CSMs Explain Emergent Discrete Semantic Ontologies
In a Dec. 4, 2025 preprint, C. M. Wyss formalizes large language models as Continuous State Machines and defines a transfer operator P whose compactness yields a discrete spectrum. The paper proves the Semantic Characterization Theorem: leading eigenfunctions induce finitely many spectral basins definable in an o-minimal structure, and extends results to stochastic and adiabatic kernels, explaining how discrete symbolic semantics emerge from continuous activations.
Key Points
- 1Formalizes LLMs as Continuous State Machines with compact transfer operator and discrete spectrum
- 2Proves Semantic Characterization Theorem linking leading eigenfunctions to finitely many invariant spectral basins
- 3Shows discrete, logically interpretable ontologies emerge from continuous activations, aiding model interpretability
Scoring Rationale
Formal theoretical advance with broad relevance; limited immediate practical application and single preprint source restricts near-term impact.
Sources
Public references used for this report.
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