Quantitative Gaussian-Process limits of Tensor Programs

What the math gives to ML

The paper supplies quantitative, architecture-agnostic finite-width control for neural computations that converge to Gaussian-process limits, including recurrent weight sharing and transformer-style attention dependencies. The transferable asset is not merely the existence of an NNGP, but an explicit Wasserstein error rate of order n^{-1/2}, which turns infinite-width approximations into engineering estimates for finite models. This can support principled width allocation: assign larger widths only to layers or contraction dimensions whose finite-width approximation constants are large. A second practical use is to regularize empirical multi-input activations toward their recursively predicted NNGP covariance, especially in shared-weight recurrent or attention blocks where independent-layer GP intuition is inaccurate.