How to make neural nets smaller while still preserving their performance.
This is a subtle problem,
As we suspect that part of their special sauce is precisely that they are overparameterized which is to say, one reason they work is precisely that they are bigger than they “need” to be.
The problem of finding the network that is *smaller than the bigger that it seems to need to be* is tricky.
My instinct is to use some sparse regularisation but this does not carry over to the deep network setting AFAICS.

Kim Martineau’s summary of the state of the art in “Lottery ticket” (Frankle and Carbin 2019) pruning strategies is fun; See also You et al. (2019a) for an elaboration.

Aghasi, Alireza, Nam Nguyen, and Justin Romberg. 2016. “Net-Trim: A Layer-Wise Convex Pruning of Deep Neural Networks,” November. http://arxiv.org/abs/1611.05162.

Borgerding, Mark, and Philip Schniter. 2016. “Onsager-Corrected Deep Networks for Sparse Linear Inverse Problems,” December. http://arxiv.org/abs/1612.01183.

Chen, Tianqi, Ian Goodfellow, and Jonathon Shlens. 2015. “Net2Net: Accelerating Learning via Knowledge Transfer,” November. http://arxiv.org/abs/1511.05641.

Chen, Wenlin, James T. Wilson, Stephen Tyree, Kilian Q. Weinberger, and Yixin Chen. 2015. “Compressing Convolutional Neural Networks,” June. http://arxiv.org/abs/1506.04449.

Cheng, Yu, Duo Wang, Pan Zhou, and Tao Zhang. 2017. “A Survey of Model Compression and Acceleration for Deep Neural Networks,” October. http://arxiv.org/abs/1710.09282.

Cutajar, Kurt, Edwin V. Bonilla, Pietro Michiardi, and Maurizio Filippone. 2017. “Random Feature Expansions for Deep Gaussian Processes.” In *PMLR*. http://proceedings.mlr.press/v70/cutajar17a.html.

Daniely, Amit. 2017. “Depth Separation for Neural Networks,” February. http://arxiv.org/abs/1702.08489.

Frankle, Jonathan, and Michael Carbin. 2019. “The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks,” March. http://arxiv.org/abs/1803.03635.

Garg, Sahil, Irina Rish, Guillermo Cecchi, and Aurelie Lozano. 2017. “Neurogenesis-Inspired Dictionary Learning: Online Model Adaption in a Changing World.” In. http://arxiv.org/abs/1701.06106.

Ghosh, Tapabrata. 2017. “QuickNet: Maximizing Efficiency and Efficacy in Deep Architectures,” January. http://arxiv.org/abs/1701.02291.

Globerson, Amir, and Roi Livni. 2016. “Learning Infinite-Layer Networks: Beyond the Kernel Trick,” June. http://arxiv.org/abs/1606.05316.

Gray, Scott, Alec Radford, and Diederik P Kingma. n.d. “GPU Kernels for Block-Sparse Weights,” 12.

Ha, David, Andrew Dai, and Quoc V. Le. 2016. “HyperNetworks,” September. http://arxiv.org/abs/1609.09106.

Hardt, Moritz, Benjamin Recht, and Yoram Singer. 2015. “Train Faster, Generalize Better: Stability of Stochastic Gradient Descent,” September. http://arxiv.org/abs/1509.01240.

He, Yihui, Ji Lin, Zhijian Liu, Hanrui Wang, Li-Jia Li, and Song Han. 2019. “AMC: AutoML for Model Compression and Acceleration on Mobile Devices,” January. http://arxiv.org/abs/1802.03494.

Howard, Andrew G., Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. 2017. “MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications,” April. http://arxiv.org/abs/1704.04861.

Iandola, Forrest N., Song Han, Matthew W. Moskewicz, Khalid Ashraf, William J. Dally, and Kurt Keutzer. 2016. “SqueezeNet: AlexNet-Level Accuracy with 50x Fewer Parameters and \(<\)0.5MB Model Size,” February. http://arxiv.org/abs/1602.07360.

Lee, Holden, Rong Ge, Tengyu Ma, Andrej Risteski, and Sanjeev Arora. 2017. “On the Ability of Neural Nets to Express Distributions.” In. http://arxiv.org/abs/1702.07028.

