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Structuring Representations Using Group Invariants
Mehran Shakerinava · Arnab Kumar Mondal · Siamak Ravanbakhsh

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #514

A finite set of invariants can identify many interesting transformation groups. For example, distances, inner products and angles are preserved by Euclidean, Orthogonal and Conformal transformations, respectively. In an equivariant representation, the group invariants should remain constant on the embedding as we transform the input. This gives a procedure for learning equivariant representations without knowing the possibly nonlinear action of the group in the input space. Rather than enforcing such hard invariance constraints on the latent space, we show how to use invariants for "symmetry regularization" of the latent, while guaranteeing equivariance through other means. We also show the feasibility of learning disentangled representations using this approach and provide favorable qualitative and quantitative results on downstream tasks, including world modeling and reinforcement learning.

Author Information

Mehran Shakerinava (McGill - Mila)
Arnab Kumar Mondal (Mila - Quebec AI Institute McGill University)
Arnab Kumar Mondal

I am a fourth-year Ph.D. candidate in Computer Science at Mcgill University and Mila - Quebec Artificial Intelligence Institute, supervised by Prof. Siamak Ravanbakhsh and Prof. Kaleem Siddiqi. My primary areas of interest include representation learning, deep reinforcement learning, self-supervised learning, equivariance and geometric deep learning. I am also interested in efficient long-range sequence modeling, uncertainty estimation, generative modeling and computer vision. Before moving to Montreal, I did my undergraduate studies in Electronics and Electrical Engineering at the Indian Institute of Technology, Kharagpur.

Siamak Ravanbakhsh (McGill / MILA)

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