Geometric Signatures of Conceptual Reorganization: A Counterfactual Embedding Framework for Detecting Scientific Revolutions
Abstract
We introduce document embedding geometry as a quantitative observable of conceptual reorganization and develop a counterfactual ablation framework for measuring how individual concepts influence the organization of scientific knowledge, providing a quantitative framework for detecting scientific revolutions. The observable is defined by the geometric perturbation induced when removing documents associated with a candidate concept from the embedding space before and after its historical emergence. Statistical validation is performed using five historical case studies spanning physics, mathematics, and machine learning: special relativity, Gödel's incompleteness theorems, the Higgs mechanism, deep learning, and the attention mechanism underlying transformer architectures. Across the historical case studies, the framework identifies measurable geometric signatures associated with conceptual reorganization, while the validation studies expose important limitations arising from document assignment and sparse historical data. These results establish embedding geometry as a medium for quantifying conceptual reorganization, providing a new approach for studying how scientific fields restructure over time.
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BibTeX
@misc{ntounis2026geometric,
title = {{Geometric Signatures of Conceptual Reorganization: A Counterfactual Embedding Framework for Detecting Scientific Revolutions}},
author = {Dimitris Ntounis and Ariel Schwartzman and Chris Chafe and Thomas A. Ryckman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14917},
eprint = {2609.14917},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14917},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometric Signatures of Conceptual Reorganization: A Counterfactual Embedding Framework for Detecting Scientific Revolutions
AU - Dimitris Ntounis
AU - Ariel Schwartzman
AU - Chris Chafe
AU - Thomas A. Ryckman
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.14917
UR - https://arxiv.org/abs/2609.14917
AB - We introduce document embedding geometry as a quantitative observable of conceptual reorganization and develop a counterfactual ablation framework for measuring how individual concepts influence the organization of scientific knowledge, providing a quantitative framework for detecting scientific revolutions. The observable is defined by the geometric perturbation induced when removing documents associated with a candidate concept from the embedding space before and after its historical emergence. Statistical validation is performed using five historical case studies spanning physics, mathematics, and machine learning: special relativity, Gödel's incompleteness theorems, the Higgs mechanism, deep learning, and the attention mechanism underlying transformer architectures. Across the historical case studies, the framework identifies measurable geometric signatures associated with conceptual reorganization, while the validation studies expose important limitations arising from document assignment and sparse historical data. These results establish embedding geometry as a medium for quantifying conceptual reorganization, providing a new approach for studying how scientific fields restructure over time.
ER -