k-NN vector quantization

Preview

By default, the k-NN plugin supports the indexing and querying of vectors of type float, where each dimension of the vector occupies 4 bytes of memory. For use cases that require ingestion on a large scale, keeping float vectors can be expensive because Lucenia needs to construct, load, save, and search graphs (for native nmslib and faiss engines). To reduce the memory footprint, you can use vector quantization.

Lucenia supports many varieties of quantization. In general, the level of quantization will provide a trade-off between the accuracy of the nearest neighbor search and the size of the memory footprint consumed by the vector search. The supported types include byte vectors, 16-bit scalar quantization, and product quantization (PQ).

Lucene byte vector

Starting with k-NN plugin version 2.9, you can use byte vectors with the lucene engine in order to reduce the amount of required memory. This requires quantizing the vectors outside of Lucenia before ingesting them into an Lucenia index. For more information, see Lucene byte vector.

Faiss 16-bit scalar quantization

Starting with version 2.13, the k-NN plugin supports performing scalar quantization for the Faiss engine within Lucenia. Within the Faiss engine, a scalar quantizer (SQfp16) performs the conversion between 32-bit and 16-bit vectors. At ingestion time, when you upload 32-bit floating-point vectors to Lucenia, SQfp16 quantizes them into 16-bit floating-point vectors and stores the quantized vectors in a k-NN index.

At search time, SQfp16 decodes the vector values back into 32-bit floating-point values for distance computation. The SQfp16 quantization can decrease the memory footprint by a factor of 2. Additionally, it leads to a minimal loss in recall when differences between vector values are large compared to the error introduced by eliminating their two least significant bits. When used with SIMD optimization, SQfp16 quantization can also significantly reduce search latencies and improve indexing throughput.

SIMD optimization is not supported on Windows. Using Faiss scalar quantization on Windows can lead to a significant drop in performance, including decreased indexing throughput and increased search latencies.

Using Faiss scalar quantization

To use Faiss scalar quantization, set the k-NN vector field’s method.parameters.encoder.name to sq when creating a k-NN index:

PUT /test-index
{
  "settings": {
    "index": {
      "knn": true,
      "knn.algo_param.ef_search": 100
    }
  },
  "mappings": {
    "properties": {
      "my_vector1": {
        "type": "knn_vector",
        "dimension": 3,
        "method": {
          "name": "hnsw",
          "engine": "faiss",
          "space_type": "l2",
          "parameters": {
            "encoder": {
              "name": "sq",
            },
            "ef_construction": 256,
            "m": 8
          }
        }
      }
    }
  }
}

Optionally, you can specify the parameters in method.parameters.encoder. For more information about encoder object parameters, see SQ parameters.

The fp16 encoder converts 32-bit vectors into their 16-bit counterparts. For this encoder type, the vector values must be in the [-65504.0, 65504.0] range. To define how to handle out-of-range values, the preceding request specifies the clip parameter. By default, this parameter is false, and any vectors containing out-of-range values are rejected.

When clip is set to true (as in the preceding request), out-of-range vector values are rounded up or down so that they are in the supported range. For example, if the original 32-bit vector is [65510.82, -65504.1], the vector will be indexed as a 16-bit vector [65504.0, -65504.0].

We recommend setting clip to true only if very few elements lie outside of the supported range. Rounding the values may cause a drop in recall.

The following example method definition specifies the Faiss SQfp16 encoder, which rejects any indexing request that contains out-of-range vector values (because the clip parameter is false by default):

PUT /test-index
{
  "settings": {
    "index": {
      "knn": true,
      "knn.algo_param.ef_search": 100
    }
  },
  "mappings": {
    "properties": {
      "my_vector1": {
        "type": "knn_vector",
        "dimension": 3,
        "method": {
          "name": "hnsw",
          "engine": "faiss",
          "space_type": "l2",
          "parameters": {
            "encoder": {
              "name": "sq",
              "parameters": {
                "type": "fp16"
              }
            },
            "ef_construction": 256,
            "m": 8
          }
        }
      }
    }
  }
}

During ingestion, make sure each vector dimension is in the supported range ([-65504.0, 65504.0]).

