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The Restricted Boltzmann Machine (RBM) is a popular density model that is also good for extracting features. A main source of tractability in RBM models is the model's assumption that given an input, hidden units activate independently from one another. Sparsity and competition in the hidden representation is believed to be beneficial, and while an RBM with competition among its hidden units would acquire some of the attractive properties of sparse coding, such constraints are not added due to the widespread belief that the resulting model would become intractable. In this work, we show how a dynamic programming algorithm developed in 1981 can be used to implement exact sparsity in the RBM's hidden units. We then expand on this and show how to pass derivatives through a layer of exact sparsity, which makes it possible to fine-tune a deep belief network (DBN) consisting of RBMs with sparse hidden layers. We show that sparsity in the RBM's hidden layer improves the performance of both the pre-trained representations and of the fine-tuned model.
Author Information
Kevin Swersky (Google)
Danny Tarlow (Google Research, Brain team)
Ilya Sutskever (OpenAI)
Richard Zemel (Columbia University)
Russ Salakhutdinov (Carnegie Mellon University)
Ryan Adams (Princeton University)
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2015 Poster: Exploring Models and Data for Image Question Answering »
Mengye Ren · Jamie Kiros · Richard Zemel -
2015 Poster: Dependent Multinomial Models Made Easy: Stick-Breaking with the Polya-gamma Augmentation »
Scott Linderman · Matthew Johnson · Ryan Adams -
2014 Workshop: Representation and Learning Methods for Complex Outputs »
Richard Zemel · Dale Schuurmans · Kilian Q Weinberger · Yuhong Guo · Jia Deng · Francesco Dinuzzo · Hal Daumé III · Honglak Lee · Noah A Smith · Richard Sutton · Jiaqian YU · Vitaly Kuznetsov · Luke Vilnis · Hanchen Xiong · Calvin Murdock · Thomas Unterthiner · Jean-Francis Roy · Martin Renqiang Min · Hichem SAHBI · Fabio Massimo Zanzotto -
2014 Workshop: Bayesian Optimization in Academia and Industry »
Zoubin Ghahramani · Ryan Adams · Matthew Hoffman · Kevin Swersky · Jasper Snoek -
2014 Workshop: Perturbations, Optimization, and Statistics »
Tamir Hazan · George Papandreou · Danny Tarlow -
2014 Poster: Just-In-Time Learning for Fast and Flexible Inference »
S. M. Ali Eslami · Danny Tarlow · Pushmeet Kohli · John Winn -
2014 Poster: A* Sampling »
Chris Maddison · Danny Tarlow · Tom Minka -
2014 Oral: A* Sampling »
Chris Maddison · Danny Tarlow · Tom Minka -
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 -
2014 Poster: A framework for studying synaptic plasticity with neural spike train data »
Scott Linderman · Christopher H Stock · Ryan Adams -
2013 Workshop: Bayesian Optimization in Theory and Practice »
Matthew Hoffman · Jasper Snoek · Nando de Freitas · Michael A Osborne · Ryan Adams · Sebastien Bubeck · Philipp Hennig · Remi Munos · Andreas Krause -
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 Workshop: Output Representation Learning »
Yuhong Guo · Dale Schuurmans · Richard Zemel · Samy Bengio · Yoshua Bengio · Li Deng · Dan Roth · Kilian Q Weinberger · Jason Weston · Kihyuk Sohn · Florent Perronnin · Gabriel Synnaeve · Pablo R Strasser · julien audiffren · Carlo Ciliberto · Dan Goldwasser -
2013 Workshop: Perturbations, Optimization, and Statistics »
Tamir Hazan · George Papandreou · Sasha Rakhlin · Danny Tarlow -
2013 Poster: Multi-Task Bayesian Optimization »
Kevin Swersky · Jasper Snoek · Ryan Adams -
2013 Poster: Message Passing Inference with Chemical Reaction Networks »
Nils E Napp · Ryan Adams -
2013 Poster: One-shot learning by inverting a compositional causal process »
Brenden M Lake · Russ Salakhutdinov · Josh Tenenbaum -
2013 Oral: Message Passing Inference with Chemical Reaction Networks »
Nils E Napp · Ryan Adams -
2013 Poster: Learning Stochastic Feedforward Neural Networks »
Yichuan Charlie Tang · Russ Salakhutdinov -
2013 Poster: A Determinantal Point Process Latent Variable Model for Inhibition in Neural Spiking Data »
Jasper Snoek · Richard Zemel · Ryan Adams -
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 Poster: On the Expressive Power of Restricted Boltzmann Machines »
James Martens · Arkadev Chattopadhya · Toni Pitassi · Richard Zemel -
2013 Poster: Learning to Pass Expectation Propagation Messages »
