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
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On the Bias-Variance Tradeoff: Textbooks Need an Update
TL;DR: It is shown that there was never strong evidence for a tradeoff in neural networks when varying the number of parameters, and it is argued that textbook and lecture revisions are in order to convey this nuanced modern understanding of the bias-variance tradeoff.
Journal ArticleDOI
A probabilistic framework for multidisciplinary design: Application to the hydrostructural optimization of supercavitating hydrofoils
Luca Bonfiglio,Paris Perdikaris,Paris Perdikaris,Jose del Águila,Jose del Águila,George Em Karniadakis,George Em Karniadakis +6 more
TL;DR: An automated workflow for performing multiresolution simulations of turbulent multiphase flows and multifidelity structural mechanics is developed, the results of which drive the machine learning analysis in pursuit of the optimal hydrofoil shape.
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Interpreting Deep Learning: The Machine Learning Rorschach Test?
TL;DR: The interpretation of DNNs appears to mimic a type of Rorschach test --- a psychological test wherein subjects interpret a series of seemingly ambiguous ink-blots, which requires a convergence of the literature.
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Automatic Gaussian Process Model Retrieval for Big Data
Fabian Berns,Christian Beecks +1 more
TL;DR: This work proposes a new approach that allows to efficiently and automatically retrieve GPMs for large-scale data and demonstrates the quality of resulting models, which clearly outperform default GPM instantiations, while maintaining reasonable model training time.
Journal ArticleDOI
Contrasting random and learned features in deep Bayesian linear regression
TL;DR: Comparing deep random feature models to deep networks in which all layers are trained provides a detailed characterization of the interplay between width, depth, data density, and prior mismatch and begins to elucidate how architectural details affect generalization performance in this simple class of deep regression models.
References
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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.
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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.
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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.