发表机构
Stanford University; SLAC National Accelerator Laboratory（斯坦福大学; SLAC国家加速器实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出反事实嵌入框架，通过移除概念相关文档的几何扰动来量化概念重组，并在五个历史案例中验证了其检测科学革命的有效性。
AI 中文摘要
我们引入文档嵌入几何作为概念重组的定量可观测指标，并开发了一个反事实消融框架，用于衡量单个概念如何影响科学知识的组织，从而为检测科学革命提供一个定量框架。该可观测指标定义为：在候选概念历史出现之前和之后，从嵌入空间中移除与该概念相关的文档所引发的几何扰动。我们使用跨越物理学、数学和机器学习的五个历史案例研究进行统计验证：狭义相对论、哥德尔不完备定理、希格斯机制、深度学习以及支撑Transformer架构的注意力机制。在这些历史案例研究中，该框架识别出与概念重组相关的可测量几何特征，而验证研究则揭示了由文档分配和稀疏历史数据引起的重要局限性。这些结果确立了嵌入几何作为量化概念重组的媒介，为研究科学领域如何随时间重构提供了新方法。
英文摘要
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.
Comments22 pages, 13 figures, 5 tables
