Group invariant machine learning by fundamental domain projections
This addresses the challenge of incorporating symmetry constraints in machine learning for applications like physics and geometry, offering a unified framework, though it appears incremental as it builds on existing intrinsic approaches.
The paper tackles the problem of supervised group invariant and equivariant machine learning by introducing a pre-processing step that projects input data into a geometric space representing symmetry group orbits, allowing use with arbitrary models. It reports improvements in accuracy on example problems, including predicting Hodge numbers of CICY matrices, compared to existing methods.
We approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using a pre-processing step, which involves projecting the input data into a geometric space which parametrises the orbits of the symmetry group. This new data can then be the input for an arbitrary machine learning model (neural network, random forest, support-vector machine etc). We give an algorithm to compute the geometric projection, which is efficient to implement, and we illustrate our approach on some example machine learning problems (including the well-studied problem of predicting Hodge numbers of CICY matrices), in each case finding an improvement in accuracy versus others in the literature. The geometric topology viewpoint also allows us to give a unified description of so-called intrinsic approaches to group equivariant machine learning, which encompasses many other approaches in the literature.