Non-Gaussian Tensor Programs

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Bibtex Paper Supplemental


Eugene Golikov, Greg Yang


Does it matter whether one randomly initializes a neural network (NN) from Gaussian, uniform, or other distributions? We show the answer is ”yes” in some parameter tensors (the so-called matrix-like parameters) but ”no” in others when the NN is wide. This is a specific instance of a more general universality principle for Tensor Programs (TP) that informs precisely when the limit of a program depends on the distribution of its initial matrices and vectors. To obtain this principle, we develop the theory of non-Gaussian Tensor Programs. As corollaries, we obtain all previous consequences of the TP framework (such as NNGP/NTK correspondence, Free Independence Principle, Dynamical Dichotomy Theorem, and μ-parametrization) for NNs with non-Gaussian weights.