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In this paper, we study the generalization performance of overparameterized3-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 overfitted3-layer NTK is upper bounded by an expression that decreases with the number ofneurons of the two hidden layers. Different from 2-layer NTK where there existsonly one hidden-layer, the 3-layer NTK involves interactions between twohidden-layers. Our upper bound reveals that, between the two hidden-layers, thetest error descends faster with respect to the number of neurons in the secondhidden-layer (the one closer to the output) than with respect to that in thefirst hidden-layer (the one closer to the input). We also show that thelearnable set of 3-layer NTK without bias is no smaller than that of 2-layerNTK models with various choices of bias in the neurons. However, in terms ofthe actual generalization performance, our results suggest that 3-layer NTK ismuch less sensitive to the choices of bias than 2-layer NTK, especially whenthe input dimension is large.

On the Generalization Power of the Overfitted Three-Layer Neural Tangent Kernel Model