Subspace Approximation
Subspace approximation is a fine-tuning technique for retrieval-augmented generation (RAG) embeddings that builds on Matryoshka methods. The core principle involves training embedding models to preserve meaningful information across nested dimensional subspaces, enabling a single model to produce effective representations at varying dimensionality levels. This approach reduces the need to maintain multiple embedding models for different computational or memory constraints.
How It Works
During training, embeddings are optimized so that lower-dimensional projections—obtained by truncating the full embedding vector—retain semantic quality. This means that a 768-dimensional embedding can be meaningfully reduced to 256 or 128 dimensions while preserving the relationships between documents needed for effective retrieval. The technique treats each dimensional level as a valid representation rather than a degradation of the full embedding.
Practical Benefits
Subspace approximation offers practical advantages in RAG systems by allowing flexible deployment. Applications can adjust embedding dimensionality based on latency requirements, memory availability, or computational resources without retraining. This is particularly valuable in resource-constrained environments or when serving queries with varying performance budgets, as lower-dimensional embeddings provide faster similarity computations while maintaining reasonable retrieval quality.