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New research details inherent difficulty in learning Lipschitz operators

By PulseAugur Editorial · [1 sources] ·

A new research paper explores the complexities of learning Lipschitz operators, which are crucial for creating surrogate models in computational science and engineering. The study, focusing on approximations with respect to Gaussian measures, establishes theoretical bounds on approximation errors and analyzes reconstruction strategies using linear samples. A key finding reveals an inherent "curse of sample complexity," indicating that no method using linear samples can achieve algebraic convergence rates. However, the research also shows that specific spectral decay properties of the underlying Gaussian measure can lead to convergence rates arbitrarily close to algebraic rates, confirming the inherent difficulty in learning these operators. AI

IMPACT Confirms intrinsic difficulty in learning Lipschitz operators, potentially guiding future research in surrogate model development.

RANK_REASON Academic paper published on arXiv detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New research details inherent difficulty in learning Lipschitz operators

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Academic paper published on arXiv detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Ben Adcock, Michael Griebel, Gregor Maier ·

    The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures

    arXiv:2410.23440v4 Announce Type: replace Abstract: Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Operator approximations can serve as efficient surro…

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