Open AccessProceedings Article
Deep Neural Networks as Gaussian Processes
Jaehoon Lee,Yasaman Bahri,Roman Novak,Samuel S. Schoenholz,Jeffrey Pennington,Jascha Sohl-Dickstein +5 more
TLDR
The exact equivalence between infinitely wide deep networks and GPs is derived and it is found that test performance increases as finite-width trained networks are made wider and more similar to a GP, and thus that GP predictions typically outperform those of finite- width networks.Abstract:
It has long been known that a single-layer fully-connected neural network with an i.i.d. prior over its parameters is equivalent to a Gaussian process (GP), in the limit of infinite network width. This correspondence enables exact Bayesian inference for infinite width neural networks on regression tasks by means of evaluating the corresponding GP. Recently, kernel functions which mimic multi-layer random neural networks have been developed, but only outside of a Bayesian framework. As such, previous work has not identified that these kernels can be used as covariance functions for GPs and allow fully Bayesian prediction with a deep neural network.
In this work, we derive the exact equivalence between infinitely wide deep networks and GPs. We further develop a computationally efficient pipeline to compute the covariance function for these GPs. We then use the resulting GPs to perform Bayesian inference for wide deep neural networks on MNIST and CIFAR-10. We observe that trained neural network accuracy approaches that of the corresponding GP with increasing layer width, and that the GP uncertainty is strongly correlated with trained network prediction error. We further find that test performance increases as finite-width trained networks are made wider and more similar to a GP, and thus that GP predictions typically outperform those of finite-width networks. Finally we connect the performance of these GPs to the recent theory of signal propagation in random neural networks.read more
Citations
More filters
Journal ArticleDOI
Investigating annotation noise for named entity recognition
Proceedings ArticleDOI
Adversarial Reprogramming Revisited
Matthias Englert,Ranko Lazić +1 more
TL;DR: It is proved that two-layer ReLU neural networks with random weights can be adversarially reprogrammed to achieve arbitrarily high accuracy on Bernoulli data models over hypercube vertices, provided the network width is no greater than its input dimension.
Convolutional Rank Filters in Deep Learning
TL;DR: A framework is proposed that generalizes rank filters, and the novel layers are applied successfully in convolution and deconvolution while combining them with linear convolutional feature maps.
Posted Content
Measuring the sensitivity of Gaussian processes to kernel choice.
William T. Stephenson,Soumya Ghosh,Tin D. Nguyen,Mikhail Yurochkin,Sameer K. Deshpande,Tamara Broderick +5 more
TL;DR: In this paper, the authors formulate the sensitivity analysis as a constrained optimization problem over a finite-dimensional space and use standard optimizers to identify substantive changes in relevant decisions made with a GP.
Posted Content
On the Dynamics of Training Attention Models
Haoye Lu,Yongyi Mao,Amiya Nayak +2 more
TL;DR: This paper sets up a simple text classification task and studies the dynamics of training a simple attention-based classification model using gradient descent, and proves that training must converge to attending to the discriminative words when the attention output is classified by a linear classifier.
References
More filters
Proceedings Article
Adam: A Method for Stochastic Optimization
Diederik P. Kingma,Jimmy Ba +1 more
TL;DR: This work introduces Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments, and provides a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework.
Book
Bayesian learning for neural networks
TL;DR: Bayesian Learning for Neural Networks shows that Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional neural network learning methods.
Journal ArticleDOI
A Unifying View of Sparse Approximate Gaussian Process Regression
TL;DR: A new unifying view, including all existing proper probabilistic sparse approximations for Gaussian process regression, relies on expressing the effective prior which the methods are using, and highlights the relationship between existing methods.
Journal Article
In Defense of One-Vs-All Classification
Ryan Rifkin,Aldebaro Klautau +1 more
TL;DR: It is argued that a simple "one-vs-all" scheme is as accurate as any other approach, assuming that the underlying binary classifiers are well-tuned regularized classifiers such as support vector machines.
Proceedings Article
Gaussian processes for Big data
TL;DR: In this article, the authors introduce stochastic variational inference for Gaussian process models, which enables the application of Gaussian Process (GP) models to data sets containing millions of data points.