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How well does a classic deep net architecture like AlexNet or VGG19 classify on a standard dataset such as CIFAR-10 when its “width”— namely, number of channels in convolutional layers, and number of nodes in fully-connected internal layers — is allowed to increase to infinity? Such questions have come to the forefront in the quest to theoretically understand deep learning and its mysteries about optimization and generalization. They also connect deep learning to notions such as Gaussian processes and kernels. A recent paper [Jacot et al., 2018] introduced the Neural Tangent Kernel (NTK) which captures the behavior of fully-connected deep nets in the infinite width limit trained by gradient descent; this object was implicit in some other recent papers. An attraction of such ideas is that a pure kernel-based method is used to capture the power of a fully-trained deep net of infinite width.
The current paper gives the first efficient exact algorithm for computing the extension of NTK to convolutional neural nets, which we call Convolutional NTK (CNTK), as well as an efficient GPU implementation of this algorithm. This results in a significant new benchmark for performance of a pure kernel-based method on CIFAR-10, being 10% higher than the methods reported in [Novak et al., 2019], and only 6% lower than the performance of the corresponding finite deep net architecture (once batch normalization etc. are turned off). Theoretically, we also give the first non-asymptotic proof showing that a fully-trained sufficiently wide net is indeed equivalent to the kernel regression predictor using NTK.
Author Information
Sanjeev Arora (Princeton University)
Simon Du (Institute for Advanced Study)
Wei Hu (Princeton University)
Zhiyuan Li (Princeton University)
Russ Salakhutdinov (Carnegie Mellon University)
Ruosong Wang (Carnegie Mellon University)
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Behnam Neyshabur · Yuhuai Wu · Russ Salakhutdinov · Nati Srebro -
2016 Poster: On Multiplicative Integration with Recurrent Neural Networks »
Yuhuai Wu · Saizheng Zhang · Ying Zhang · Yoshua Bengio · Russ Salakhutdinov -
2016 Poster: Review Networks for Caption Generation »
Zhilin Yang · Ye Yuan · Yuexin Wu · William Cohen · Russ Salakhutdinov -
2016 Poster: Stochastic Variational Deep Kernel Learning »
Andrew Wilson · Zhiting Hu · Russ Salakhutdinov · Eric Xing -
2015 : Importance Weighted Autoencoders »
Russ Salakhutdinov -
2015 : Generating Images from Captions with Attention »
Russ Salakhutdinov -
2015 Poster: Skip-Thought Vectors »
Jamie Kiros · Yukun Zhu · Russ Salakhutdinov · Richard Zemel · Raquel Urtasun · Antonio Torralba · Sanja Fidler -
2015 Poster: Learning Wake-Sleep Recurrent Attention Models »
Jimmy Ba · Russ Salakhutdinov · Roger Grosse · Brendan J Frey -
2015 Spotlight: Learning Wake-Sleep Recurrent Attention Models »
Jimmy Ba · Russ Salakhutdinov · Roger Grosse · Brendan J Frey -
2015 Poster: Path-SGD: Path-Normalized Optimization in Deep Neural Networks »
Behnam Neyshabur · Russ Salakhutdinov · Nati Srebro -
2014 Poster: Learning Generative Models with Visual Attention »
Yichuan Charlie Tang · Nitish Srivastava · Russ Salakhutdinov -
2014 Poster: A Multiplicative Model for Learning Distributed Text-Based Attribute Representations »
Jamie Kiros · Richard Zemel · Russ Salakhutdinov -
2014 Demonstration: Toronto Deep Learning »
Jamie Kiros · Russ Salakhutdinov · Nitish Srivastava · Yichuan Charlie Tang -
2014 Oral: Learning Generative Models with Visual Attention »
Yichuan Charlie Tang · Nitish Srivastava · Russ Salakhutdinov -
2013 Workshop: Deep Learning »
Yoshua Bengio · Hugo Larochelle · Russ Salakhutdinov · Tomas Mikolov · Matthew D Zeiler · David Mcallester · Nando de Freitas · Josh Tenenbaum · Jian Zhou · Volodymyr Mnih -
