In the LP/N = Θ(1) regime, Bayesian predictive posteriors for deep MLPs equal those of data-dependent kernels to first order, with a criterion identifying data processes that benefit from larger effective depth.
[Yan21] Greg Yang.Tensor Programs III: Neural Matrix Laws
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Bayesian Inference with Shaped Deep Non-linear MLPs
In the LP/N = Θ(1) regime, Bayesian predictive posteriors for deep MLPs equal those of data-dependent kernels to first order, with a criterion identifying data processes that benefit from larger effective depth.