Scalable and equivariant spherical CNNs by DISCO convolutions — No existing spherical convolutional neural network (CNN) framework is both computationally scalable and rotationally equivariant. Continuous approaches capture rotational equivariance but are often prohibitively computationally demanding. Discrete approaches offer more favorable computational performance but at the cost of equivariance. We develop a hybrid discrete-continuous (DISCO) group convolution that is simultaneously…

Continuous vs discrete approaches on the sphere — Ideally geometric deep learning techniques on groups would encode equivariance to group transformations, to provide well-behaved representation spaces and excellent performance, while also being computationally efficient. However, no single approach provides both of these desirable properties. Continuous approaches offer excellent equivariance but with a very large computational cost. Discrete approaches…

Scattering networks on the sphere for scalable and rotationally equivariant spherical CNNs — Conventional spherical CNNs are not scalable to high resolution classification tasks. In this post we present spherical scattering layers — a novel spherical layer that reduces the dimensionality of the input data while retaining relevant information, while also being rotationally equivariant. Scattering networks work by employing predefined convolutional filters from…

Unlocking AI for 360° spherical data — While AI is now commonplace for standard types of data, such as structured, sequential and image data, the application of AI is severly curtailed for other more complex forms of data. These more complex datasets typical exhibit non-trivial geometry. The field of geometric AI, or geometric deep learning, has emerged…

AI for complex data — Deep learning is hard. While universal approximation theorems show that sufficiently complex neural networks can in principle approximate “anything”, there is no guarantee that we can find good models. Great progress in deep learning has nevertheless been made by judicious choice of model architectures. These model architectures encode inductive biases…

Geometric AI allows you to step inside 360° VR photos and videos — Today’s virtual reality (VR) experiences fall short of the realism users expect. Current VR technology essentially falls into two categories: those based on 3D models with computer generated imagery (CGI); and those based on panoramic 360° imagery. CGI-based experiences are interactive and support novel views but are far from photorealistic…

Machine learning assisted computation of the marginal likelihood — Bayesian model comparison provides a principled statistical framework for selecting an appropriate model to describe observational data, naturally trading off model complexity and goodness of fit. However, it requires computation of the Bayesian model evidence, also called the marginal likelihood, which is computationally challenging. …

Hybrid rotationally equivariant spherical CNNs — Notions of spherical convolution offer a promising route to unlocking the potential of deep learning for the variety of problems in which spherical data are prevalent. However, the introduction of non-linearity is a challenge. In this post we explore how ideas originating in quantum physics may be applied to overcome…

Spherical CNNs By encoding an understanding of the translational symmetry of the physical world, convolutional neural networks (CNNs) have revolutionised computer vision. …