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Poster
Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes
Greg Yang

Wed Dec 11 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #242
in Theory -- Statistical Physics of Learning »

ide neural networks with random weights and biases are Gaussian processes, as originally observed by Neal (1995) and more recently by Lee et al.~(2018) and Matthews et al.~(2018) for deep fully-connected networks, as well as by Novak et al.~(2019) and Garriga-Alonso et al.~(2019) for deep convolutional networks. We show that this Neural Network-Gaussian Process correspondence surprisingly extends to all modern feedforward or recurrent neural networks composed of multilayer perceptron, RNNs (e.g. LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization, and/or layer normalization. More generally, we introduce a language for expressing neural network computations, and our result encompasses all such expressible neural networks. This work serves as a tutorial on the \emph{tensor programs} technique formulated in Yang (2019) and elucidates the Gaussian Process results obtained there. We provide open-source implementations of the Gaussian Process kernels of simple RNN, GRU, transformer, and batchnorm+ReLU network at github.com/thegregyang/GP4A. Please see our arxiv version for the complete and up-to-date version of this paper.

Keywords: Recurrent Networks · Statistical Physics of Learning · Theory · Deep Learning
[ Paper]  [ Slides] 

Author Information

Greg Yang (Microsoft Research)

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