Sampling and Identity-Testing Without Approximate Tensorization of Entropy

William Gay, William He, Nicholas Kocurek, Ryan O’Donnell
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:34375-34392, 2026.

Abstract

We study the problems of approximate sampling from and distribution testing of mixture models, where the modes satisfy a functional inequality called approximate tensorization of entropy (ATE). While it is known that ATE makes these tasks more efficient in the unimodal setting, mixtures of few distributions satisfying ATE do not necessarily satisfy ATE overall, leading to a lack of theoretical guarantees for multimodal distributions, which are a key challenging case of modern generative models. We show this gap can be overcome by establishing the following pair of results for mixtures of ATE distributions: 1) We show fast mixing of Glauber dynamics from a data-based initialization, with optimal sample complexity, for mixtures of distributions satisfying modified log-Sobolev inequalities, building on similar results in (Koehler et al., 2024, Huang et al., 2024) for mixtures satisfying the weaker Poincaré inequality. 2) Answering an open question from (Blanca et al., 2023), we give efficient identity-testers for mixtures of ATE distributions in the coordinate-conditional sampling access model.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-gay26a, title = {Sampling and Identity-Testing Without Approximate Tensorization of Entropy}, author = {Gay, William and He, William and Kocurek, Nicholas and O'Donnell, Ryan}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {34375--34392}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/gay26a/gay26a.pdf}, url = {https://proceedings.mlr.press/v306/gay26a.html}, abstract = {We study the problems of approximate sampling from and distribution testing of mixture models, where the modes satisfy a functional inequality called approximate tensorization of entropy (ATE). While it is known that ATE makes these tasks more efficient in the unimodal setting, mixtures of few distributions satisfying ATE do not necessarily satisfy ATE overall, leading to a lack of theoretical guarantees for multimodal distributions, which are a key challenging case of modern generative models. We show this gap can be overcome by establishing the following pair of results for mixtures of ATE distributions: 1) We show fast mixing of Glauber dynamics from a data-based initialization, with optimal sample complexity, for mixtures of distributions satisfying modified log-Sobolev inequalities, building on similar results in (Koehler et al., 2024, Huang et al., 2024) for mixtures satisfying the weaker Poincaré inequality. 2) Answering an open question from (Blanca et al., 2023), we give efficient identity-testers for mixtures of ATE distributions in the coordinate-conditional sampling access model.} }
Endnote
%0 Conference Paper %T Sampling and Identity-Testing Without Approximate Tensorization of Entropy %A William Gay %A William He %A Nicholas Kocurek %A Ryan O’Donnell %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-gay26a %I PMLR %P 34375--34392 %U https://proceedings.mlr.press/v306/gay26a.html %V 306 %X We study the problems of approximate sampling from and distribution testing of mixture models, where the modes satisfy a functional inequality called approximate tensorization of entropy (ATE). While it is known that ATE makes these tasks more efficient in the unimodal setting, mixtures of few distributions satisfying ATE do not necessarily satisfy ATE overall, leading to a lack of theoretical guarantees for multimodal distributions, which are a key challenging case of modern generative models. We show this gap can be overcome by establishing the following pair of results for mixtures of ATE distributions: 1) We show fast mixing of Glauber dynamics from a data-based initialization, with optimal sample complexity, for mixtures of distributions satisfying modified log-Sobolev inequalities, building on similar results in (Koehler et al., 2024, Huang et al., 2024) for mixtures satisfying the weaker Poincaré inequality. 2) Answering an open question from (Blanca et al., 2023), we give efficient identity-testers for mixtures of ATE distributions in the coordinate-conditional sampling access model.
APA
Gay, W., He, W., Kocurek, N. & O’Donnell, R.. (2026). Sampling and Identity-Testing Without Approximate Tensorization of Entropy. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:34375-34392 Available from https://proceedings.mlr.press/v306/gay26a.html.

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