Lobacheva, Ekaterina, Nadezhda Chirkova, and Dmitry Vetrov. 2017. “Bayesian Sparsification of Recurrent Neural Networks.” In *Workshop on Learning to Generate Natural Language*. http://arxiv.org/abs/1708.00077.

Louizos, Christos, Max Welling, and Diederik P. Kingma. 2017. “Learning Sparse Neural Networks Through $L_0$ Regularization,” December. http://arxiv.org/abs/1712.01312.

Molchanov, Dmitry, Arsenii Ashukha, and Dmitry Vetrov. 2017. “Variational Dropout Sparsifies Deep Neural Networks.” In *Proceedings of ICML*. http://arxiv.org/abs/1701.05369.

Narang, Sharan, Eric Undersander, and Gregory Diamos. 2017. “Block-Sparse Recurrent Neural Networks,” November. http://arxiv.org/abs/1711.02782.

Pan, Wei, Hao Dong, and Yike Guo. 2016. “DropNeuron: Simplifying the Structure of Deep Neural Networks,” June. http://arxiv.org/abs/1606.07326.

Renda, Alex, Jonathan Frankle, and Michael Carbin. 2020. “Comparing Rewinding and Fine-Tuning in Neural Network Pruning,” March. http://arxiv.org/abs/2003.02389.

Scardapane, Simone, Danilo Comminiello, Amir Hussain, and Aurelio Uncini. 2016. “Group Sparse Regularization for Deep Neural Networks,” July. http://arxiv.org/abs/1607.00485.

Shi, Lei, Shikun Feng, and ZhifanZhu. 2016. “Functional Hashing for Compressing Neural Networks,” May. http://arxiv.org/abs/1605.06560.

Srinivas, Suraj, and R. Venkatesh Babu. 2016. “Generalized Dropout,” November. http://arxiv.org/abs/1611.06791.

Steeg, Greg Ver, and Aram Galstyan. 2015. “The Information Sieve,” July. http://arxiv.org/abs/1507.02284.

Ullrich, Karen, Edward Meeds, and Max Welling. 2017. “Soft Weight-Sharing for Neural Network Compression.” *arXiv Preprint arXiv:1702.04008*. https://arxiv.org/abs/1702.04008.

Urban, Gregor, Krzysztof J. Geras, Samira Ebrahimi Kahou, Ozlem Aslan, Shengjie Wang, Rich Caruana, Abdelrahman Mohamed, Matthai Philipose, and Matt Richardson. 2016. “Do Deep Convolutional Nets Really Need to Be Deep (or Even Convolutional)?” March. http://arxiv.org/abs/1603.05691.

Wang, Yunhe, Chang Xu, Chao Xu, and Dacheng Tao. 2019. “Packing Convolutional Neural Networks in the Frequency Domain.” *IEEE Transactions on Pattern Analysis and Machine Intelligence* 41 (10): 2495–2510. https://doi.org/10.1109/TPAMI.2018.2857824.

Wang, Yunhe, Chang Xu, Shan You, Dacheng Tao, and Chao Xu. 2016. “CNNpack: Packing Convolutional Neural Networks in the Frequency Domain.” In *Advances in Neural Information Processing Systems 29*, edited by D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon, and R. Garnett, 253–61. Curran Associates, Inc. http://papers.nips.cc/paper/6390-cnnpack-packing-convolutional-neural-networks-in-the-frequency-domain.pdf.

Wang, Zhangyang, Shiyu Chang, Qing Ling, Shuai Huang, Xia Hu, Honghui Shi, and Thomas S. Huang. 2016. “Stacked Approximated Regression Machine: A Simple Deep Learning Approach.” In. https://arxiv.org/abs/1608.04062.

You, Haoran, Chaojian Li, Pengfei Xu, Yonggan Fu, Yue Wang, Xiaohan Chen, Richard G. Baraniuk, Zhangyang Wang, and Yingyan Lin. 2019a. “Drawing Early-Bird Tickets: Toward More Efficient Training of Deep Networks.” In. https://openreview.net/forum?id=BJxsrgStvr.

———. 2019a. “Drawing Early-Bird Tickets: Toward More Efficient Training of Deep Networks.” In. https://openreview.net/forum?id=BJxsrgStvr.

Zhao, Liang. 2017. “Fast Algorithms on Random Matrices and Structured Matrices.” http://academicworks.cuny.edu/gc_etds/2073/.