Neural networks don't beat curse of dimensionality, study claims

A new paper proposes a bit-complexity framework for evaluating approximation methods, arguing that the traditional 'curse of dimensionality' is misleading. The research suggests that when computational bit complexity is considered, neural networks do not fundamentally outperform classical methods like polynomial approximation or finite elements. The study indicates that perceived advantages of neural networks, such as dimension-independent rates, may stem from differences in function class complexity rather than inherent architectural superiority, with the true limitation being a 'curse of bit complexity' governed by metric entropy. AI

IMPACT This research suggests that perceived advantages of neural networks may be overstated when considering computational bit complexity, potentially influencing future architectural development and evaluation methods.

RANK_REASON The cluster contains a single academic paper discussing theoretical aspects of neural network performance. [lever_c_demoted from research: ic=1 ai=1.0]

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• approximation theory
• arXiv
• Bit complexity of computing solutions for symmetric hyperbolic systems of PDEs with guaranteed precision
• curse of dimensionality
• Deep Neural Networks
• Neural Networks

• paper
• other

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