Accurate and Efficient Statistical Testing for Word Semantic Breadth

Semantic type mismatch between a noun and its context is central to coercion phenomena. This paper introduces a graph-based method to examine how lexical and contextual type information is reflected in word embeddings. We select nouns from ten semantic types, annotate corpus instances for type matching (matching vs. coercion vs. other mismatch vs. unrestricted), and construct graphs using BERT and sense-enhanced embeddings. Two metrics -- Neighbor Type Probability (NTP) and Neighbor Type Entropy (NTE) -- are proposed to analyze neighborhood type distributions. Results show that graphs constructed with sense-enhanced embeddings reflect semantic type information better, and matching and mismatch sentences can be distinguished through the proposed metrics.

We present LatentDiff, a scalable framework for semantic dataset comparison that operates directly in the latent space of pretrained vision encoders. By combining sparse autoencoder-based divergence testing with density ratio estimation, LatentDiff identifies interpretable semantic differences between datasets at a fraction of the computational cost of caption-based alternatives. We also introduce Noisy-Diff, a benchmark capturing realistic sparse distribution shifts that cause existing methods to struggle. Experiments demonstrate that LatentDiff achieves superior accuracy while remaining robust to settings where an extremely small fraction of images (from 5% to <1% ) differ semantically.

How much meaning does a text carry? Shannon's theory measures uncertainty over symbols and is intentionally indifferent to meaning, while pairwise metrics such as BERTScore compare two texts rather than characterizing one. We develop a geometric framework that measures semantic content from the structure of a text's sentence embeddings. The framework has three parts. First, within a fixed embedding and baseline, six natural axioms uniquely determine a scalar measure up to scale, a frame-conditional uniqueness theorem. The resulting scalar is empirically too coarse, motivating a richer representation. Second, we propose a three-coordinate semantic profile capturing novelty (displacement from generic discourse), breadth (diversity of distinct ideas), and integration (connectedness among them), together with a discrete minimal unit (the semantic quantum) whose resolution is fixed by a clustering threshold $τ$. Third, we prove a no-go theorem: no scalar summary of the profile can simultaneously satisfy analytic stability under paraphrase and concatenation, ordinal robustness across text scales, and cross-representation comparability. We exhibit two practical scalars, $S_{\mathrm{minmax}}$ and $S_{\mathrm{rank}}$, each occupying a distinct corner of this trade-off triangle. Validation across 23 synthetic categories, 5 Project Gutenberg novels, and 3 embedding models confirms the trade-off. The recommended rank-normalized configuration passes 25 of 28 ordinal checks as point estimates (21 of 28 after Benjamini-Hochberg correction), outperforming seven baselines including unigram entropy and a BERTScore-based novelty signal. A separate variational result connects the breadth coordinate to the log-determinant of a determinantal point process (Spearman $ρ= 0.985$ over 507 Gutenberg chapters), giving an optimization-theoretic foundation for breadth.