The 3D Word Embedding Galaxy
Cosine similarity geometry and semantic vector arithmetic (King - Man + Woman = Queen).
What is The 3D Word Embedding Galaxy?
Word Embeddings are dense multi-dimensional vector representations of words learned by natural language processing models (such as Word2Vec, GloVe, and FastText). By mapping words into a geometric coordinate galaxy where semantic distance correlates with conceptual similarity, it enables algebraic reasoning over language, famously demonstrated by vector arithmetic: King - Man + Woman = Queen.
How the Interactive Simulation Works
Navigate a 3D galaxy of semantic vectors and test geometric vector offsets across concepts, antonyms, and analogies.
Mathematical Formulation & Computational Complexity
The simulation dynamically resolves the state transition function given by:
Cosine similarity between dense $D$-dimensional word vectors executes in $\mathcal{O}(D)$ operations per pair, while project-wide nearest neighbor queries operate at $\mathcal{O}(V \cdot D)$ for vocabulary $V$. Linear vector arithmetic demonstrates how geometric semantic vectors capture analogies such as $\vec{v}_{\text{king}} - \vec{v}_{\text{man}} + \vec{v}_{\text{woman}} \approx \vec{v}_{\text{queen}}$.
Industrial AI & Real-World Engineering Applications
Dense vector retrieval matching user natural language queries with enterprise knowledge documents.
Aligning vector spaces across different human languages to perform zero-shot translation lookup.
Grouping contract provisions by conceptual similarity rather than literal keyword matching.