Platonic Projection Structures: Operator-Induced Observability in Representation Learning
Platonic Projection Structures (PPS) is an operator-theoretic framework characterizing observability in representation learning. It models observation via a self-adjoint positive semidefinite operator ($\Pi$) acting on latent states, defining observables as $\langle v, \Pi v\rangle$. This structure unifies quantum measurement and deep learning inference. The key finding is that latent components in the kernel of $\Pi$ are structurally inaccessible from induced observables.