[BUG] Different score translations for ann search and exact search

[wdongyu]

What is the bug?
After introducing the settings index.knn.advanced.approximate_threshold in #2188, we may encounter such a scenario that two segments exist in one single shard. Suppose Segment_1 includes a graph and segment_2 does not, and they both include the same vector X.

When we conduct a search with a vector Q, we will get two different scores for the same vector X, because score translations for ann search and exact search are sightly different. For example, for cosine metric we have a score( 1 / (2 - cos(Q, X))) in ann search, but get another score ((1 + cos(Q, X)) / 2) in exact search.

How can one reproduce the bug?
Steps to reproduce the behavior:

1. Create a index with nmslib and cosine distance, set index.knn.advanced.approximate_threshold to -1, so that it never build a graph:

PUT test_nmslib_cosine
{
  "settings": {
    "index.knn": true,
    "index.knn.advanced.approximate_threshold": "-1",
    "index.number_of_shards": 1,
    "index.number_of_replicas": 0
  },
  "mappings": {
    "properties": {
      "target_field": {
        "type": "knn_vector",
        "dimension": 2,
        "method": {
          "engine": "nmslib",
          "space_type": "cosinesimil",
          "name": "hnsw"
        }
      }
    }
  }
}

2. Ingest a doc with vector[0.6, 0.8]:

POST test_nmslib_cosine/_doc/1?refresh
{
  "target_field": [0.6, 0.8] 
}

3. update index.knn.advanced.approximate_threshold to 1, so that it always build a graph:

PUT test_nmslib_cosine/_settings
{
  "index.knn.advanced.approximate_threshold": "1"
}

5. Ingest another doc with vector[0.6, 0.8]:

POST test_nmslib_cosine/_doc/2?refresh
{
  "target_field": [0.6, 0.8] 
}

6. Search the data:

POST test_nmslib_cosine/_search
{
  "query": {
    "knn": {
      "target_field": {
        "vector": [1, 2],
        "k": 10
      }
    }
  }
}

7. Get the result:

"hits": [
      {
        "_index": "test_nmslib_cosine",
        "_id": "1",
        "_score": 0.99193496,    // -> score = (1 + cos([1, 2], [0.6, 0.8])) / 2
        "_source": {
          "target_field": [
            0.6,
            0.8
          ]
        }
      },
      {
        "_index": "test_nmslib_cosine",
        "_id": "2",
        "_score": 0.98412585,  // -> score = 1 / (2 - cos([1, 2], [0.6, 0.8]))
        "_source": {
          "target_field": [
            0.6,
            0.8
          ]
        }
      }
    ]

What is the expected behavior?
Should get a consistent score for the same query and data vector.

What is your host/environment?

• OS: Any OS
• Version 2.18.0

Do you have any screenshots?
If applicable, add screenshots to help explain your problem.

Do you have any additional context?
Add any other context about the problem.

[vamshin]

@wdongyu good catch! if we make the score calculation consistent, that should fix the problem.

[navneet1v]

@wdongyu thanks for reporting this issue. I think this comes because for exact search we use Lucene based score translation and for native libs it is different. @VijayanB please take a look at this and lets ensure that we use a consistent score calculations.