Matryoshka Representation Learning: Mathematical Foundations, Nested Subspace Optimization, and Adaptive Dimension Truncation in Modern Embedding Systems
In modern deep learning systems, embedding vectors serve as the foundational intermediate representation for search, recommendation, retrieval-augmented generation (RAG), and zero-shot classification. Historically, these representations have been rigid: a model trained to produce 1536-dimensional or 2048-dimensional vectors outputs a fixed-width array for every input. Downstream systems must ingest, store, index, and compute distance metrics across the entire dimensional width, regardless of whe









