Gaussian Process for Any Neural Architecture: Reference Implementations

Update July 2020

The 2nd paper in the Tensor Programs series, Neural Tangent Kernel for Any Architecture, is now out! It shows that the infinite-width limit of a neural network of any architecture is well-defined (in the technical sense that the tangent kernel (NTK) of any randomly initialized neural network converges in the large width limit) and can be computed. The associated repo implements this infinite-width neural network for RNN, Transformer, and a Batchnorm+ReLU MLP.

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This repo is a companion to the paper

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

which shows that the Gaussian process behavior arises in wide, randomly initialized, neural networks regardless of architecture.

Despite what the title suggests, this repo does not implement the infinite-width GP kernel for every architecture, but rather demonstrates the derivation and implementation for a few select architectures.

Architecture | Notebook | Colab --------------------|------------------------------|------- Simple RNN | Notebook | GRU | Notebook | Transformer | Notebook| Batchnorm+ReLU MLP | Notebook |

Plots.ipynb also reproduces Figure (3) of the paper.

We have included the GloVe embeddings ExampleGloVeVecs.npy of example sentences we feed into the networks, as well as their normalized Gram matrix ExampleGloVeCov.npy. GloVe.ipynb recreates them; if you wish to try the kernels on custom sentences, then modify GloVe.ipynb as appropriate.

<p> <img src="allkernels.png" width="1000" > </p>