Symmetries, Equivariance, Group and Representation Theory

Understanding how to treat symmetries in data is therefore essential to artificial intelligence in science if we aspire to gain insight into the intrinsic, objective properties of the physical world, independent of our observational or representational biases. We study examples for equivariance to discrete and continuous symmetry transformations, and describe how the tensor product is used in practice. After that, we try to elucidate the physical and mathematical foundations for the underlying theory, such as symmetry groups, irreducible representations, tensor products, spherical harmonics