Semantic Substrate Theory: An Operator-Theoretic Framework for Geometric Semantic Drift
arXiv:2602.18699v1 Announce Type: new 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
arXiv:2602.18699v1 Announce Type: new 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.
Executive Summary
This paper introduces Semantic Substrate Theory, a novel operator-theoretic framework that unifies various signals of semantic drift in a single, time-indexed substrate. The proposed framework combines embedding geometry with local diffusion, enabling the measurement of node-level neighborhood drift, coarse Ricci curvature, and recursive drift. The authors also introduce the concept of bridge mass as a predictor of future neighborhood rewiring. While the model provides a comprehensive theory and test contracts, empirical performance is left for subsequent studies.
Key Points
- ▸ Semantic Substrate Theory integrates multiple signals of semantic drift into a unified framework.
- ▸ The theory combines embedding geometry with local diffusion to measure node-level neighborhood drift and coarse Ricci curvature.
- ▸ Recursive drift stability is probed through iterated semantic operators.
Merits
Strength of Integrative Approach
The proposed framework brings together disparate signals of semantic drift, providing a unified explanation for complex phenomena.
Precision of Model Components
The combination of embedding geometry and local diffusion enables precise measurement of node-level neighborhood drift and coarse Ricci curvature.
Demerits
Limited Empirical Support
The paper defers empirical performance to subsequent studies, leaving the robustness of the theory in question.
Expert Commentary
While the Semantic Substrate Theory offers a promising approach to understanding semantic drift, its limitations in empirical support and potential applications in specific domains require further investigation. Nevertheless, the theory's potential to integrate disparate signals of semantic drift and provide a unified explanation for complex phenomena makes it an important contribution to the field. Future studies should prioritize the development of empirical support and applications in various domains to fully realize the theory's potential.
Recommendations
- ✓ Future studies should prioritize empirical validation of the theory and framework, focusing on real-world applications and datasets.
- ✓ Researchers should explore the potential applications of the theory in various domains, including natural language processing, computer vision, and data governance.