# Accurate and Efficient Statistical Testing for Word Semantic Breadth

arXiv: https://arxiv.org/abs/2605.08048 · HTML: https://mlsanity.com/paper/2605.08048/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 12 of 12)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [Smarter, Better, Faster, Longer: A Modern Bidirectional Encoder for Fast, Memory Efficient, and Long Context Finetuning and Inference](https://mlsanity.com/paper/2412.13663/) (2024)
- [Analysing Lexical Semantic Change with Contextualised Word Representations](https://mlsanity.com/paper/2004.14118/) (2020)
- [UiO-UvA at SemEval-2020 Task 1: Contextualised Embeddings for Lexical Semantic Change Detection](https://mlsanity.com/paper/2005.00050/) (2020)
- [HyperLex: A Large-Scale Evaluation of Graded Lexical Entailment](https://mlsanity.com/paper/1608.02117/) (2016)
- [A Systematic Comparison of Contextualized Word Embeddings for Lexical Semantic Change](https://mlsanity.com/paper/2402.12011/) (2024)
- [Exact Paired-Permutation Testing for Structured Test Statistics](https://mlsanity.com/paper/2205.01416/) (2022)
- [Unsupervised Word Polysemy Quantification with Multiresolution Grids of Contextual Embeddings](https://mlsanity.com/paper/2003.10224/) (2020)
- [Statistical Uncertainty in Word Embeddings: GloVe-V](https://mlsanity.com/paper/2406.12165/) (2024)
- [Educational Cone Model in Embedding Vector Spaces](https://mlsanity.com/paper/2512.04227/) (2025)
- [Norm of Mean Contextualized Embeddings Determines their Variance](https://mlsanity.com/paper/2409.11253/) (2024)

## Abstract (arXiv)

Measuring the breadth of a word's meaning, or its spread across contexts, has become feasible with contextualized token embeddings. A word type can be represented as a cloud of token vectors, with dispersion-based statistics serving as proxies for contextual diversity (Nagata and Tanaka-Ishii, ACL2025). These measurements are useful for deciding appropriate sense distinctions when constructing thesauri and domain-specific dictionaries. However, when comparing the breadth of two word types, naive hypothesis testing on dispersion can be misleading: differences in semantic direction can masquerade as dispersion differences, inflating Type-I error and yielding "statistically significant" outcomes even when there is no true breadth difference. This is problematic because significance testing should distinguish genuine effects from incidental fluctuations in small-difference regimes. We propose a Householder-aligned permutation test to isolate dispersion differences from directional differences. Our method applies a single Householder reflection to align the mean directions of the two word types and then performs a permutation test on the aligned token clouds, yielding calibrated, non-parametric p-values. For practicality, we introduce a GPU-oriented implementation that batches permutations and linear algebra operations. Empirically, our alignment reduced Type-I error by 32.5% while preserving sensitivity to genuine breadth differences, and achieved a 23x speedup over the CPU baseline.