A1408
Title: Geometry-aware semantic complexity indices for legal texts in transformer embedding spaces
Authors: Marco Ortu - University of Cagliari (Italy) [presenting]
Luca Frigau - University of Cagliari (Italy)
Giulia Contu - University of Cagliari (Italy)
Francesco Mola - University of Cagliari (Italy)
Abstract: A geometry-aware statistical framework for constructing Semantic Complexity indices from transformer-based sentence embeddings is proposed. The motivation is that common operations on embeddings, including variance, centroid distance and k-means clustering, implicitly assume Euclidean geometry, although contextual embedding spaces are typically anisotropic and concentrated around lower-dimensional curved structures. Within this framework, a Legal Semantic Complexity Index is defined as a geometric functional combining centroid dispersion, inter-centroid separation, Semantic coherence, conceptual density and lexical ambiguity. The same components can be extended to a Legislative Quality Index when external interpretive feedback is available over time. The methodological contribution is the comparison of alternative geometries for high-dimensional Semantic representations. Euclidean, spherical and manifold-based formulations of the Index are considered, and their effects on Complexity scores, article clustering and stability are assessed. An empirical study uses a corpus of approximately 7500 articles of Italian codified law extracted from Akoma Ntoso documents and embedded with a domain-specific Legal transformer model. The analysis examines the distributional and geometric structure of the embedding space, quantifies the sensitivity of the proposed indices to metric choice, and evaluates the robustness of Semantic clusters across geometric representations.
