Reciprocal rank fusion
editReciprocal rank fusion
editReciprocal 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
editYou can use RRF as part of a search to combine and rank documents using separate sets of top documents (result sets) from a combination of child retrievers using an RRF retriever. A minimum of two child retrievers is required for ranking.
An RRF retriever is an optional object defined as part of a search request’s retriever parameter. The RRF retriever object contains the following parameters:
-
retrievers -
(Required, array of retriever objects)
A list of child retrievers to specify which sets of returned top documents will have the RRF formula applied to them. Each child retriever carries an equal weight as part of the RRF formula. Two or more child retrievers are required.
-
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 to60. -
rank_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 size.
rank_window_sizemust be greater than or equal tosizeand greater than or equal to1. Defaults to thesizeparameter.
An example request using RRF:
resp = client.search(
index="example-index",
retriever={
"rrf": {
"retrievers": [
{
"standard": {
"query": {
"term": {
"text": "shoes"
}
}
}
},
{
"knn": {
"field": "vector",
"query_vector": [
1.25,
2,
3.5
],
"k": 50,
"num_candidates": 100
}
}
],
"rank_window_size": 50,
"rank_constant": 20
}
},
)
print(resp)
const response = await client.search({
index: "example-index",
retriever: {
rrf: {
retrievers: [
{
standard: {
query: {
term: {
text: "shoes",
},
},
},
},
{
knn: {
field: "vector",
query_vector: [1.25, 2, 3.5],
k: 50,
num_candidates: 100,
},
},
],
rank_window_size: 50,
rank_constant: 20,
},
},
});
console.log(response);
GET example-index/_search
{
"retriever": {
"rrf": {
"retrievers": [
{
"standard": {
"query": {
"term": {
"text": "shoes"
}
}
}
},
{
"knn": {
"field": "vector",
"query_vector": [1.25, 2, 3.5],
"k": 50,
"num_candidates": 100
}
}
],
"rank_window_size": 50,
"rank_constant": 20
}
}
}
In the above example, we execute the knn and standard retrievers independently of each other.
Then we use the rrf retriever to combine the results.
|
First, we execute the kNN search specified by the |
|
|
Second, we execute the query specified by the |
|
|
Then, on a coordinating node, we combine the kNN search top documents with the query top documents and rank them based on the RRF formula using parameters from the |
Note that if k from a knn search is larger than rank_window_size, the results are truncated to rank_window_size.
If k is smaller than rank_window_size, the results are k size.
Reciprocal rank fusion supported features
editThe rrf retriever supports:
The rrf retriever does not currently support:
Using unsupported features as part of a search with an rrf retriever results in an exception.
It is best to avoid providing a point in time as part of the request, as RRF creates one internally that is shared by all sub-retrievers to ensure consistent results.
Reciprocal rank fusion using multiple standard retrievers
editThe rrf retriever provides a way to combine and rank multiple standard retrievers.
A primary use case is combining top documents from a traditional BM25 query and an ELSER query to achieve improved relevance.
An example request using RRF with multiple standard retrievers:
resp = client.search(
index="example-index",
retriever={
"rrf": {
"retrievers": [
{
"standard": {
"query": {
"term": {
"text": "blue shoes sale"
}
}
}
},
{
"standard": {
"query": {
"sparse_vector": {
"field": "ml.tokens",
"inference_id": "my_elser_model",
"query": "What blue shoes are on sale?"
}
}
}
}
],
"rank_window_size": 50,
"rank_constant": 20
}
},
)
print(resp)
const response = await client.search({
index: "example-index",
retriever: {
rrf: {
retrievers: [
{
standard: {
query: {
term: {
text: "blue shoes sale",
},
},
},
},
{
standard: {
query: {
sparse_vector: {
field: "ml.tokens",
inference_id: "my_elser_model",
query: "What blue shoes are on sale?",
},
},
},
},
],
rank_window_size: 50,
rank_constant: 20,
},
},
});
console.log(response);
GET example-index/_search
{
"retriever": {
"rrf": {
"retrievers": [
{
"standard": {
"query": {
"term": {
"text": "blue shoes sale"
}
}
}
},
{
"standard": {
"query": {
"sparse_vector":{
"field": "ml.tokens",
"inference_id": "my_elser_model",
"query": "What blue shoes are on sale?"
}
}
}
}
],
"rank_window_size": 50,
"rank_constant": 20
}
}
}
In the above example, we execute each of the two standard retrievers independently of each other.
