Finite Versus Infinite Neural Networks: an Empirical Study

• URL: http://arxiv.org/abs/2007.15801v2
• Date: Tue, 8 Sep 2020 06:25:57 GMT
• Title: Finite Versus Infinite Neural Networks: an Empirical Study
• Authors: Jaehoon Lee, Samuel S. Schoenholz, Jeffrey Pennington, Ben Adlam, Lechao Xiao, Roman Novak, Jascha Sohl-Dickstein
• Abstract summary: kernel methods outperform fully-connected finite-width networks. Centered and ensembled finite networks have reduced posterior variance. Weight decay and the use of a large learning rate break the correspondence between finite and infinite networks.
• Score: 69.07049353209463
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We perform a careful, thorough, and large scale empirical study of the correspondence between wide neural networks and kernel methods. By doing so, we resolve a variety of open questions related to the study of infinitely wide neural networks. Our experimental results include: kernel methods outperform fully-connected finite-width networks, but underperform convolutional finite width networks; neural network Gaussian process (NNGP) kernels frequently outperform neural tangent (NT) kernels; centered and ensembled finite networks have reduced posterior variance and behave more similarly to infinite networks; weight decay and the use of a large learning rate break the correspondence between finite and infinite networks; the NTK parameterization outperforms the standard parameterization for finite width networks; diagonal regularization of kernels acts similarly to early stopping; floating point precision limits kernel performance beyond a critical dataset size; regularized ZCA whitening improves accuracy; finite network performance depends non-monotonically on width in ways not captured by double descent phenomena; equivariance of CNNs is only beneficial for narrow networks far from the kernel regime. Our experiments additionally motivate an improved layer-wise scaling for weight decay which improves generalization in finite-width networks. Finally, we develop improved best practices for using NNGP and NT kernels for prediction, including a novel ensembling technique. Using these best practices we achieve state-of-the-art results on CIFAR-10 classification for kernels corresponding to each architecture class we consider.

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