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Infinite-width neural networks face limitations in calculus of variations problems

By PulseAugur Editorial · [1 sources] ·

A new research paper explores limitations in using infinite-width neural networks, specifically Barron functions, for problems in the calculus of variations. The study demonstrates that these networks can struggle with complex scenarios like the bending and folding of elastic shells, where they may only describe straight folds instead of curved ones. However, the research also shows that for a broad category of first-order integral functionals, there is no significant energy gap between Barron functions and Lipschitz functions. AI

IMPACT Highlights theoretical limitations of neural networks in modeling complex physical phenomena, potentially guiding future research in scientific machine learning.

RANK_REASON The cluster contains an academic paper detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

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

Infinite-width neural networks face limitations in calculus of variations problems

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The cluster contains an academic paper detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Nima Rezaei, Stephan Wojtowytsch ·

    The Barron-Lipschitz Energy Gap and Depth Separation Phenomena in Scientific Machine Learning

    arXiv:2607.25905v1 Announce Type: cross Abstract: We illustrate in several examples that even neural networks of infinite width (specifically, Barron functions) may encounter substantial obstacles when used as a model class for problems in the calculus of variations. An instance …

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