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Neural networks are powerful functions with widespread use, but thetheoretical behaviour of these functions is not fully understood. Creating deepneural networks by stacking many layers has achieved exceptional performance inmany applications and contributed to the recent explosion of these methods.Previous works have shown that depth can exponentially increase theexpressibility of the network. However, as networks get deeper and deeper, theyare more susceptible to becoming degenerate. We observe this degeneracy in thesense that on initialization, inputs tend to become more and more correlated asthey travel through the layers of the network. If a network has too manylayers, it tends to approximate a (random) constant function, making iteffectively incapable of distinguishing between inputs. This seems to affectthe training of the network and cause it to perform poorly, as we empiricallyinvestigate in this paper. We use a simple algorithm that can accuratelypredict the level of degeneracy for any given fully connected ReLU networkarchitecture, and demonstrate how the predicted degeneracy relates to trainingdynamics of the network. We also compare this prediction to predictions derivedusing infinite width networks.

Network Degeneracy as an Indicator of Training Performance: Comparing Finite and Infinite Width Angle Predictions