Geometric Deep Learning ⁽³⁾

Escnn, built on PyTorch, is a library that, in the spirit of Geometric Deep Learning, provides a high-level interface to designing and training group-equivariant neural networks. This post introduces important mathematical concepts, the library’s key actors, and essential library use. Today, we resume our exploration of group equivariance. This is the third post in the series. The first was a high-level introduction: what this is all about; how equivariance is operationalized; and why it is of relevance to many deep-learning applications. The second sought to concretize the key ideas by developing a group-equivariant CNN from scratch. That being instructive, but too tedious for practical use, today we look at a carefully designed, highly-performant library that hides the technicalities and enables…

We code up a simple group-equivariant convolutional neural network (GCNN) that is equivariant to rotation. The world may be upside down, but the network will know. Convolutional neural networks (CNNs) are great – they’re able to detect features in an image no matter where. Well, not exactly. They’re not indifferent to just any kind of movement. Shifting up or down, or left or right, is fine; rotating around an axis is not. That’s because of how convolution works: traverse by row, then traverse by column (or the other way round). If we want “more” (e.g., successful detection of an upside-down object), we need to extend convolution to an operation that is rotation-equivariant. An operation that is equivariant to some type…

This post introduces deep learning on graphs by mapping its central concept - message passing - to minimal usage patterns of PyTorch Geometric’s foundation-laying MessagePassing class. Exploring those patterns, we gain some basic, very concrete insights into how graph DL works. If, in deep-learning world, the first half of the last decade has been the age of images, and the second, that of language, one could say that now, we’re living in the age of graphs. At least, that’s what commonly cited research metrics suggest. But as we’re all aware, deep-learning research is anything but an ivory tower. To see real-world implications, it suffices to reflect on how many things can be modeled as graphs. Some things quite naturally “are”…