Researchers have developed a new method for approximating multivariate Hölder-continuous functions using feedforward neural networks. The study establishes the minimum number of hidden neurons required for arbitrary accuracy in the uniform norm, proving that for d>=2 dimensions, a network with two hidden layers can achieve this with widths d and 1. The proposed constructions utilize explicit grid addressing and integer encoding of quantized function values, achieving bit complexity that closely matches theoretical lower bounds. AI
IMPACT This research advances the theoretical understanding of neural network capabilities for approximating complex mathematical functions.
RANK_REASON Academic paper detailing a new theoretical approach to neural network approximation. [lever_c_demoted from research: ic=1 ai=1.0]
Read on arXiv cs.NE (Neural & Evolutionary) →
- arXiv
- exponential function
- feedforward neural network
- floor function
- grid addressing
- Hölder-continuous functions
- Integer Encoding Genetic Algorithm for Optimizing Redundancy Allocation of Series-parallel Systems
- measure-theoretic entropy
- uniform norm
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