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Poster
Non-Gaussian Tensor Programs
Eugene Golikov · Greg Yang

Thu Dec 01 09:00 AM -- 11:00 AM (PST) @ Hall J #535
in Poster Session 5 »

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.

Keywords: Deep Learning Theory · tensor programs · infinitely wide networks

Author Information

Eugene Golikov (École polytechnique fédérale de Lausanne)

MSc in Fluid Mechanics @ Moscow SU MSc in Computer Science @ HSE Doing a PhD in DL theory @ EPFL

Greg Yang (Microsoft Research)

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