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A real deployment would use an approximate index, apply its own compression, rescore with full-precision vectors, and often mix in BM25 and a reranker
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Honey, I shrunk the embeddings: Matryoshka vs. PCA – Dylan Castillo

https://dylancastillo.co/posts/matryoshka-vs-pca
But Doug Turnbull’s article about using Principal Component Analysis (PCA), to reduce vector dimensions made me curious: how would this older, simpler technique compare with MRL