What Are BM25 and SPLADE? Sparse Learned Retrieval Explained

What Are BM25 and SPLADE?

BM25 (Best Match 25) is a probabilistic sparse retrieval algorithm that has been the dominant document ranking method in search engines for over two decades. It scores documents based on the frequency of query terms in the document, adjusted for document length and the rarity of the term across the corpus. Elasticsearch, OpenSearch, Apache Solr, and most search engines use BM25 as their default scoring function.

SPLADE (Sparse Learned Retrieval via BERT) extends sparse retrieval by using a BERT-based language model to expand the document's term representation to include related vocabulary from the full tokeniser vocabulary. This solves BM25's primary weakness: vocabulary mismatch, where a query uses different words than the relevant document and BM25 scores the document at zero.

Both BM25 and SPLADE produce sparse vectors: vectors where the vast majority of dimensions are zero. Only terms that appear in the document (BM25) or are predicted to be related to the document's content (SPLADE) have non-zero values. This makes sparse retrieval fast via inverted index lookup and interpretable: you can see exactly which terms drove the relevance score.

How BM25 and SPLADE Affect AI Search Coverage

BM25 is not dead in the AI search era. Many AI search systems use sparse retrieval as a first-stage retriever precisely because it is fast and handles exact term queries reliably. SPLADE is increasingly deployed for first-stage retrieval in sophisticated pipelines.

• Exact terminology still matters: For product names, brand names, technical terms, and proper nouns, BM25 remains highly effective. Content that includes the exact terminology users search for will score well in the sparse retrieval component of a hybrid system.
• Semantic variation improves dense retrieval coverage: Using synonyms, related terms, and paraphrases throughout the content improves performance in the dense retrieval component. This aligns with good content writing practice: covering a topic thoroughly naturally introduces vocabulary variation.
• BM25 penalises keyword stuffing: The TF saturation and length normalisation in BM25 mean that repeating a keyword 20 times in a short document produces a worse score than naturally integrating the term in a comprehensive document. BM25's design directly discourages keyword stuffing.
• SPLADE expansion benefits content about common topics: If your content covers well-established topics (machine learning, SEO, marketing), SPLADE's expansion will reach queries that use the standard vocabulary of that topic, even if your content does not use every specific term.
• AI search systems combine signals: Optimising for AI search means producing content that performs well in both sparse and dense retrieval — precise in terminology and rich in semantic variation.

BM25 Explained

BM25 computes a relevance score for each document given a query by summing three components for each query term: how often the term appears in the document (TF), how rare the term is across all documents (IDF), and a normalisation for document length.

The key innovation over simple TF-IDF is TF saturation, controlled by parameter k1 (typically 1.2 to 2.0). In TF-IDF, a document with 10 occurrences of a query term scores 10x higher than one with 1 occurrence. In BM25, the saturation curve means 10 occurrences scores only about 2-3x higher. This prevents short but highly repetitive documents from outranking longer, more comprehensive documents that mention the query term naturally.

Document length normalisation, controlled by parameter b (typically 0.75), penalises long documents relative to short ones for the same term frequency. A short document mentioning "machine learning" three times is considered more focused on that topic than a 10,000-word article that also mentions it three times. Setting b=0 disables length normalisation; setting b=1 applies full normalisation.

BM25 retrieval is implemented as an inverted index lookup: for each query term, the index directly returns the list of documents containing that term with their pre-computed statistics. Scoring is computed only for documents that contain at least one query term. This makes BM25 retrieval much faster than dense vector search for high-recall scenarios at low latency, which is why it remains the baseline for first-stage retrieval in many hybrid systems.

BM25's Limitations

BM25's fundamental limitation is that it requires exact or near-exact term overlap between query and document. If a query uses the term "car" and the relevant document only uses "automobile" and "vehicle", BM25 scores that document at zero. This vocabulary mismatch problem is the primary driver for combining BM25 with semantic (dense) retrieval.

BM25 also has no understanding of term relationships. The query "not broken" is scored identically to "broken" for BM25 because it sums individual term frequencies without understanding negation. Dense embedding models handle negation and other linguistic structures through the contextual representations produced by transformer encoders.

Despite these limitations, BM25 outperforms many neural retrieval approaches for highly specific queries with rare, exact terminology. A query for a precise product code or technical identifier is better served by exact match scoring than by semantic approximation. This complementarity is why hybrid retrieval systems combining BM25 and dense retrieval consistently outperform either approach alone.

SPLADE: Learned Sparse Retrieval

SPLADE addresses vocabulary mismatch by using a BERT model with a masked language model (MLM) head to produce sparse vectors over the full tokeniser vocabulary. Rather than only assigning weights to terms that appear verbatim in the document, SPLADE produces weights for terms that BERT predicts are contextually related to the document's content.

For a document discussing "search engine ranking algorithms", SPLADE might assign non-zero weights to "information retrieval", "relevance scoring", "query processing", and "web index", in addition to the terms explicitly in the document. These expansions allow SPLADE to match queries that use this related vocabulary, eliminating the vocabulary mismatch that would defeat BM25.

Critically, SPLADE vectors remain sparse. Most of the vocabulary dimensions are zero. This means SPLADE vectors can still be used with inverted indexes for efficient retrieval, unlike dense vectors which require approximate nearest neighbour search. The sparsity is enforced through a regularisation term in the SPLADE training loss that penalises non-zero dimensions.

SPLADE-v2 and subsequent variants (DistilSPLADE, SPLADE-v3) have achieved performance on BEIR (Benchmark for Information Retrieval) competitive with or exceeding dense retrieval models, while maintaining the interpretability and inverted-index compatibility of sparse vectors.

Sparse vs Dense Retrieval

Sparse retrieval (BM25, SPLADE) and dense retrieval (bi-encoder embeddings) have complementary strengths. Sparse retrieval excels at exact term matching, rare terminology, and product-specific queries. Dense retrieval excels at paraphrasing, semantic similarity, and cross-lingual matching.

Head-to-head benchmarks consistently show that neither approach dominates the other across all query types. Dense retrieval outperforms BM25 significantly on out-of-domain data where terminology varies. BM25 outperforms dense retrieval on datasets with precise technical queries where exact term matching is critical.

This complementarity is why production AI search systems nearly always use both: dense retrieval for semantic coverage, sparse retrieval for exact match precision, and Reciprocal Rank Fusion to merge the two ranked lists into a single result set. Elasticsearch's approximate k-nearest neighbour search, Vespa, and Qdrant all support this hybrid retrieval pattern natively.

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