提出几何语义漂移的统一理论框架,解析嵌入空间动态变化机制。
Semantic Substrate Dynamics Theory: An Operator-Theoretic Framework for Geometric Semantic Drift
- 用时序底物模型分离语义漂移中的局部扰动与跨域跃迁
- 通过曲率与桥质量指标刻画基域与连接结构的几何特性
- 适用于研究生成模型迭代过程中的语义演化规律
现有语义漂移研究呈现嵌入位移、邻域变化、分布偏移和递归轨迹不稳等异质信号,缺乏统一解释。本文提出语义底物动力学理论(SSDT),将这些信号视为一个时序底物 St = (X, dt, Pt) 的可观测量,该底物将嵌入几何与局部扩散核耦合。底物可区分域内扰动、域间穿越、递归不稳定性及干预顺序效应,而单一检测评分无法恢复此类差异。粗略里奇曲率作为密集结构描述符,刻画图中基域与桥接结构的几何特征;桥质量为节点级负曲率聚合量,是罕见但真实的桥结构稀疏描述符。在递归生成中,节点相对于原点的位移可分解为径向分量与切向分量,从而分离有限偏离与持续重释。理论预测以可证伪形式给出,并预设拒绝规则:未来重连的首要指示器是局部密度统计,而非曲率聚合量。本文提供形式化模型、假设、可观测角色与测试契约,实证性能留待后续验证。
原文摘要 · Abstract (English)
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.
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