Matryoshka vs. PCA: The Old-School Trick That Beats MRL Truncation

Vector databases are the default answer for storing and searching LLM embeddings, but as collections grow, the cost and latency of high-dimensional vectors bite. AI labs pushed Matryoshka Representation Learning (MRL) as the fix: train the model so the first few dimensions carry the most signal, then truncate at inference. It works — but only on models trained for it, and the quality drop at very small dimensions is steep.

Dylan Castillo ran a benchmark that pits MRL truncation against a much older technique: Principal Component Analysis (PCA). The results are a reminder that sometimes the boring, pre-deep-learning tool is the right one.

The experiment

Castillo took two MRL-trained models — OpenAI's text-embedding-3-small (1,536 dims) and Alibaba's qwen3-embedding-8b (4,096 dims) — and reduced their embeddings to 512, 256, 128, 64, and 32 dimensions using both truncation and PCA. He evaluated retrieval quality (NDCG@10) across eight BEIR datasets. He also added text-embedding-ada-002, a non-MRL model, as a control to see if PCA's performance depends on MRL training.

PCA wins at small dimensions

At 512 dimensions, truncation holds a slight edge. But as dimensions shrink, PCA catches up and then pulls ahead. On text-embedding-3-small, PCA retains 65% of quality at 32 dims versus 46% for truncation. On qwen3-embedding-8b, the gap is smaller (71% vs 68%) but still favors PCA. Across datasets, PCA wins on seven of eight for 3-small and six of eight for qwen3 at the smallest sizes.

The control test answered the second question: PCA works just as well on ada-002, which never had MRL training. So the advantage isn't an artifact of MRL's organized embedding space — PCA is a general-purpose shrinker.

The catch: operational complexity

PCA isn't free. You have to fit a projection matrix on a sample of your embeddings, store and version it, and apply the same version consistently when indexing and querying. Out-of-domain PCA — fitting on MS MARCO and reusing everywhere — degrades quality, so you likely need to fit per corpus. That's real overhead, but for a big index it might be worth it.

PCA matched or outperformed MRL truncation at nearly every dimension across both MRL-trained models.

The full code and data are on GitHub, so you can reproduce the numbers and decide for yourself.