AI Embeddings Dimension Explorer

Dimensions are the length of the vector that represents a piece of text. A 1536-dimensional embedding is a list of 1536 floating-point numbers. More dimensions generally capture more semantic nuance, but require more storage and computation. The optimal dimensionality depends on your task — for simple similarity search, 384–512 dims often performs as well as 1536+ dims.

Cosine similarity measures the angle between two vectors, not their magnitude. It ranges from -1 (opposite meaning) to 1 (identical meaning), with 0 meaning unrelated. It's the standard metric for semantic search because it's scale-invariant — the absolute values of the numbers don't matter, only their relative proportions.

float32 stores each dimension as a 4-byte number (32-bit precision). float16 uses 2 bytes (16-bit), halving storage at minor precision loss. int8 quantization uses 1 byte — 75% smaller than float32. For production RAG systems with millions of vectors, quantization can reduce RAM/disk costs by 2–4× with negligible quality impact on most retrieval tasks.

text-embedding-3-small is OpenAI's newer model that outperforms ada-002 on MTEB benchmarks while costing 5× less ($0.02 vs $0.10 per 1M tokens). It also supports dimension reduction — you can truncate to 512 or 1024 dims for lower storage without retraining, a feature ada-002 lacks. For new projects, prefer text-embedding-3-small or text-embedding-3-large.

Use local models (nomic-embed-text, all-MiniLM-L6-v2, BGE-large) when: (1) data privacy requires no external API calls, (2) you need zero per-token cost at scale, (3) latency requirements are strict and network round-trips matter. Trade-offs: you manage GPU/CPU infrastructure, and quality is generally slightly below top cloud models.

MRL is the technique behind text-embedding-3-small and text-embedding-3-large's configurable dimensions. The model is trained such that the first N dimensions of the full embedding are still semantically meaningful — you can truncate to any supported dimension without losing proportional quality. This enables storage/quality tradeoffs without re-embedding your corpus.