  In this paper, we study the generalization performance of overparameterized
3-layer NTK models. We show that, for a specific set of ground-truth functions
(which we refer to as the "learnable set"), the test error of the overfitted
3-layer NTK is upper bounded by an expression that decreases with the number of
neurons of the two hidden layers. Different from 2-layer NTK where there exists
only one hidden-layer, the 3-layer NTK involves interactions between two
hidden-layers. Our upper bound reveals that, between the two hidden-layers, the
test error descends faster with respect to the number of neurons in the second
hidden-layer (the one closer to the output) than with respect to that in the
first hidden-layer (the one closer to the input). We also show that the
learnable set of 3-layer NTK without bias is no smaller than that of 2-layer
NTK models with various choices of bias in the neurons. However, in terms of
the actual generalization performance, our results suggest that 3-layer NTK is
much less sensitive to the choices of bias than 2-layer NTK, especially when
the input dimension is large.
