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Reciprocal rank fusion

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Reciprocal rank fusion

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This functionality is in technical preview and may be changed or removed in a future release. The syntax will likely change before GA. Elastic will apply best effort to fix any issues, but features in technical preview are not subject to the support SLA of official GA features.

Reciprocal rank fusion (RRF) is a method for combining multiple result sets with different relevance indicators into a single result set. RRF requires no tuning, and the different relevance indicators do not have to be related to each other to achieve high-quality results.

RRF uses the following formula to determine the score for ranking each document:

score = 0.0
for q in queries:
    if d in result(q):
        score += 1.0 / ( k + rank( result(q), d ) )
return score

# where
# k is a ranking constant
# q is a query in the set of queries
# d is a document in the result set of q
# result(q) is the result set of q
# rank( result(q), d ) is d's rank within the result(q) starting from 1

Reciprocal rank fusion API

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You can use RRF as part of a search to combine and rank documents using multiple result sets from

  • 1 query and 1 or more kNN searches
  • 2 or more kNN searches

The rrf parameter is an optional object defined as part of a search request’s rank parameter. The rrf object contains the following parameters:

rank_constant
(Optional, integer) This value determines how much influence documents in individual result sets per query have over the final ranked result set. A higher value indicates that lower ranked documents have more influence. This value must be greater than or equal to 1. Defaults to 60.
window_size
(Optional, integer) This value determines the size of the individual result sets per query. A higher value will improve result relevance at the cost of performance. The final ranked result set is pruned down to the search request’s <<search-size-param, size>. window_size must be greater than or equal to size and greater than or equal to 1. Defaults to 100.

An example request using RRF:

GET example-index/_search
{
    "query": {
        "term": {
            "text": "shoes"
        }
    },
    "knn": {
        "field": "vector",
        "query_vector": [1.25, 2, 3.5],
        "k": 50,
        "num_candidates": 100
    },
    "rank": {
        "rrf": {
            "window_size": 50,
            "rank_constant": 20
        }
    }
}

In the above example, we first execute the kNN search to get its global top 50 results. Then we execute the query to get its global top 50 results. Afterwards, on a coordinating node, we combine the knn search results with the query results and rank them based on the RRF method to get the final top 10 results.

Note that if k from a knn search is larger than window_size, the results are truncated to window_size. If k is smaller than window_size, the results are k size.

Reciprocal rank fusion supported features

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RRF does support:

RRF does not currently support:

Using unsupported features as part of a search using RRF will result in an exception.

Reciprocal rank fusion full example

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We begin by creating a mapping for an index with a text field, a vector field, and an integer field along with indexing several documents. For this example we are going to use a vector with only a single dimension to make the ranking easier to explain.

PUT example-index
{
  "mappings": {
        "properties": {
            "text" : {
                "type" : "text"
            },
            "vector": {
                "type": "dense_vector",
                "dims": 1,
                "index": true,
                "similarity": "l2_norm"
            },
            "integer" : {
                "type" : "integer"
            }
        }
    }
}

PUT example-index/_doc/1
{
    "text" : "rrf",
    "vector" : [5],
    "integer": 1
}

PUT example-index/_doc/2
{
    "text" : "rrf rrf",
    "vector" : [4],
    "integer": 2
}

PUT example-index/_doc/3
{
    "text" : "rrf rrf rrf",
    "vector" : [3],
    "integer": 1
}

PUT example-index/_doc/4
{
    "text" : "rrf rrf rrf rrf",
    "integer": 2
}

PUT example-index/_doc/5
{
    "vector" : [0],
    "integer": 1
}

POST example-index/_refresh

We now execute a search using RRF with a query, a kNN search, and a terms aggregation.

GET example-index/_search
{
    "query": {
        "term": {
            "text": "rrf"
        }
    },
    "knn": {
        "field": "vector",
        "query_vector": [3],
        "k": 5,
        "num_candidates": 5
    },
    "rank": {
        "rrf": {
            "window_size": 5,
            "rank_constant": 1
        }
    },
    "size": 3,
    "aggs": {
        "int_count": {
            "terms": {
                "field": "integer"
            }
        }
    }
}

And we receive the response with ranked hits and the terms aggregation result. Note that _score is null, and we instead use _rank to show our top-ranked documents.

