Provable Bounds for Learning Some Deep Representations

Sanjeev Arora; Aditya Bhaskara; Rong Ge; Tengyu Ma

Provable Bounds for Learning Some Deep Representations

Sanjeev Arora, Aditya Bhaskara, Rong Ge, Tengyu Ma ;

Proceedings of the 31st International Conference on Machine Learning, PMLR 32(1):584-592, 2014.

Abstract

We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an n node multilayer neural net that has degree at most n^γ for some γ< 1 and each edge has a random edge weight in [-1,1]. Our algorithm learns almost all networks in this class with polynomial running time. The sample complexity is quadratic or cubic depending upon the details of the model. The algorithm uses layerwise learning. It is based upon a novel idea of observing correlations among features and using these to infer the underlying edge structure via a global graph recovery procedure. The analysis of the algorithm reveals interesting structure of neural nets with random edge weights.

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@InProceedings{pmlr-v32-arora14, title = {Provable Bounds for Learning Some Deep Representations}, author = {Sanjeev Arora and Aditya Bhaskara and Rong Ge and Tengyu Ma}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {584--592}, year = {2014}, editor = {Eric P. Xing and Tony Jebara}, volume = {32}, number = {1}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/arora14.pdf}, url = {http://proceedings.mlr.press/v32/arora14.html}, abstract = {We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an n node multilayer neural net that has degree at most n^γ for some γ< 1 and each edge has a random edge weight in [-1,1]. Our algorithm learns almost all networks in this class with polynomial running time. The sample complexity is quadratic or cubic depending upon the details of the model. The algorithm uses layerwise learning. It is based upon a novel idea of observing correlations among features and using these to infer the underlying edge structure via a global graph recovery procedure. The analysis of the algorithm reveals interesting structure of neural nets with random edge weights.} }

%0 Conference Paper %T Provable Bounds for Learning Some Deep Representations %A Sanjeev Arora %A Aditya Bhaskara %A Rong Ge %A Tengyu Ma %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-arora14 %I PMLR %J Proceedings of Machine Learning Research %P 584--592 %U http://proceedings.mlr.press %V 32 %N 1 %W PMLR %X We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an n node multilayer neural net that has degree at most n^γ for some γ< 1 and each edge has a random edge weight in [-1,1]. Our algorithm learns almost all networks in this class with polynomial running time. The sample complexity is quadratic or cubic depending upon the details of the model. The algorithm uses layerwise learning. It is based upon a novel idea of observing correlations among features and using these to infer the underlying edge structure via a global graph recovery procedure. The analysis of the algorithm reveals interesting structure of neural nets with random edge weights.

TY - CPAPER TI - Provable Bounds for Learning Some Deep Representations AU - Sanjeev Arora AU - Aditya Bhaskara AU - Rong Ge AU - Tengyu Ma BT - Proceedings of the 31st International Conference on Machine Learning PY - 2014/01/27 DA - 2014/01/27 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-arora14 PB - PMLR SP - 584 DP - PMLR EP - 592 L1 - http://proceedings.mlr.press/v32/arora14.pdf UR - http://proceedings.mlr.press/v32/arora14.html AB - We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an n node multilayer neural net that has degree at most n^γ for some γ< 1 and each edge has a random edge weight in [-1,1]. Our algorithm learns almost all networks in this class with polynomial running time. The sample complexity is quadratic or cubic depending upon the details of the model. The algorithm uses layerwise learning. It is based upon a novel idea of observing correlations among features and using these to infer the underlying edge structure via a global graph recovery procedure. The analysis of the algorithm reveals interesting structure of neural nets with random edge weights. ER -