  Using a mean-field theory of signal propagation, we analyze the evolution of
correlations between two signals propagating forward through a deep ReLU
network with correlated weights. Signals become highly correlated in deep ReLU
networks with uncorrelated weights. We show that ReLU networks with
anti-correlated weights can avoid this fate and have a chaotic phase where the
signal correlations saturate below unity. Consistent with this analysis, we
find that networks initialized with anti-correlated weights can train faster
(in a teacher-student setting) by taking advantage of the increased
expressivity in the chaotic phase. Combining this with a previously proposed
strategy of using an asymmetric initialization to reduce dead node probability,
we propose an initialization scheme that allows faster training and learning
than the best-known initializations.
