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Visual Guides/Embeddings: Words as Numbers in Space
LLMs

Embeddings: Words as Numbers in Space

Explore a hand-built word embedding space. Click words, try arithmetic like king − man + woman ≈ queen, and see how meaning emerges from geometry. Every similarity number on this page is computed live from the vectors shown.

Exploration ProgressClick a word · Try word arithmetic

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1The Word Space

Click any word to select it and see its nearest neighbors.

This is a hand-built illustration: 18 words with 16-dimensional vectors we constructed from named features (plus a little noise), shown through a fixed 2D projection. The arithmetic on these vectors is real, and every number below is computed from them at runtime. Real embeddings are learned from data instead of built by hand, and use hundreds to thousands of dimensions.

kingqueenmanwomanboygirlparisberlintokyofrancegermanyjapandogwolfcatcartruckbus
Royalty
Person
City
Country
Animal
Vehicle

2Word Arithmetic

Adding and subtracting word vectors moves you along meaningful directions in the space. The result below is found by computing the vector, then searching the vocabulary for its nearest neighbor.

As in classic word2vec analogy lookups, the three input words are excluded from the candidate list. In real embedding spaces an input word is often the closest vector to the raw result, so the standard evaluation drops the inputs; we follow the same rule here.

Select an example above to see the vector operation visualized on the word space.

3Inside the Vectors

These are the actual 16-dimensional vectors behind two words in the plot above. Our toy dimensions have names only because we built them by hand.

paris→[0.00, 0.00, 0.00, 0.00, 1.00, 1.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, -0.03, -0.07]
humanroyalfemaleyoungplacecapitalfrancegermanyjapananimalcaninedomesticvehiclesizenoise-1noise-2
berlin→[0.00, 0.00, 0.00, 0.00, 1.00, 1.00, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.05, 0.03]
humanroyalfemaleyoungplacecapitalfrancegermanyjapananimalcaninedomesticvehiclesizenoise-1noise-2

Paris and Berlin share the place and capital features, so their bars mostly line up; they differ on the country dimensions. That overlap is exactly why their cosine similarity is 0.66.

One important difference from real systems: our dimensions are individually readable because we chose the features ourselves. Real embedding models learn vectors with 768 to 1536 dimensions from data, and those dimensions are generally not interpretable one at a time. Meaning lives in directions and in the relative geometry of the space as a whole, not in any single coordinate.

4Why Embeddings Matter

Embeddings are the foundation of modern NLP applications.

🔍Semantic Search

Find documents by meaning, not just keywords. "best running shoes" matches "top jogging footwear" because their embeddings are close.

🎯Recommendations

Items close in embedding space are similar. If you liked article A, articles near A's embedding are surfaced next.

🌐Translation

Languages share embedding structure. "dog" in English and "chien" in French sit in the same region of multilingual space.

★

Key Insight

Modern LLMs use contextual embeddings: the same word gets a different vector depending on its context, so “bank” in “river bank” and “savings bank” are represented differently, letting the model handle polysemy. Contextual embeddings actually predate transformer language models: ELMo (2018) produced them with bidirectional LSTMs. Transformer models like BERT and GPT then made them the dominant approach, replacing static embeddings like word2vec, where each word has one fixed vector like in our toy space above.

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