Semantic Substrate Theory: An Operator-Theoretic Framework for Geometric Semantic Drift
This foundational theory addresses the problem of fragmented semantic drift analysis for researchers in natural language processing and machine learning, but it is incremental as it builds on existing concepts without empirical validation.
The paper tackles the lack of a unified theory for semantic drift by proposing a formal framework that combines embedding geometry with local diffusion, introducing measures like node-level neighborhood drift and bridge mass to predict future rewiring.
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.