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anisotropy baseline

An anisotropy baseline is a reference measurement used in natural language processing and representation learning to quantify and correct for the inherent directional bias present in an embedding space. In many neural language models, vector representations are anisotropic, meaning they cluster tightly within a narrow cone rather than dispersing uniformly in all directions, which causes unrelated words or tokens to exhibit artificially high similarity scores. The anisotropy baseline establishes the expected background similarity, commonly computed as the average cosine similarity or dominant variance across pairs of randomly sampled word representations in a given model layer. By subtracting or normalizing against this baseline, researchers and practitioners can isolate genuine contextual or semantic similarity from the structural geometric distortions of the vector space.

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How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings

How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings

Kawin Ethayarajh

OrganizationsStanford University

Why you should read this

Reveals the geometric behavior of BERT, ELMo, and GPT-2 embeddings across layers, proving that upper layers generate more context-specific representations while static word vectors account for less than five percent of their variance.

Replacing static word embeddings with contextualized word representations has yielded significant improvements on many NLP tasks. However, just how contextual are the contextualized representations produced by models such as ELMo and BERT? Are there infinitely many context-specific representations for each word, or are words essentially assigned one of a finite number of word-sense representations? For one, we find that the contextualized representations of all words are not isotropic in any layer of the contextualizing model. While representations of the same word in different contexts still have a greater cosine similarity than those of two different words, this self-similarity is much lower in upper layers. This suggests that upper layers of contextualizing models produce more context-specific representations, much like how upper layers of LSTMs produce more task-specific representations. In all layers of ELMo, BERT, and GPT-2, on average, less than 5% of the variance in a word's contextualized representations can be explained by a static embedding for that word, providing some justification for the success of contextualized representations.

Added

2026-09-25