{
    "took": ...,
    "timed_out" : false,
    "_shards" : {
        "total" : 1,
        "successful" : 1,
        "skipped" : 0,
        "failed" : 0
    },
    "hits" : {
        "total" : {
            "value" : 5,
            "relation" : "eq"
        },
        "max_score" : null,
        "hits" : [
            {
                "_index" : "example-index",
                "_id" : "3",
                "_score" : null,
                "_rank" : 1,
                "_source" : {
                    "integer" : 1,
                    "vector" : [
                        3
                    ],
                    "text" : "rrf rrf rrf"
                }
            },
            {
                "_index" : "example-index",
                "_id" : "2",
                "_score" : null,
                "_rank" : 2,
                "_source" : {
                    "integer" : 2,
                    "vector" : [
                        4
                    ],
                    "text" : "rrf rrf"
                }
            },
            {
                "_index" : "example-index",
                "_id" : "4",
                "_score" : null,
                "_rank" : 3,
                "_source" : {
                    "integer" : 2,
                    "text" : "rrf rrf rrf rrf"
                }
            }
        ]
    },
    "aggregations" : {
        "int_count" : {
            "doc_count_error_upper_bound" : 0,
            "sum_other_doc_count" : 0,
            "buckets" : [
                {
                    "key" : 1,
                    "doc_count" : 3
                },
                {
                    "key" : 2,
                    "doc_count" : 2
                }
            ]
        }
    }
}

Let’s break down how these hits were ranked. We start by running the query and the kNN search separately to collect what their individual hits are.

First, we look at the hits for the query.

"hits" : [
    {
        "_index" : "example-index",
        "_id" : "4",
        "_score" : 0.16152832,              
        "_source" : {
            "integer" : 2,
            "text" : "rrf rrf rrf rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "3",                        
        "_score" : 0.15876243,
        "_source" : {
            "integer" : 1,
            "vector" : [3],
            "text" : "rrf rrf rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "2",                        
        "_score" : 0.15350538,
        "_source" : {
            "integer" : 2,
            "vector" : [4],
            "text" : "rrf rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "1",                        
        "_score" : 0.13963442,
        "_source" : {
            "integer" : 1,
            "vector" : [5],
            "text" : "rrf"
        }
    }
]

rank 1, _id 4

rank 2, _id 3

rank 3, _id 2

rank 4, _id 1

Note that our first hit doesn’t have a value for the vector field. Now, we look at the results for the kNN search.

"hits" : [
    {
        "_index" : "example-index",
        "_id" : "3",                   
        "_score" : 1.0,
        "_source" : {
            "integer" : 1,
            "vector" : [3],
            "text" : "rrf rrf rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "2",                   
        "_score" : 0.5,
        "_source" : {
            "integer" : 2,
            "vector" : [4],
            "text" : "rrf rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "1",                   
        "_score" : 0.2,
        "_source" : {
            "integer" : 1,
            "vector" : [5],
            "text" : "rrf"
        }
    },
    {
        "_index" : "example-index",
        "_id" : "5",                   
        "_score" : 0.1,
        "_source" : {
            "integer" : 1,
            "vector" : [0]
        }
    }
]

rank 1, _id 3

rank 2, _id 2

rank 3, _id 1

rank 4, _id 5

We can now take the two individually ranked result sets and apply the RRF formula to them to get our final ranking.

# doc  | query     | knn       | score
_id: 1 = 1.0/(1+4) + 1.0/(1+3) = 0.4500
_id: 2 = 1.0/(1+3) + 1.0/(1+2) = 0.5833
_id: 3 = 1.0/(1+2) + 1.0/(1+1) = 0.8333
_id: 4 = 1.0/(1+1)             = 0.5000
_id: 5 =             1.0/(1+4) = 0.2000

We rank the documents based on the RRF formula with a window_size of 5 truncating the bottom 2 docs in our RRF result set with a size of 3. We end with _id: 3 as _rank: 1, _id: 2 as _rank: 2, and _id: 4 as _rank: 3. This ranking matches the result set from the original RRF search as expected.

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