# Semantic Substrate Dynamics Theory: An Operator-Theoretic Framework for Geometric Semantic Drift

arXiv: https://arxiv.org/abs/2602.18699 · HTML: https://mlsanity.com/paper/2602.18699/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 21 Feb 2026.

## Builds on (most cited first, 6 of 6)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Diachronic Word Embeddings Reveal Statistical Laws of Semantic Change](https://mlsanity.com/paper/1605.09096/) (2016)
- [SemEval-2020 Task 1: Unsupervised Lexical Semantic Change Detection](https://mlsanity.com/paper/2007.11464/) (2020)
- [Diachronic word embeddings and semantic shifts: a survey](https://mlsanity.com/paper/1806.03537/) (2018)
- [Analysing Lexical Semantic Change with Contextualised Word Representations](https://mlsanity.com/paper/2004.14118/) (2020)
- [Dynamic Word Embeddings](https://mlsanity.com/paper/1702.08359/) (2017)

## Abstract (arXiv)

Studies of semantic drift report heterogeneous signals, including embedding displacement, neighbor change, distributional divergence, and recursive trajectory instability, without a shared account that relates them. Semantic Substrate Dynamics Theory (SSDT) treats these signals as observables of one time-indexed substrate, St = (X, dt, Pt), that couples embedding geometry to a local diffusion kernel. The contribution is commensurability with a mechanism layer: the substrate separates within-basin churn from basin crossing, recursion-induced instability, and intervention-order effects, distinctions that a single detection score does not recover. Coarse Ricci curvature functions as a dense structural descriptor of basin and bridge geometry across the graph, and bridge mass, a node-level aggregate of incident negative curvature, functions as a sparse descriptor of the genuine bridge structure that is typically uncommon in embedding graphs. For recursive generation, node displacement relative to an origin decomposes into a radial component and a tangential component, which separates bounded departure from continuing reinterpretation. The predictions are stated in falsifiable form with a pre-declared rejection rule, and the predicted leading indicator of future rewiring is a local density statistic rather than the curvature aggregate. This manuscript provides the formal model, the assumptions, the observable roles, and the test contracts; empirical performance is deferred.