Approximation Rates for Neural Networks with Encodable Weights in Smoothness Spaces

Understand

We examine the necessary and sufficient complexity of neural networks to approximate functions from different smoothness spaces under the restriction of encodable network weights.

• Based on an entropy argument, we start by proving lower bounds for the number of nonzero encodable weights for neural network approximation in Besov spaces, Sobolev spaces and more.
• These results are valid for all sufficiently smooth activation functions.
• Afterwards, we provide a unifying framework for the construction of approximate partitions of unity by neural networks with fairly general activation functions.