New research quantifies sampling complexity for log-concave and log-Sobolev distributions

A new research paper explores the query complexity of sampling from smooth distributions in d-dimensional space. The study proves that for strongly log-concave targets with a condition number of 2, any randomized sampler requires at least $\exp({\Omega(\log^{1/3} d)})$ queries, indicating a limitation on polylogarithmic dimension dependence. Furthermore, for targets satisfying an $\alpha$-log-Sobolev inequality with condition number $\kappa$, an $\Omega(\kappa)$ query lower bound is established for dimensions $d\gtrsim\log^2\kappa$, demonstrating that log-Sobolev sampling is more complex than strongly log-concave sampling. AI

IMPACT Establishes theoretical limits on sampling algorithms, potentially guiding future research in generative models and statistical inference.

RANK_REASON The cluster contains an academic paper detailing theoretical research on sampling complexity. [lever_c_demoted from research: ic=1 ai=1.0]

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• arXiv
• Hugging Face
• Log-Sobolev inequalities for infinite-dimensional Gibbs measures with non-quadratic interactions
• log-Sobolev sampling
• $\mathbb R^d$
• tensor polynomial

• paper
• other

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