Nested KNN Score Mismatch In Elasticsearch: A Deep Dive

Navigating the intricacies of Elasticsearch can sometimes feel like exploring a vast ocean. One particular area that can present challenges is the implementation of nested k-Nearest Neighbors (kNN) searches, especially when using the bbq_hnsw index. In this comprehensive guide, we will dive deep into a specific issue: the score mismatch observed between parent hits and inner hits during nested kNN searches. We'll explore the problem, the steps to reproduce it, and potential reasons behind this behavior, ensuring you gain a robust understanding of how to tackle this issue.

The Challenge: Score Mismatch in Nested kNN Searches

When performing a Nested kNN Search on an Elasticsearch index that utilizes bbq_hnsw, it's not uncommon to encounter a scenario where the _score of the top-level document hit differs slightly from the _score of the corresponding inner hit found under inner_hits.hits. This discrepancy, while seemingly minor, can raise questions about the accuracy and reliability of the search results. Imagine, for instance, you are building a recommendation system where precise similarity scores are crucial. A mismatch in scores can lead to suboptimal recommendations, impacting user experience and system performance.

To illustrate this issue, let’s consider a real-world example. Suppose you have documents representing products, and each product has a nested field called embeddings containing vector embeddings that capture the product's features. You want to find products similar to a given query vector. In a perfect scenario, the top-level hit's score should align perfectly with the score of the most relevant inner hit. However, in practice, you might observe that the top-level document receives a score of, say, 0.3541979, while the best matching inner hit has a score of 0.35047227. While these values are close, the difference can be significant in certain applications.

This discrepancy prompts an important question: Why do these scores differ? To answer this, we need to understand the mechanics of nested kNN searches and the factors influencing score calculation within Elasticsearch. The score mismatch isn't necessarily an indication of an error, but rather a manifestation of how Elasticsearch processes nested queries and aggregates scores. The top-level score represents the overall relevance of the document, considering all its nested objects, while the inner hit score reflects the relevance of a specific nested object within that document. The aggregation of these individual scores into a single top-level score can introduce subtle differences.

Reproducing the Issue: A Step-by-Step Guide

To fully grasp the score mismatch problem, it's essential to reproduce it in a controlled environment. This hands-on approach allows you to observe the behavior firsthand and gain deeper insights. Here’s a step-by-step guide to replicate the issue in your Elasticsearch setup.

Step 1: Creating the Index with bbq_hnsw

First, you need to create an index in Elasticsearch configured to use the bbq_hnsw (Block-Based k-Nearest Neighbors Hierarchical Navigable Small World Graph) algorithm. This involves defining a mapping that specifies the data types and indexing parameters for your fields. The key here is to include a nested field with a dense_vector type, which will store your embeddings. Let's walk through the JSON payload required to create such an index.

PUT /hnsw
{
  "mappings": {
    "dynamic": false,
    "properties": {
      "embeddings": {
        "type": "nested",
        "properties": {
          "embedding": {
            "type": "dense_vector",
            "dims": 768,
            "index": true,
            "similarity": "l2_norm",
            "index_options": {
              "type": "bbq_hnsw",
              "m": 32,
              "ef_construction": 256,
              "rescore_vector": {
                "oversample": 3
              }
            }
          }
        }
      }
    }
  }
}

In this mapping:

• dynamic: false ensures that only the fields defined in the mapping are indexed, preventing accidental indexing of new fields.
• embeddings: This is the crucial nested field. Nested fields allow you to index arrays of objects independently, which is essential for kNN searches within nested structures.
• embedding: Within the embeddings nested field, this is the dense_vector field. It stores the vector embeddings, with dims specifying the vector dimension (in this case, 768). index: true enables indexing for this field, and `similarity: