arXiv:2605.27769v1 Announce Type: cross Abstract: We study the query complexity of sampling from high-dimensional Gaussian distributions using gradient information. In the standard oracle model, exact gradients expose only matrix-vector products with the precision matrix, leading to polynomial approximation barriers and a characteristic \(\sqrt{\kappa}\) dependence on the condition number. We show that this barrier disappears when the sampler is allowed to query \emph{smoothed scores}, namely gradients of the logarithms of the Gaussian-convolved densities. For a Gaussian target with precision
The paper directly addresses a fundamental algorithmic barrier in high-dimensional sampling, a core challenge in modern AI research, particularly as models scale.
Improved sampling methods can significantly enhance the efficiency and capability of AI models, impacting areas from generative AI to complex simulations and scientific discovery.
This research suggests a potential pathway to overcome long-standing complexity barriers in sampling, enabling more efficient and accurate AI computations without previous conditioning number limitations.
- · AI researchers and developers
- · Machine learning platforms
- · Generative AI companies
- · Drug discovery and materials science
- · Companies reliant on less efficient traditional sampling methods
More efficient training and inference for certain high-dimensional AI models.
Reduced computational costs and faster development cycles for advanced AI applications.
Acceleration of scientific research and discovery through more powerful simulation and data analysis tools.
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Read at arXiv cs.LG