2013 Poster: One-shot learning by inverting a compositional causal process »
Brenden M Lake · Russ Salakhutdinov · Josh Tenenbaum -
2013 Poster: Learning Stochastic Feedforward Neural Networks »
Yichuan Charlie Tang · Russ Salakhutdinov -
2013 Poster: Discriminative Transfer Learning with Tree-based Priors »
Nitish Srivastava · Russ Salakhutdinov -
2013 Poster: Annealing between distributions by averaging moments »
Roger Grosse · Chris Maddison · Russ Salakhutdinov -
2013 Oral: Annealing between distributions by averaging moments »
Roger Grosse · Chris Maddison · Russ Salakhutdinov -
2013 Poster: The Power of Asymmetry in Binary Hashing »
Behnam Neyshabur · Nati Srebro · Russ Salakhutdinov · Yury Makarychev · Payman Yadollahpour -
2012 Poster: Hamming Distance Metric Learning »
Mohammad Norouzi · Russ Salakhutdinov · David Fleet -
2012 Poster: Matrix reconstruction with the local max norm »
Rina Foygel · Nati Srebro · Russ Salakhutdinov -
2012 Poster: Multimodal Learning with Deep Boltzmann Machines »
Nitish Srivastava · Russ Salakhutdinov -
2012 Poster: Provable ICA with Unknown Gaussian Noise, with Implications for Gaussian Mixtures and Autoencoders »
Sanjeev Arora · Rong Ge · Ankur Moitra · Sushant Sachdeva -
2012 Poster: A Better Way to Pre-Train Deep Boltzmann Machines »
Russ Salakhutdinov · Geoffrey E Hinton -
2012 Oral: Multimodal Learning with Deep Boltzmann Machines »
Nitish Srivastava · Russ Salakhutdinov -
2012 Poster: Cardinality Restricted Boltzmann Machines »
Kevin Swersky · Danny Tarlow · Ilya Sutskever · Richard Zemel · Russ Salakhutdinov · Ryan Adams -
2011 Workshop: Challenges in Learning Hierarchical Models: Transfer Learning and Optimization »
Quoc V. Le · Marc'Aurelio Ranzato · Russ Salakhutdinov · Josh Tenenbaum · Andrew Y Ng -
2011 Poster: Learning to Learn with Compound HD Models »
Russ Salakhutdinov · Josh Tenenbaum · Antonio Torralba -
2011 Spotlight: Learning to Learn with Compound HD Models »
Russ Salakhutdinov · Josh Tenenbaum · Antonio Torralba -
2011 Poster: Learning with the weighted trace-norm under arbitrary sampling distributions »
Rina Foygel · Russ Salakhutdinov · Ohad Shamir · Nati Srebro -
2011 Poster: Transfer Learning by Borrowing Examples »
Joseph Lim · Russ Salakhutdinov · Antonio Torralba -
2010 Workshop: Transfer Learning Via Rich Generative Models. »
Russ Salakhutdinov · Ryan Adams · Josh Tenenbaum · Zoubin Ghahramani · Tom Griffiths -
2010 Poster: Collaborative Filtering in a Non-Uniform World: Learning with the Weighted Trace Norm »
Russ Salakhutdinov · Nati Srebro -
2010 Poster: Practical Large-Scale Optimization for Max-norm Regularization »
Jason D Lee · Benjamin Recht · Russ Salakhutdinov · Nati Srebro · Joel A Tropp -
2009 Workshop: Approximate Learning of Large Scale Graphical Models »
Russ Salakhutdinov · Amir Globerson · David Sontag -
2009 Poster: Replicated Softmax: an Undirected Topic Model »
Russ Salakhutdinov · Geoffrey E Hinton -
2009 Poster: Learning in Markov Random Fields using Tempered Transitions »
Russ Salakhutdinov -
2009 Poster: Modelling Relational Data using Bayesian Clustered Tensor Factorization »
Ilya Sutskever · Russ Salakhutdinov · Josh Tenenbaum -
2008 Poster: Evaluating probabilities under high-dimensional latent variable models »
Iain Murray · Russ Salakhutdinov -
2008 Spotlight: Evaluating probabilities under high-dimensional latent variable models »
Iain Murray · Russ Salakhutdinov -
2007 Poster: Probabilistic Matrix Factorization »
Russ Salakhutdinov · Andriy Mnih -
2007 Oral: Probabilistic Matrix Factorization »
Russ Salakhutdinov · Andriy Mnih -
2007 Poster: Using Deep Belief Nets to Learn Covariance Kernels for Gaussian Processes »
Russ Salakhutdinov · Geoffrey E Hinton