UR - https://arxiv.org/abs/2609.00953
AB - The efficiency of Bayesian optimization (BO) of atomic configurations depends strongly on how configurations are encoded. We introduce the Weisfeiler-Lehman (WL) subtree kernel, which views configurations as element-labeled graphs and measures their similarity by how many local structural patterns they share, into Bayesian-optimization-based configuration search. Because this kernel is reproduced as the plain inner product of explicit features (L^2-normalized histograms of local topological patterns), introducing it reduces to introducing the corresponding features: the encoding enters existing BO frameworks as an ordinary descriptor. In a benchmark ground-state configuration search of cubic BC_2N evaluated with a universal machine-learning interatomic potential, the WL encoding reached the ground state almost immediately after a shared random initialization of 100 samples in every one of five independent rounds (108±5 evaluations on average), whereas the one-hot baseline required 280±122 evaluations; the WL-driven sampler first exhausted the degenerate ground-state group and then discovered the metastable degenerate groups from the bottom up, in order of increasing energy.
ER -