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Deep LearningMathematics & Statistics

geometric deep learning

nounAlso: GDL, equivariant deep learning, symmetry-aware deep learning

In plain wordsAn approach to designing neural networks around the shapes and symmetries of the data, whether grids, graphs, surfaces or 3-D structures, so the network respects how that data can be moved or rearranged.

  1. A research program and unifying framework that derives neural-network architectures from the geometric structure of their data domain and the symmetries a model should respect. In the '5G' blueprint of Michael Bronstein and colleagues (grids, groups, graphs, geodesics and gauges), each domain comes with a symmetry group and a matching architecture: images on grids with translations (CNNsconvolutional neural network, n.: A kind of neural network built for images and other grid-like data. It slides small pattern detectors across the input, finding edges first, then shapes, then whole objects.), sets and graphs with permutations (GNNsgraph neural network, n.: A neural network for data shaped like a web of connections, such as molecules, social networks or road maps, in which each point repeatedly gathers information from its neighbors. and transformerstransformer, n.: The design behind today's chatbots and much of modern AI. It handles text by letting every word look at every other word and decide which of them matter for understanding it.), spaces with rotations and other group actions (group-equivariantequivariance, n.: A property of a model whose output changes in step with its input: move the cat in a photo, and the network's internal 'cat' signal moves the same way. networks), and curved surfaces and manifolds with geodesics and gauge transformations (mesh and gauge-equivariant CNNs). Architectures are assembled from equivariant layers, local pooling and invariantinvariance, n.: A property of a model whose answer does not change when the input is altered in an irrelevant way, such as a photo classifier that still says 'cat' when the cat moves or the picture is flipped. readouts, an approach its proponents compare to Felix Klein's Erlangen program, which classified geometries by their symmetry groups. It underpins much of AI for science, including molecular and materials modeling and protein-structure prediction.

    Geometric deep learning explains why the same design principles produce CNNs for images and GNNs for molecules.

Origin

The name took hold with Michael Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam and Pierre Vandergheynst's survey 'Geometric Deep Learning: Going Beyond Euclidean Data' (arXiv 2016; IEEE Signal Processing Magazine, 2017). Bronstein, Bruna, Taco Cohen and Petar Veličković's proto-book 'Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges' (arXiv, April 2021) recast it as an 'Erlangen program' for deep learning.

Related

See also
  • equivarianceequivariance, n.: A property of a model whose output changes in step with its input: move the cat in a photo, and the network's internal 'cat' signal moves the same way.
  • invarianceinvariance, n.: A property of a model whose answer does not change when the input is altered in an irrelevant way, such as a photo classifier that still says 'cat' when the cat moves or the picture is flipped.
  • graph neural networkgraph neural network, n.: A neural network for data shaped like a web of connections, such as molecules, social networks or road maps, in which each point repeatedly gathers information from its neighbors.
  • convolutional neural networkconvolutional neural network, n.: A kind of neural network built for images and other grid-like data. It slides small pattern detectors across the input, finding edges first, then shapes, then whole objects.
  • inductive biasinductive bias, n.: The assumptions built into a learning method that decide how it fills the gaps between the examples it was shown, such as that similar inputs get similar answers. Every learner needs some to cope with new cases.
  • AlphaFoldAlphaFold, prop. n.: A DeepMind AI system that predicts the 3D shape of proteins from their chemical sequence, often about as accurately as laboratory experiments. It cracked a problem biologists had worked on for 50 years and won a Nobel Prize.

Sources

  1. Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A. & Vandergheynst, P. (2017). Geometric Deep Learning: Going Beyond Euclidean Data. IEEE Signal Processing Magazine, 34(4), 18–42.
  2. Bronstein, M. M., Bruna, J., Cohen, T. & Veličković, P. (2021). Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges. arXiv:2104.13478. arxiv.org/abs/2104.13478

Mentioned in

graph neural networkgraph neural network, n.: A neural network for data shaped like a web of connections, such as molecules, social networks or road maps, in which each point repeatedly gathers information from its neighbors., equivarianceequivariance, n.: A property of a model whose output changes in step with its input: move the cat in a photo, and the network's internal 'cat' signal moves the same way., invarianceinvariance, n.: A property of a model whose answer does not change when the input is altered in an irrelevant way, such as a photo classifier that still says 'cat' when the cat moves or the picture is flipped., neural operatorneural operator, n.: A neural network that learns how a whole physical system responds, such as how a fluid flows given its starting state, so it can stand in for slow simulations and answer new cases quickly.