Rotation Invariant CNN

This Stack Overflow post explores a question I had reading about Convolutional Neural Networks: Why rotation-invariant neural networks are not used in winners of the popular competitions?

The answer is - networks are optimized for performance, not for theoretical ‘cleanliness’. In theory, it’s cleaner to implement G-invariance in the CNN. In practice, it is equivalent, and simpler, to augment the data by G-transformations, for a group G.

One of the references therein, Group Equivariant Convolutional Networks, by T.S. Cohen and M.Welling, explains how to add two new layer types, to implelemnt G-invariance directly in the CNN.

Also see these talks:

Geometric Deep Learning

• Michael Bronstein: Geometric Deep Learning: the Erlangen Programme of ML (2021)
  • Geometric Deep Learning: Grids, Groups, Graphs,Geodesics, and Gauges, M. Bronstein et al (2021)
  • ML Street Talk #60: Geometric Deep Learning Blueprint (2021)
• Max Welling
  • ML Street Talk #36: Max Welling: Quantum, Manifolds & Symmetries in ML (2021)
  • IAS Seminar on Theoretical ML: Graph Nets: The Next Generation (2020)
    • In practice, graph neural nets have at most 5-6 layers. Deeper than that, they saturate. So unlike ResNets, which can have hundreds, or even thousands of layersm graph neural nets are shallow.
    • The subgraphs for the kernel library consist of the entire set of subgraphs.
    • You can do maxpooling between layers of graphs, to shrink the higher layers.
    • Equivariant graphs are data efficient. In some sense, data efficiency is equivalent to accuracy.
    • Spherical gauge symmetric models can be used to detect storms on earth.
    • They did some, but not many exotic manifolds.
    • Most exciting work is for molecule property prediction, using the 3D roto-translation equivariant attention networks.
• W. Wu et al: PointConv: Deep Convolutional Networks on 3D Point Clouds