Why it matters

Sparse retrieval complements dense. Understanding shapes design.

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The architecture

BM25: tf-idf variant score.

SPLADE: learned sparse via MLM head.

Sparse retrieval spectrumBM25lexical tf-idf variantSPLADElearned sparseComplement densehybrid RRFElasticsearch + OpenSearch + custom for BM25; SPLADE via learned model
Sparse retrieval math.
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How it works end to end

BM25 formula tf * idf with saturation.

SPLADE learned via MLM.

Inverted indexes for scale.