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Equivariance with Learned Canonical Mappings
Oumar Kaba · Arnab Mondal · Yan Zhang · Yoshua Bengio · Siamak Ravanbakhsh

Sat Dec 03 09:00 AM -- 09:05 AM (PST) @
Event URL: https://openreview.net/forum?id=pVD1k8ge25a »

Symmetry-based neural networks often constrain the architecture in order to achieve invariance or equivariance to a group of transformations. In this paper, we propose an alternative that avoids this architectural constraint by learning to produce canonical representation of the data. These canonical mappings can readily be plugged into non-equivariant backbone architectures. We offer explicit ways to implement them for many groups of interest. We show that this approach enjoys universality while providing interpretable insights. Our main hypothesis is that learning a neural network to perform the canonicalization will perform better than doing it using predefined heuristics. Our results show that learning the canonical mappings indeed leads to better results and that the approach achieves great performance in practice.

Author Information

Oumar Kaba (Mila, McGill University)
Arnab Mondal (Mcgill University)
Yan Zhang (Samsung - SAIT AI Lab Montreal)
Yoshua Bengio (Mila / U. Montreal)

Yoshua Bengio is Full Professor in the computer science and operations research department at U. Montreal, scientific director and founder of Mila and of IVADO, Turing Award 2018 recipient, Canada Research Chair in Statistical Learning Algorithms, as well as a Canada AI CIFAR Chair. He pioneered deep learning and has been getting the most citations per day in 2018 among all computer scientists, worldwide. He is an officer of the Order of Canada, member of the Royal Society of Canada, was awarded the Killam Prize, the Marie-Victorin Prize and the Radio-Canada Scientist of the year in 2017, and he is a member of the NeurIPS advisory board and co-founder of the ICLR conference, as well as program director of the CIFAR program on Learning in Machines and Brains. His goal is to contribute to uncover the principles giving rise to intelligence through learning, as well as favour the development of AI for the benefit of all.

Siamak Ravanbakhsh (McGill / MILA)

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