arXiv:2607.05175v1 Announce Type: new Abstract: We characterize observability in representation learning through Platonic Projection Structures (PPS), an operator-theoretic framework for analyzing representation accessibility under partial observation. Rather than treating observable outputs as direct reflections of latent representations, PPS models observation through a self-adjoint positive semidefinite operator acting on a latent representation space. A system is represented as a triple $(H, \Pi, O)$, where $H$ is a latent representation space, $\Pi \succeq 0$ is an observation operator, a
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Read at arXiv cs.LG