aiqbench analysis
This paper introduces finite-horizon energy learning, a method that adapts Metropolis–Hastings acceptance energies for discrete graph generation tasks where sampling terminates before equilibrium is reached. By leveraging frozen pretrained models and an unbiased gradient estimator derived from coupled proposal branches, the approach improves sample fidelity on molecular graphs without requiring discriminator evaluations during inference or differentiation through discrete states. The results demonstrate significant reductions in total variation distance and Fréchet ChemNet Distance compared to standard equilibrium-corrected energy baselines across multiple short-horizon settings.
Learning Graph Energies for Finite-Time Generation
arXiv:2610.19946v1 Announce Type: new Abstract: Energy-based models can represent distributions over discrete structures such as molecular graphs, but an energy that is accurate at equilibrium need not yield accurate samples when the sampler stops after a fixed number of steps. We introduce finite-horizon energy learning, which adapts the acceptance energy of a Metropolis--Hastings sampler to the distribution it returns after a prescribed number of steps, with initialization, proposals, and annealing schedule held fixed. For graph generation, a frozen pretrained model supplies initialization and proposals, and a learned energy governs acceptance. A training-only discriminator scores completed samples, and coupled continuations of the accepted and rejected branches of a proposal give an acceptance-gradient estimator that is unbiased for a fixed discriminator under stated conditions, without equilibrated negative samples or differentiation through discrete states. Generation uses the learned energy in the original single-trajectory sampler, without discriminator evaluations or reranking. On twelve pairwise binary targets with exactly evaluated terminal laws, learned energies have lower median terminal total variation than the equilibrium-correct energy in every tested short-horizon setting, and than its numerically tuned scalar multiple in most settings. On MOSES, a learned two-coefficient combination of pretrained Graph Energy Matching (GEM) potentials lowers FCD by 3.7--10.5\% relative to scale-calibrated GEM at matched sampling steps, with validity gains at the shortest budget and a sub-point validity trade-off at higher budgets.
Abstract:Energy-based models can represent distributions over discrete structures such as molecular graphs, but an energy that is accurate at equilibrium need not yield accurate samples when the sampler stops after a fixed number of steps. We introduce finite-horizon energy learning, which adapts the acceptance energy of a Metropolis--Hastings sampler to the distribution it returns after a prescribed number of steps, with initialization, proposals, and annealing schedule held fixed. For graph generation, a frozen pretrained model supplies initialization and proposals, and a learned energy governs acceptance. A training-only discriminator scores completed samples, and coupled continuations of the accepted and rejected branches of a proposal give an acceptance-gradient estimator that is unbiased for a fixed discriminator under stated conditions, without equilibrated negative samples or differentiation through discrete states. Generation uses the learned energy in the original single-trajectory sampler, without discriminator evaluations or reranking. On twelve pairwise binary targets with exactly evaluated terminal laws, learned energies have lower median terminal total variation than the equilibrium-correct energy in every tested short-horizon setting, and than its numerically tuned scalar multiple in most settings. On MOSES, a learned two-coefficient combination of pretrained Graph Energy Matching (GEM) potentials lowers FCD by 3.7--10.5\% relative to scale-calibrated GEM at matched sampling steps, with validity gains at the shortest budget and a sub-point validity trade-off at higher budgets.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.19946 [cs.LG]
(or arXiv:2610.19946v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.19946 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 315 words
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