Then we use the rrf retriever to combine the results.
|
First we run the |
|
|
Next we run the |
|
|
The |
Not only does this remove the need to figure out what the appropriate weighting is using linear combination, but RRF is also shown to give improved relevance over either query individually.
Reciprocal rank fusion using sub searches
editRRF using sub searches is no longer supported. Use the retriever API instead. See using multiple standard retrievers for an example.
Reciprocal rank fusion full example
editWe 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.
resp = client.indices.create(
index="example-index",
mappings={
"properties": {
"text": {
"type": "text"
},
"vector": {
"type": "dense_vector",
"dims": 1,
"index": True,
"similarity": "l2_norm",
"index_options": {
"type": "hnsw"
}
},
"integer": {
"type": "integer"
}
}
},
)
print(resp)
resp1 = client.index(
index="example-index",
id="1",
document={
"text": "rrf",
"vector": [
5
],
"integer": 1
},
)
print(resp1)
resp2 = client.index(
index="example-index",
id="2",
document={
"text": "rrf rrf",
"vector": [
4
],
"integer": 2
},
)
print(resp2)
resp3 = client.index(
index="example-index",
id="3",
document={
"text": "rrf rrf rrf",
"vector": [
3
],
"integer": 1
},
)
print(resp3)
resp4 = client.index(
index="example-index",
id="4",
document={
"text": "rrf rrf rrf rrf",
"integer": 2
},
)
print(resp4)
resp5 = client.index(
index="example-index",
id="5",
document={
"vector": [
0
],
"integer": 1
},
)
print(resp5)
resp6 = client.indices.refresh(
index="example-index",
)
print(resp6)
const response = await client.indices.create({
index: "example-index",
mappings: {
properties: {
text: {
type: "text",
},
vector: {
type: "dense_vector",
dims: 1,
index: true,
similarity: "l2_norm",
index_options: {
type: "hnsw",
},
},
integer: {
type: "integer",
},
},
},
});
console.log(response);
const response1 = await client.index({
index: "example-index",
id: 1,
document: {
text: "rrf",
vector: [5],
integer: 1,
},
});
console.log(response1);
const response2 = await client.index({
index: "example-index",
id: 2,
document: {
text: "rrf rrf",
vector: [4],
integer: 2,
},
});
console.log(response2);
const response3 = await client.index({
index: "example-index",
id: 3,
document: {
text: "rrf rrf rrf",
vector: [3],
integer: 1,
},
});
console.log(response3);
const response4 = await client.index({
index: "example-index",
id: 4,
document: {
text: "rrf rrf rrf rrf",
integer: 2,
},
});
console.log(response4);
const response5 = await client.index({
index: "example-index",
id: 5,
document: {
vector: [0],
integer: 1,
},
});
console.log(response5);
const response6 = await client.indices.refresh({
index: "example-index",
});
console.log(response6);
PUT example-index
{
"mappings": {
"properties": {
"text" : {
"type" : "text"
},
"vector": {
"type": "dense_vector",
"dims": 1,
"index": true,
"similarity": "l2_norm",
"index_options": {
"type": "hnsw"
}
},
"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 an rrf retriever with a standard retriever specifying a BM25 query, a knn retriever specifying a kNN search, and a terms aggregation.
resp = client.search(
index="example-index",
retriever={
"rrf": {
"retrievers": [
{
"standard": {
"query": {
"term": {
"text": "rrf"
}
}
}
},
{
"knn": {
"field": "vector",
"query_vector": [
3
],
"k": 5,
"num_candidates": 5
}
}
],
"rank_window_size": 5,
"rank_constant": 1
}
},
size=3,
aggs={
"int_count": {
"terms": {
"field": "integer"
}
}
},
)
print(resp)
const response = await client.search({
index: "example-index",
retriever: {
rrf: {
retrievers: [
{
standard: {
query: {
term: {
text: "rrf",
},
},
},
},
{
knn: {
field: "vector",
query_vector: [3],
k: 5,
num_candidates: 5,
},
},
],
rank_window_size: 5,
rank_constant: 1,
},
},
size: 3,
aggs: {
int_count: {
terms: {
field: "integer",
},
},
},
});
console.log(response);
GET example-index/_search
{
"retriever": {
"rrf": {
"retrievers": [
{
"standard": {
"query": {
"term": {
"text": "rrf"
}
}
}
},
{
"knn": {
"field": "vector",
"query_vector": [3],
"k": 5,
"num_candidates": 5
}
}
],
"rank_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.
