… for our work---on ReLU approximation in section 2 and Besov smoothness classes in section
3. Finally, in sec… The reader familiar with results on ReLU/RePU approximation and wavelet …

… Finally, in Section 5, we comment on the curse of dimension, and introduce a novel function
class, which can be approximated by ReLU neural networks at a rate independent of the …

… networks approximate functions with classical smoothness to the same accuracy as classical
linear methods of approximation, eg, approximation by … of depth describe certain classes of …

… deep ReLU network function classes and recall important embedding properties. The network
approximation … with smooth local coordinate maps and the main approximation error bound…

… 4], we have studied the approximation by deep ReLU neural networks, of functions from the
Hölder-Zygmund space of mixed smoothness defined on the … for functions from the classes U …

… We prove that using very deep networks one can approximate … In fact, the depth of the
networks must necessarily grow … Depth separation in relu networks for approximating smooth …

… that neural networks can approximate certain classes of functions with … deep neural networks
with nonsmooth activations to approximate functions supported on a d-dimensional smooth …

… to “best in class” schemes for several important function classes of high and infinite smoothness.
… For example, in Corollary 3.3 we establish ReLU approximation rate bounds in Besov …

… a new approximation and estimation error analysis of deep learning with the ReLU activation
for … In this section, we define the function classes for which we develop error bounds. In …

… 0 , 1 ] d , the smoothness classes W w , q , γ from [5] reduce to classes of functions that have
… Our results show that deep ReLU networks, even at a moderate width, are universal function …