Nicolas Heess · Danny Tarlow · John Winn -
2013 Oral: Annealing between distributions by averaging moments »
Roger Grosse · Chris Maddison · Russ Salakhutdinov -
2013 Poster: Contrastive Learning Using Spectral Methods »
James Y Zou · Daniel Hsu · David Parkes · Ryan Adams -
2013 Poster: The Power of Asymmetry in Binary Hashing »
Behnam Neyshabur · Nati Srebro · Russ Salakhutdinov · Yury Makarychev · Payman Yadollahpour -
2012 Workshop: Perturbations, Optimization, and Statistics »
Tamir Hazan · George Papandreou · Danny Tarlow -
2012 Poster: Hamming Distance Metric Learning »
Mohammad Norouzi · Russ Salakhutdinov · David Fleet -
2012 Poster: Collaborative Ranking With 17 Parameters »
Maksims Volkovs · Richard Zemel -
2012 Poster: Bayesian n-Choose-k Models for Classification and Ranking »
Kevin Swersky · Danny Tarlow · Richard Zemel · Ryan Adams · Brendan J Frey -
2012 Poster: ImageNet Classification with Deep Convolutional Neural Networks »
Alex Krizhevsky · Ilya Sutskever · Geoffrey E Hinton -
2012 Poster: Priors for Diversity in Generative Latent Variable Models »
James Y Zou · Ryan Adams -
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: A Better Way to Pre-Train Deep Boltzmann Machines »
Russ Salakhutdinov · Geoffrey E Hinton -
2012 Spotlight: ImageNet Classification with Deep Convolutional Neural Networks »
Alex Krizhevsky · Ilya Sutskever · Geoffrey E Hinton -
2012 Oral: Multimodal Learning with Deep Boltzmann Machines »
Nitish Srivastava · Russ Salakhutdinov -
2012 Poster: Efficient Sampling for Bipartite Matching Problems »
Maksims Volkovs · Richard Zemel -
2012 Poster: Practical Bayesian Optimization of Machine Learning Algorithms »
Jasper Snoek · Hugo Larochelle · 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 Workshop: Bayesian Nonparametric Methods: Hope or Hype? »
Emily Fox · Ryan Adams -
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 Workshop: Monte Carlo Methods for Bayesian Inference in Modern Day Applications »
Ryan Adams · Mark A Girolami · Iain Murray -
2010 Oral: Tree-Structured Stick Breaking for Hierarchical Data »
Ryan Adams · Zoubin Ghahramani · Michael Jordan -
2010 Oral: Slice sampling covariance hyperparameters of latent Gaussian models »
Iain Murray · Ryan Adams -
2010 Poster: Tree-Structured Stick Breaking for Hierarchical Data »
Ryan Adams · Zoubin Ghahramani · Michael Jordan -
2010 Poster: Collaborative Filtering in a Non-Uniform World: Learning with the Weighted Trace Norm »
Russ Salakhutdinov · Nati Srebro -
2010 Poster: Slice sampling covariance hyperparameters of latent Gaussian models »
Iain Murray · Ryan Adams -
2010 Poster: Practical Large-Scale Optimization for Max-norm Regularization »
Jason D Lee · Benjamin Recht · Russ Salakhutdinov · Nati Srebro · Joel A Tropp -
2010 Talk: Opening Remarks and Awards »
Richard Zemel · Terrence Sejnowski · John Shawe-Taylor -
2009 Workshop: Approximate Learning of Large Scale Graphical Models »
Russ Salakhutdinov · Amir Globerson · David Sontag -
2009 Placeholder: Opening Remarks »
Richard Zemel -
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: Using matrices to model symbolic relationship »
Ilya Sutskever · Geoffrey E Hinton -
2008 Poster: Comparing model predictions of response bias and variance in cue combination »
Rama Natarajan · Iain Murray · Ladan Shams · Richard Zemel -
2008 Spotlight: Using matrices to model symbolic relationship »
Ilya Sutskever · Geoffrey E Hinton -
2008 Poster: The Gaussian Process Density Sampler »
Ryan Adams · Iain Murray · David MacKay -
2008 Poster: The Recurrent Temporal Restricted Boltzmann Machine »
Ilya Sutskever · Geoffrey E Hinton · Graham Taylor -
2008 Poster: Learning Hybrid Models for Image Annotation with Partially Labeled Data »
Xuming He · Richard Zemel -
2008 Spotlight: The Gaussian Process Density Sampler »
Ryan Adams · Iain Murray · David MacKay -
2008 Poster: Evaluating probabilities under high-dimensional latent variable models »
Iain Murray · Russ Salakhutdinov -
2008 Poster: Competing RBM density models for classification of fMRI images »
Tanya Schmah · Geoffrey E Hinton · Richard Zemel -
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 -
2006 Poster: Using Combinatorial Optimization within Max-Product Belief Propagation »
John Duchi · Danny Tarlow · Gal Elidan · Daphne Koller -
2006 Spotlight: Using Combinatorial Optimization within Max-Product Belief Propagation »
John Duchi · Danny Tarlow · Gal Elidan · Daphne Koller