We have both the ranker’s score and the _rank option 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" : ...,
"hits" : [
{
"_index" : "example-index",
"_id" : "3",
"_score" : 0.8333334,
"_source" : {
"integer" : 1,
"vector" : [
3
],
"text" : "rrf rrf rrf"
}
},
{
"_index" : "example-index",
"_id" : "2",
"_score" : 0.5833334,
"_source" : {
"integer" : 2,
"vector" : [
4
],
"text" : "rrf rrf"
}
},
{
"_index" : "example-index",
"_id" : "4",
"_score" : 0.5,
"_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 standard retriever specifying a query and the knn retriever specifying a kNN search separately to collect what their individual hits are.
First, we look at the hits for the query from the standard retriever.
"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"
}
}
]
Note that our first hit doesn’t have a value for the vector field.
Now, we look at the results for the kNN search from the knn retriever.
"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]
}
}
]
We can now take the two individually ranked result sets and apply the RRF formula to them using parameters from the rrf retriever 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 rank_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.
Explain in RRF
editIn addition to individual query scoring details, we can make use of the explain=true parameter to get information on how the RRF scores for each document were computed.
Working with the example above, and by adding explain=true to the search request, we’d now have a response that looks like the following:
{
"hits":
[
{
"_index": "example-index",
"_id": "3",
"_score": 0.8333334,
"_explanation":
{
"value": 0.8333334,
"description": "rrf score: [0.8333334] computed for initial ranks [2, 1] with rankConstant: [1] as sum of [1 / (rank + rankConstant)] for each query",
"details":
[
{
"value": 2,
"description": "rrf score: [0.33333334], for rank [2] in query at index [0] computed as [1 / (2 + 1]), for matching query with score: ",
"details":
[
{
"value": 0.15876243,
"description": "weight(text:rrf in 0) [PerFieldSimilarity], result of:",
"details":
[
...
]
}
]
},
{
"value": 1,
"description": "rrf score: [0.5], for rank [1] in query at index [1] computed as [1 / (1 + 1]), for matching query with score: ",
"details":
[
{
"value": 1,
"description": "within top k documents",
"details":
[]
}
]
}
]
}
}
...
]
}
|
the final RRF score for document with |
|
|
a description on how this score was computed based on the ranks of this document in each individual query |
|
|
details on how the RRF score was computed for each of the queries |
|
|
the |
|
|
standard |
|
|
the |
In addition to the above, explain in RRF also supports named queries using the _name parameter.
Using named queries allows for easier and more intuitive understanding of the RRF score computation, especially when dealing with multiple queries.
So, we would now have:
GET example-index/_search
{
"retriever": {
"rrf": {
"retrievers": [
{
"standard": {
"query": {
"term": {
"text": "rrf"
}
}
}
},
{
"knn": {
"field": "vector",
"query_vector": [3],
"k": 5,
"num_candidates": 5,
"_name": "my_knn_query"
}
}
],
"rank_window_size": 5,
"rank_constant": 1
}
},
"size": 3,
"aggs": {
"int_count": {
"terms": {
"field": "integer"
}
}
}
}
The response would now include the named query in the explanation:
{
"hits":
[
{
"_index": "example-index",
"_id": "3",
"_score": 0.8333334,
"_explanation":
{
"value": 0.8333334,
"description": "rrf score: [0.8333334] computed for initial ranks [2, 1] with rankConstant: [1] as sum of [1 / (rank + rankConstant)] for each query",
"details":
[
{
"value": 2,
"description": "rrf score: [0.33333334], for rank [2] in query at index [0] computed as [1 / (2 + 1]), for matching query with score: ",
"details":
[
...
]
},
{
"value": 1,
"description": "rrf score: [0.5], for rank [1] in query [my_knn_query] computed as [1 / (1 + 1]), for matching query with score: ",
"details":
[
...
]
}
]
}
}
...
]
}
Pagination in RRF
editWhen using rrf you can paginate through the results using the from parameter.
As the final ranking is solely dependent on the original query ranks, to ensure consistency when paginating, we have to make sure that while from changes, the order of what we have already seen remains intact.
To that end, we’re using a fixed rank_window_size as the whole available result set upon which we can paginate.
This essentially means that if:
-
from + size≤rank_window_size: we could getresults[from: from+size]documents back from the finalrrfranked result set -
from + size>rank_window_size: we would get 0 results back, as the request would fall outside the availablerank_window_size-sized result set.
