CONCEPT
Geometric Deep Learning
The unification of neural network architecture around the mathematics of symmetry—the discovery, proposed by Bronstein, Bruna, Cohen, and Veličković in 2021, that the bewildering zoo of successful AI architectures is really one thing seen through the lens of group theory, and that building symmetry into the architecture by construction is the principled path to capability.
Geometric deep learning is the most ambitious recent attempt to bring mathematical order to the design of neural networks, and it reaches, deliberately and by name, for the nineteenth-century mathematics of symmetry that
Évariste Galois did more than anyone to begin. The central claim is that each successful neural architecture is successful because it respects the symmetries of its data domain: convolutional networks are what you get when you demand invariance to translations on a grid; graph neural networks emerge from invariance to permutations of nodes; networks for three-dimensional molecular structures respect the rotation group of space;
transformer architectures respect the permutation symmetry of their inputs. What looked like a zoo of unrelated inventions is, on this view, a single principle—build in the symmetry group of the domain—instantiated across different groups. The framework’s explicit model is Felix Klein’s Erlangen Programme of