{"ID":5937025,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-09T14:49:40.386444797Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.05175","arxiv_id":"2607.05175","title":"Platonic Projection Structures: Operator-Induced Observability in Representation Learning","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 $(H, Π, O)$, 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 equivalence classes of latent states indistinguishable under observation. We show that quantum measurement and representation inference under linear observation models share this operator-theoretic structure while differing in the algebraic properties of their observation operators; the correspondence is structural rather than physical. Representation transfer and knowledge distillation can likewise be interpreted as approximate preservation of observable geometry through $ΦΠ_T \\approx Π_S Φ$. PPS also reveals a structural limitation of output-based interpretability: latent components in $\\ker(Π)$ are inaccessible from induced observables, imposing intrinsic constraints on attribution and explanation methods. Controlled empirical validations demonstrate kernel-invariant observability, projection-induced attribution gaps, and rank-controlled observable geometry in latent representation spaces. PPS thus provides an explicit characterization of observability through operator-induced quotient geometry and a unified perspective on representation accessibility, interpretability, and projection-mediated inference.","short_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 thr...","url_abs":"https://arxiv.org/abs/2607.05175","url_pdf":"https://arxiv.org/pdf/2607.05175v1","authors":"[\"Kazuo Ishii\",\"Bishnu Prasad Gautam\",\"Jieling Wu\",\"Javaid Saher\"]","published":"2026-07-06T14:57:26Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}