# Embedding Geometry: Cosine Similarity, Euclidean Distance, Isotropy and BERTology Findings

> Source: https://sukruyusufkaya.com/en/learn/llm-muhendisligi/embedding-geometry-cosine-isotropy-bertology
> Updated: 2026-05-13T13:00:27.289Z
> Category: LLM Mühendisliği
> Module: Module 7: Embedding Layer — The Vector Space of Meaning
**TLDR:** Topology of embedding vector space: cosine similarity vs Euclidean distance vs dot product (which when, mathematical relationships), isotropy (vectors balanced across directions, Gao 2019 'representation degeneration'), anisotropy problem in BERT/GPT embeddings, mitigation (whitening, normalization). BERTology findings: which information in which layer (Rogers 2020). Practical analysis for Turkish.