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.
Free probability and random matrices
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abstract
The concept of freeness was introduced by Voiculescu in the context of operator algebras. Later it was observed that it is also relevant for large random matrices. We will show how the combination of various free probability results with a linearization trick allows to address successfully the problem of determining the asymptotic eigenvalue distribution of general selfadjoint polynomials in independent random matrices.
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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.