Neural networks with superexpressive activations and integer weights

• URL: http://arxiv.org/abs/2105.09917v1
• Date: Thu, 20 May 2021 17:29:08 GMT
• Title: Neural networks with superexpressive activations and integer weights
• Authors: Aleksandr Beknazaryan
• Abstract summary: An example of an activation function $sigma$ is given such that networks with activations $sigma, lfloorcdotrfloor$, integer weights and a fixed architecture is given. The range of integer weights required for $varepsilon$-approximation of H"older continuous functions is derived.
• Score: 91.3755431537592
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: An example of an activation function $\sigma$ is given such that networks with activations $\{\sigma, \lfloor\cdot\rfloor\}$, integer weights and a fixed architecture depending on $d$ approximate continuous functions on $[0,1]^d$. The range of integer weights required for $\varepsilon$-approximation of H\"older continuous functions is derived, which leads to a convergence rate of order $n^{\frac{-2\beta}{2\beta+d}}\log_2n$ for neural network regression estimation of unknown $\beta$-H\"older continuous function with given $n$ samples.

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