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Revisiting Spatial Invariance with Low-Rank Local Connectivity
Gamaleldin Elsayed · Prajit Ramachandran · Jon Shlens · Simon Kornblith

Tue Jul 14 10:00 AM -- 10:45 AM & Tue Jul 14 09:00 PM -- 09:45 PM (PDT) @ Virtual

Convolutional neural networks are among the most successful architectures in deep learning with this success at least partially attributable to the efficacy of spatial invariance as an inductive bias. Locally connected layers, which differ from convolutional layers only in their lack of spatial invariance, usually perform poorly in practice. However, these observations still leave open the possibility that some degree of relaxation of spatial invariance may yield a better inductive bias than either convolution or local connectivity. To test this hypothesis, we design a method to relax the spatial invariance of a network layer in a controlled manner; we create a \textit{low-rank} locally connected layer, where the filter bank applied at each position is constructed as a linear combination of basis set of filter banks with spatially varying combining weights. By varying the number of basis filter banks, we can control the degree of relaxation of spatial invariance. In experiments with small convolutional networks, we find that relaxing spatial invariance improves classification accuracy over both convolution and locally connected layers across MNIST, CIFAR-10, and CelebA datasets, thus suggesting that spatial invariance may be an overly restrictive prior.

Author Information

Gamaleldin Elsayed (Google Research, Brain Team)

Gamaleldin F. Elsayed is a Research Scientist at Google DeepMind interested in deep learning and computational neuroscience research. In particular, his research is focused on studying properties and problems of artificial neural networks and designing better machine learning models with inspiration from neuroscience. In 2017, he completed his PhD in Neuroscience from Columbia University at the Center for Theoretical Neuroscience. During his PhD, he contributed to the field of computational neuroscience through designing machine learning methods for identifying and validating structures in complex neural data. Prior to that, he completed his B.S. from The American University in Cairo with a major in Electronics Engineering and a minor in Computer Science, and earned M.S. degrees in electrical engineering from KAUST and Washington University in St. Louis. Before his Graduate studies, he was also a professional athlete and Olympian Fencer. He competed at The 2008 Olympic Games in Beijing with the Egyptian Saber team.

Prajit Ramachandran (Google)
Jon Shlens (Google Brain)
Simon Kornblith (Google Brain)

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