Large width limits have been a recent focus of deep learning research: modulo computational practicalities, do wider networks outperform narrower ones? Answering this question has been challenging, as conventional networks gain representational power with width, potentially masking any negative effects.

Large width limits have been a recent focus of deep learning research: modulo computational practicalities, do wider networks outperform narrower ones? Answering this question has been challenging, as conventional networks gain representational power with width, potentially masking any negative effects. In doing so, we aim to understand how width affects (standard) neural networks once they have sufficient capacity for a given modeling task. Our theoretical and empirical results on Deep GP suggest that large width can be detrimental to hierarchical models. Surprisingly, we prove that even nonparametric Deep GP converge to Gaussian processes, effectively becoming shallower without any increase in representational power.