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We suggest analyzing neural networks through the prism of space constraints.
The perceptron: A probabilistic model for information storage and organization in the brain
Rosenblatt, Frank · 1958
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A theory of the learnable
Valiant, Leslie G · 1984
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Training a 3-node neural network is NP-complete
Blum, Avrim and Rivest, Ronald L · 1988
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Rigorous learning curve bounds from statistical mechanics
Haussler, David, Kearns, Michael, Seung, H Sebastian, and Tishby, Naftali · 1996
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Algorithmic stability and sanity-check bounds for leave-one-out cross-validation
Kearns, Michael and Ron, Dana · 1999
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Computable shell decomposition bounds
Langford, John and McAllester, David A · 2000
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Stability and generalization
Bousquet, Olivier and Elisseeff, André · 2002
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Pseudo-random graphs
Krivelevich, Michael and Sudakov, Benny · 2006
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Learning multiple layers of features from tiny images
Krizhevsky, Alex and Hinton, Geoffrey · 2009
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Imagenet classification with deep convolutional neural networks
Krizhevsky, Alex, Sutskever, Ilya, and Hinton, Geoffrey E · 2012
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Provable bounds for learning some deep representations
Arora, Sanjeev, Bhaskara, Aditya, Ge, Rong, and Ma, Tengyu · 2014
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Deep symmetry networks
Gens, Robert and Domingos, Pedro M · 2014
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Livni, Roi, Shalev-Shwartz, Shai, and Shamir, Ohad · 2014
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Understanding machine learning: From theory to algorithms
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Fundamental limits of online and distributed algorithms for statistical learning and estimation
Shamir, O · 2014
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Very deep convolutional networks for large-scale image recognition
Simonyan, Karen and Zisserman, Andrew · 2014
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Deep learning
LeCun, Yann, Bengio, Yoshua, and Hinton, Geoffrey · 2015
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Exploiting cyclic symmetry in convolutional neural networks
Dieleman, Sander, De Fauw, Jeffrey, and Kavukcuoglu, Koray · 2016
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The power of depth for feedforward neural networks
Eldan, Ronen and Shamir, Ohad · 2016
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Optimal architectures in a solvable model of deep networks
Kadmon, Jonathan and Sompolinsky, Haim · 2016
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Time-space hardness of learning sparse parities
Kol, G., Raz, R., and Tal, A · 2016
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On the expressive power of deep neural networks
Raghu, Maithra, Poole, Ben, Kleinberg, Jon, Ganguli, Surya, and Sohl-Dickstein, Jascha · 2016
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Imagenet large scale visual recognition challenge
Russakovsky, Olga, Deng, Jia, Su, Hao, Krause, Jonathan, Satheesh, Sanjeev, Ma, Sean, Huang, Zhiheng, Karpathy, Andrej, Khosla, Aditya, Bernstein, Michael, et al · 2015
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Going deeper with convolutions
Szegedy, Christian, Liu, Wei, Jia, Yangqing, Sermanet, Pierre, Reed, Scott, Anguelov, Dragomir, Erhan, Dumitru, Vanhoucke, Vincent, and Rabinovich, Andrew · 2015
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Deep learning and the information bottleneck principle
Tishby, Naftali and Zaslavsky, Noga · 2015
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Group equivariant convolutional networks
Cohen, Taco S and Welling, Max · 2016
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Toward deeper understanding of neural networks: The power of initialization and a dual view on expressivity
Daniely, Amit, Frostig, Roy, and Singer, Yoram · 2016
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Raz, Ran · 2016
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Depth separation in relu networks for approximating smooth non-linear functions
Safran, Itay and Shamir, Ohad · 2016
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Distribution-specific hardness of learning neural networks
Shamir, Ohad · 2016
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Mixing implies lower bounds for space bounded learning
Moshkovitz, Dana and Moshkovitz, Michal · 2017
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A time-space lower bound for a large class of learning problems
Raz, Ran · 2017
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Understanding deep learning requires rethinking generalization
Zhang, Chiyuan, Bengio, Samy, Hardt, Moritz, Recht, Benjamin, and Vinyals, Oriol · 2017
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