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

Abstract

Wide 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 *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.

Appearing in NeurIPS 2019; 10 pages of main text; 12 figures, 11 programs; 73 pages total

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Cited by in corpus (15)

• Neural Networks and Quantum Field Theory
• Nonperturbative renormalization for the neural network-QFT correspondence
• Bayesian Deep Ensembles via the Neural Tangent Kernel
• Tensor Programs IIb: Architectural Universality of Neural Tangent Kernel Training Dynamics
• Taylorized Training: Towards Better Approximation of Neural Network Training at Finite Width
• Generalization bounds for deep learning
• Infinite Neural Network Quantum States: Entanglement and Training Dynamics
• The Recurrent Neural Tangent Kernel
• Non-asymptotic approximations of neural networks by Gaussian processes
• Scale Mixtures of Neural Network Gaussian Processes
• On the Dynamics of Training Attention Models
• Exploring the Uncertainty Properties of Neural Networks' Implicit Priors in the Infinite-Width Limit
• The Future is Log-Gaussian: ResNets and Their Infinite-Depth-and-Width Limit at Initialization
• Enhanced Recurrent Neural Tangent Kernels for Non-Time-Series Data
• Implicit Acceleration and Feature Learning in Infinitely Wide Neural Networks with Bottlenecks