Platonic Projection Structures: Operator-Induced Observability in Representation Learning
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 $(H, Π, O)$, where $H$ is a latent representation space, $Π\succeq 0$ is an observation operator, and $O(v)=\langle v,Πv\rangle$ defines an induced scalar observable. Observability is characterized by the quotient geometry $H/\ker(Π)$, representing ...
| Authors | Kazuo Ishii, Bishnu Prasad Gautam, Jieling Wu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 6 July 2026 |
| Last updated at source | 14 October 2026 |
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