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Poster
projUNN: efficient method for training deep networks with unitary matrices
Bobak Kiani · Randall Balestriero · Yann LeCun · Seth Lloyd

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #542
in Poster Session 4 »
In learning with recurrent or very deep feed-forward networks, employing unitary matrices in each layer can be very effective at maintaining long-range stability. However, restricting network parameters to be unitary typically comes at the cost of expensive parameterizations or increased training runtime. We propose instead an efficient method based on rank-$k$ updates -- or their rank-$k$ approximation -- that maintains performance at a nearly optimal training runtime. We introduce two variants of this method, named Direct (projUNN-D) and Tangent (projUNN-T) projected Unitary Neural Networks, that can parameterize full $N$-dimensional unitary or orthogonal matrices with a training runtime scaling as $O(kN^2)$. Our method either projects low-rank gradients onto the closest unitary matrix (projUNN-T) or transports unitary matrices in the direction of the low-rank gradient (projUNN-D). Even in the fastest setting ($k=1$), projUNN is able to train a model's unitary parameters to reach comparable performances against baseline implementations. In recurrent neural network settings, projUNN closely matches or exceeds benchmarked results from prior unitary neural networks. Finally, we preliminarily explore projUNN in training orthogonal convolutional neural networks, which are currently unable to outperform state of the art models but can potentially enhance stability and robustness at large depth.
[ Paper]  [ Poster]  [ OpenReview] 

Author Information

Bobak Kiani (Massachusetts Institute of Technology)
Randall Balestriero (Meta AI, FAIR)
Yann LeCun (Facebook)

Yann LeCun is Director of AI Research at Facebook, and Silver Professor of Data Science, Computer Science, Neural Science, and Electrical Engineering at New York University. He received the Electrical Engineer Diploma from ESIEE, Paris in 1983, and a PhD in Computer Science from Université Pierre et Marie Curie (Paris) in 1987. After a postdoc at the University of Toronto, he joined AT&T Bell Laboratories in Holmdel, NJ in 1988. He became head of the Image Processing Research Department at AT&T Labs-Research in 1996, and joined NYU as a professor in 2003, after a brief period as a Fellow of the NEC Research Institute in Princeton. From 2012 to 2014 he directed NYU's initiative in data science and became the founding director of the NYU Center for Data Science. He was named Director of AI Research at Facebook in late 2013 and retains a part-time position on the NYU faculty. His current interests include AI, machine learning, computer perception, mobile robotics, and computational neuroscience. He has published over 180 technical papers and book chapters on these topics as well as on neural networks, handwriting recognition, image processing and compression, and on dedicated circuits for computer perception.

Seth Lloyd (MIT)

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