Theory

Pipeline showing atoms converted to smooth density, symmetrized via Haar integration, and projected to invariant features

Atom-Density Representations for Machine Learning

Introduces a Dirac notation formalism for atomic environments that unifies SOAP power spectra, Behler-Parrinello symmetry functions, and other density-based structural representations under a single theoretical framework.

Machine Learning

Three-panel diagram showing symmetry group decomposition, equivariant mapping from world states to representations, and block-diagonal disentangled decomposition

Defining Disentangled Representations via Group Theory

Proposes the first principled mathematical definition of disentangled representations by connecting symmetry group decompositions to independent subspaces in a representation’s vector space.