At critical initialization, the infinite-depth neural tangent kernel converges to the fixed-point output correlation matrix divided by an activation-dependent constant, making learning dynamics equivalent to correlation propagation.
In particular, it shows that the asymptotic NTK is strongly governed by the correlation dynamics
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Correlation flow governs learning at criticality
At critical initialization, the infinite-depth neural tangent kernel converges to the fixed-point output correlation matrix divided by an activation-dependent constant, making learning dynamics equivalent to correlation propagation.