Information Routing in Atomistic Foundation Models: How Equivariance Creates Linearly Disentangled Representations

Researchers introduce Composition Projection Decomposition (CPD) to analyze how atomistic foundation models organize information in their representations. The study finds that tensor product equivariant architectures like MACE create linearly disentangled representations where geometric information is easily accessible, while handcrafted descriptors entangle information nonlinearly.