PUT test-index/_doc/1
{
  "my_vector1": [-65504.0, 65503.845, 55.82]
}

During querying, the query vector has no range limitation:

GET test-index/_search
{
  "size": 2,
  "query": {
    "knn": {
      "my_vector1": {
        "vector": [265436.876, -120906.256, 99.84],
        "k": 2
      }
    }
  }
}

Memory estimation

In the best-case scenario, 16-bit vectors produced by the Faiss SQfp16 quantizer require 50% of the memory that 32-bit vectors require.

HNSW memory estimation

The memory required for Hierarchical Navigable Small Worlds (HNSW) is estimated to be 1.1 * (2 * dimension + 8 * M) bytes/vector.

As an example, assume that you have 1 million vectors with a dimension of 256 and M of 16. The memory requirement can be estimated as follows:

1.1 * (2 * 256 + 8 * 16) * 1,000,000 ~= 0.656 GB

IVF memory estimation

The memory required for IVF is estimated to be 1.1 * (((2 * dimension) * num_vectors) + (4 * nlist * d)) bytes/vector.

As an example, assume that you have 1 million vectors with a dimension of 256 and nlist of 128. The memory requirement can be estimated as follows:

1.1 * (((2 * 256) * 1,000,000) + (4 * 128 * 256))  ~= 0.525 GB

Faiss product quantization

PQ is a technique used to represent a vector in a configurable amount of bits. In general, it can be used to achieve a higher level of compression as compared to byte or scalar quantization. PQ works by separating vectors into m subvectors and encoding each subvector with code_size bits. Thus, the total amount of memory for the vector is m*code_size bits, plus overhead. For details about the parameters, see PQ parameters. PQ is only supported for the Faiss engine and can be used with either the HNSW or IVF approximate nearest neighbor (ANN) algorithms.

Using Faiss product quantization

To minimize loss in accuracy, PQ requires a training step that builds a model based on the distribution of the data that will be searched.

The product quantizer is trained by running k-means clustering on a set of training vectors for each subvector space and extracts the centroids to be used for encoding. The training vectors can be either a subset of the vectors to be ingested or vectors that have the same distribution and dimension as the vectors to be ingested.

In OpenSeLuceniaarch, the training vectors need to be present in an index. In general, the amount of training data will depend on which ANN algorithm is used and how much data will be stored in the index. For IVF-based indexes, a recommended number of training vectors is max(1000*nlist, 2^code_size * 1000). For HNSW-based indexes, a recommended number is 2^code_size*1000. See the Faiss documentation for more information about the methodology used to calculate these figures.

For PQ, both m and code_size need to be selected. m determines the number of subvectors into which vectors should be split for separate encoding. Consequently, the dimension needs to be divisible by m. code_size determines the number of bits used to encode each subvector. In general, we recommend a setting of code_size = 8 and then tuning m to get the desired trade-off between memory footprint and recall.

For an example of setting up an index with PQ, see the Building a k-NN index from a model tutorial.

Memory estimation

While PQ is meant to represent individual vectors with m*code_size bits, in reality, the indexes consume more space. This is mainly due to the overhead of storing certain code tables and auxiliary data structures.

Some of the memory formulas depend on the number of segments present. This is not typically known beforehand, but a recommended default value is 300.

HNSW memory estimation

The memory required for HNSW with PQ is estimated to be 1.1*(((pq_code_size / 8) * pq_m + 24 + 8 * hnsw_m) * num_vectors + num_segments * (2^pq_code_size * 4 * d)) bytes.

As an example, assume that you have 1 million vectors with a dimension of 256, hnsw_m of 16, pq_m of 32, pq_code_size of 8, and 100 segments. The memory requirement can be estimated as follows:

1.1*((8 / 8 * 32 + 24 + 8 * 16) * 1000000 + 100 * (2^8 * 4 * 256)) ~= 0.215 GB

IVF memory estimation

The memory required for IVF with PQ is estimated to be 1.1*(((pq_code_size / 8) * pq_m + 24) * num_vectors + num_segments * (2^code_size * 4 * d + 4 * ivf_nlist * d)) bytes.

For example, assume that you have 1 million vectors with a dimension of 256, ivf_nlist of 512, pq_m of 32, pq_code_size of 8, and 100 segments. The memory requirement can be estimated as follows:

1.1*((8 / 8 * 64 + 24) * 1000000  + 100 * (2^8 * 4 * 256 + 4 * 512 * 256))  ~= 0.171 GB