An important thing to note here is that since rank_window_size is all the results that we’ll get to see from the individual query components, pagination guarantees consistency, i.e. no documents are skipped or duplicated in multiple pages, iff rank_window_size remains the same.
If rank_window_size changes, then the order of the results might change as well, even for the same ranks.
To illustrate all of the above, let’s consider the following simplified example where we have two queries, queryA and queryB and their ranked documents:
| queryA | queryB | _id: | 1 | 5 | _id: | 2 | 4 | _id: | 3 | 3 | _id: | 4 | 1 | _id: | | 2 |
For rank_window_size=5 we would get to see all documents from both queryA and queryB.
Assuming a rank_constant=1, the rrf scores would be:
# doc | queryA | queryB | score _id: 1 = 1.0/(1+1) + 1.0/(1+4) = 0.7 _id: 2 = 1.0/(1+2) + 1.0/(1+5) = 0.5 _id: 3 = 1.0/(1+3) + 1.0/(1+3) = 0.5 _id: 4 = 1.0/(1+4) + 1.0/(1+2) = 0.533 _id: 5 = 0 + 1.0/(1+1) = 0.5
So the final ranked result set would be [1, 4, 2, 3, 5] and we would paginate over that, since rank_window_size == len(results).
In this scenario, we would have:
-
from=0, size=2would return documents [1,4] with ranks[1, 2] -
from=2, size=2would return documents [2,3] with ranks[3, 4] -
from=4, size=2would return document [5] with rank[5] -
from=6, size=2would return an empty result set as it there are no more results to iterate over
Now, if we had a rank_window_size=2, we would only get to see [1, 2] and [5, 4] documents for queries queryA and queryB respectively.
Working out the math, we would see that the results would now be slightly different, because we would have no knowledge of the documents in positions [3: end] for either query.
# doc | queryA | queryB | score _id: 1 = 1.0/(1+1) + 0 = 0.5 _id: 2 = 1.0/(1+2) + 0 = 0.33 _id: 4 = 0 + 1.0/(1+2) = 0.33 _id: 5 = 0 + 1.0/(1+1) = 0.5
The final ranked result set would be [1, 5, 2, 4], and we would be able to paginate on the top rank_window_size results, i.e. [1, 5].
So for the same params as above, we would now have:
-
from=0, size=2would return [1,5] with ranks[1, 2] -
from=2, size=2would return an empty result set as it would fall outside the availablerank_window_sizeresults.
Aggregations in RRF
editThe rrf retriever supports aggregations from all specified sub-retrievers. Important notes about aggregations:
- They operate on the complete result set from all sub-retrievers
-
They are not limited by the
rank_window_sizeparameter - They process the union of all matching documents
For example, consider the following document set:
{
"_id": 1, "termA": "foo",
"_id": 2, "termA": "foo", "termB": "bar",
"_id": 3, "termA": "aardvark", "termB": "bar",
"_id": 4, "termA": "foo", "termB": "bar"
}
Perform a term aggregation on the termA field using an rrf retriever:
{
"retriever": {
"rrf": {
"retrievers": [
{
"standard": {
"query": {
"term": {
"termB": "bar"
}
}
}
},
{
"standard": {
"query": {
"match_all": { }
}
}
}
],
"rank_window_size": 1
}
},
"size": 1,
"aggs": {
"termA_agg": {
"terms": {
"field": "termA"
}
}
}
}
The aggregation results will include all matching documents, regardless of rank_window_size.
{
"foo": 3,
"aardvark": 1
}
Highlighting in RRF
editUsing the rrf retriever, you can add highlight snippets to show relevant text snippets in your search results. Highlighted snippets are computed based
on the matching text queries defined on the sub-retrievers.
Highlighting on vector fields, using either the knn retriever or a knn query, is not supported.
A more specific example of highlighting in RRF can also be found in the retrievers examples page.
Inner hits in RRF
editThe rrf retriever supports inner hits functionality, allowing you to retrieve
related nested or parent/child documents alongside your main search results. Inner hits can be
specified as part of any nested sub-retriever and will be propagated to the top-level parent
retriever. Note that the inner hit computation will take place only at end of rrf retriever’s
evaluation on the top matching documents, and not as part of the query execution of the nested
sub-retrievers.
When defining multiple inner_hits sections across sub-retrievers:
-
Each
inner_hitssection must have a unique name - Names must be unique across all sub-retrievers in the search request