A similarity metric assigns a numerical score to how closely a query, document, phrase, or other representation corresponds to another. Search systems use the score to compare candidates and rank results. section 3.1.1 section 13.8
For text search, represent both inputs in a shared space before comparing them. A vocabulary-based representation gives every known term a dimension, while dense embeddings encode contextual meaning. Cosine similarity compares separately generated embeddings; cross-encoders instead encode the query and document together and return a context-sensitive score. section 3.1.1 section 13.8
Choose the comparison strategy according to the ranking task:
- Use vector similarity to retrieve semantically related candidates, including phrases whose wording differs but whose meaning is related. section 13.4.3
- Use a cross-encoder to rerank a smaller candidate set when shared query-document context matters more than independent encoding speed. section 13.8
- Account for scale: comparing every pair among n phrases produces n² comparisons and increases computational and storage costs. section 13.4.3
From “apple juice” to ranked documents
Map the query “apple juice” and each document into the same term vector space. The query has nonzero values for “apple” and “juice”; linear algebra then measures its similarity to each document. In a semantic example, embeddings rank “it’s raining hard” close to “it is wet outside,” even though the wording differs. section 3.1.1 section 13.4.3
Listing 13.28 Reranking search results with a cross-encoder
from sentence_transformers import CrossEncoder
cross_encoder = \ #1
CrossEncoder("cross-encoder/ms-marco-MiniLM-L-6-v2") #1
query = "mountain hike"
search_results = semantic_search_with_engine( #2
embeddings_collection, query, limit=50) #2
pairs_to_score = [[query, doc["title"]] #3
for doc in search_results] #3
cross_scores = cross_encoder.predict(pairs_to_score, #4
activation_fct=torch.nn.Sigmoid()) #5
reranked_results = rerank(search_results, cross_scores) #6
display_results(query, reranked_results[:10])
A runnable reranking pipeline shows how to generate an initial semantic-search result set, score query-document pairs with a cross-encoder, and reorder the results. section 13.8
