Projective Random Sketching and Relational Manifold Recovery in Dense Sentence Embeddings

Semantic search systems represent every text as a long list of numbers called an embedding. These vectors can consume substantial memory and become expensive to store and search, especially on phones, edge devices, and large servers.

This paper shows that embeddings can be compressed to just a few dozen dimensions while still preserving a substantial ability to determine whether two texts belong to the same topic.

Public experiment: 1,000 texts, 4 topics, using MiniLM embeddings with 384 dimensions.

• Full vector (384 dimensions): ~93% same-topic neighbors
• Compressed vector (32 dimensions): ~74%
• Memory reduction: ~92%
• Random chance: 25%

The full embedding is still better—the compression is not magic. The important result is that a large fraction of the useful semantic information survives aggressive dimensionality reduction, at a fraction of the original memory cost.

This could be useful for faster semantic search, smaller vector indexes, on-device AI, edge applications, RAG retrieval, and lower-cost text-matching systems.