Interactive Demo: Word Vectors in Linear Algebra

Word Prediction as Vector Geometry

A Linear Algebra Demo on Word Similarity

In modern AI, words are represented as numerical vectors. This interactive tool demonstrates how linear algebra, specifically cosine similarity, is used to measure how "close" two words are. A high similarity score suggests a strong contextual relationship.

How to use this demo:

The network graph shows the selected word (in blue) and its most closely related words.
The thickness and label of a line indicate the cosine similarity score.
Click an edge to see the detailed math calculation below.
Click any other node to make it the new center of the graph.
Double-click the background to reset the view if you get lost.

How does this work? The Linear Algebra inside AI.

1. Word Embeddings (Vectors): Large Language Models (LLMs) learn a "word embedding," which is a mapping of every word to a high-dimensional vector. Here, we use simple 3D vectors for demonstration. Words with similar meanings are placed near each other in this vector space.

2. Cosine Similarity: To measure the "similarity" between two word vectors, we calculate the cosine of the angle ($ \theta $) between them. $$ \cos(\theta) = \frac{\vec{a} \cdot \vec{b}}{\|\vec{a}\| \|\vec{b}\|} $$ A smaller angle results in a cosine similarity closer to 1 (highly similar).