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[2602.18699] Semantic Substrate Theory: An Operator-Theoretic Framework for Geometric Semantic Drift
Summary
This paper introduces Semantic Substrate Theory, an operator-theoretic framework that formalizes various signals of semantic drift, integrating embedding geometry and local diffusion to enhance understanding of neighborhood changes in semantic networks.
Why It Matters
Understanding semantic drift is crucial for advancing machine learning models, particularly in natural language processing and AI. This framework aims to unify disparate signals into a coherent theory, potentially improving model stability and performance in dynamic environments.
Key Takeaways
- Proposes a unified framework for analyzing semantic drift signals.
- Introduces 'bridge mass' as a predictor for neighborhood rewiring.
- Combines embedding geometry with local diffusion for enhanced analysis.
- Specifies formal models and assumptions that can be empirically tested.
- Sets the stage for future studies to validate the proposed theory.
Computer Science > Computation and Language arXiv:2602.18699 (cs) [Submitted on 21 Feb 2026] Title:Semantic Substrate Theory: An Operator-Theoretic Framework for Geometric Semantic Drift Authors:Stephen Russell View a PDF of the paper titled Semantic Substrate Theory: An Operator-Theoretic Framework for Geometric Semantic Drift, by Stephen Russell View PDF HTML (experimental) Abstract:Most semantic drift studies report multiple signals e.g., embedding displacement, neighbor changes, distributional divergence, and recursive trajectory instability, without a shared explanatory theory that relates them. This paper proposes a formalization of these signals in one time-indexed substrate, $S_t=(X,d_t,P_t)$, combining embedding geometry with local diffusion. Within this substrate, node-level neighborhood drift measures changes in local conditional distributions, coarse Ricci curvature measures local contractivity of semantic diffusion, and recursive drift probes stability of iterated semantic operators. This manuscript specifies the formal model, assumptions, and tests that can refute the model. Herein, the paper introduces bridge mass, a node-level aggregate of incident negative curvature, as a predictor of future neighborhood rewiring. This paper provides the theory and test contracts; empirical performance is deferred to subsequent studies. Subjects: Computation and Language (cs.CL); Artificial Intelligence (cs.AI) Cite as: arXiv:2602.18699 [cs.CL] (or arXiv:2602.18699v1 [cs...
