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Quick ADC

Description

The Quick ADC project is a C++14 implementation of fast distance computation techniques for nearest neighbor search in large databases of high-dimensional vectors.

Quick ADC builds on Product Quantization (PQ), a widespread nearest neighbor search solution. PQ compresses high-dimensional vectors into short codes of a few bytes (usually 8-16 bytes). This makes it possible to store very large databases (billions of vectors) entirely in RAM. To answer nearest neighbor queries, PQ relies on Asymmetric Distance Computation (ADC). ADC computes distances between the query vector and short codes using lookup tables stored in the L1 Cache. ADC offers only limited performance because of the latency of the L1 Cache (4-5 cycles), and the lack of parallelism of L1 cache accesses (max. 2 concurrent accesses). Our technique, Quick ADC, achieves 4-6x better performance than ADC by storing lookup tables in SIMD registers, which offer high parallelism and low latency (16 concurrent accesses in 1 cycle).

Quick ADC builds on the same key principle as PQ Fast Scan. However, PQ Fast Scan and Quick ADC use different techniques to obtain lookup tables that fit SIMD registers. PQ Fast Scan relies on a reorganization of a lists of codes, which prevents combining it with inverted indexes, another common search acceleration technique. On the contrary, Quick ADC relies on the use of 4-bit quantizers instead of common 8-bit quantizers. Quick ADC can be combined with inverted indexes. Quick ADC comes at the price of a slight decrease in accuracy but this decrease is often negligible.

Contact:
Nicolas Le Souarnec: nicolas.le-scouarnec technicolor.com
Fabien André: fabien.andre technicolor.com
Please replace the space by an at sign if you want to send us a mail. You may also open a Github issue.

Publication

F. Andre, A.-M. Kermarrec, and N. Le Scouarnec. Accelerated Nearest Neighbor Search with Quick ADC, ICMR, 2017. Publication presented at ICMR'17: PDF, Slides, Poster

License

The Quick ADC project is made available under the Clear BSD license terms (See LICENSE file).

Copyright (c) 2017 – Technicolor R&D France

Building

Requirements

Hardware:

  • Processor supporting AVX and AVX2 (Intel Haswell or newer)

We have tested Quick ADC on Intel Haswell, Broadwell and Skylake processors but we expect it to work on newer generations of Intel processors, as well as AMD Ryzen processors.

Software:

  • Linux distribution from 2016 or newer (Debian 9 or newer, Ubuntu 16.04 or newer etc.)
  • g++ 5.4 or newer
  • CMake 2.8 or higher
  • OpenCV Core libraries
  • A sequential (mono-threaded) BLAS implementation – Do not install from packages, see below
  • Cereal 1.2.2 – See below

On Debian-based distributions, you can install g++, opencv core and cmake with the following command:

$ sudo apt-get install build-essential gcc g++ cmake libopencv-core-dev

We recommend creating a working directory for the compilation of this project and its dependencies:

$ mkdir qadc-project
$ cd qadc-project

Sequential BLAS implementation

Quick ADC requires a high-performance sequential BLAS implementation, i.e., a BLAS implementation that uses only a single thread. Quick ADC already calls BLAS functions from multiple threads. Therefore, a BLAS implementation which spawns multiple threads will lead to oversubscription, and severely degrade performance. The BLAS implementations included in most Linux distributions are multi-threaded, which is why you need to compile a sequential BLAS implementation from source.

You can automatically download and compile a sequential version of OpenBLAS using the getdeps.sh script we provide:

$ sudo apt-get install gfortran wget
$ git clone https://github.com/technicolor-research/quick-adc
$ sudo bash quick-adc/getdeps.sh

The getdeps.sh script also downloads Cereal, so you may skip the next step if you use it. You may use the Intel MKL or ATLAS BLAS implementations instead of OpenBLAS, but again, make sure to link with the sequential versions of these libraries.

Cereal

Quick ADC requires the Cereal serialization library. The getdeps.sh script automatically downloads Cereal, so you don't need to do anything more if you used it. Otherwise, download and unpack Cereal. Cereal is a header-only library so you don't need to compile it. Make sure to download version 1.2.2 because we have found previous versions to contain bugs.

Building Quick ADC

If you have not downloaded the project yet:

$ git clone https://github.com/technicolor-research/quick-adc

You can adjust path and library names in the quick-adc/LibsPath.cmake file. You may need to change OPENCV_CORE_LIB from opencv_core to opencv if your distribution only provides a full OpenCV implementation (and does not offer a distinct package for OpenCV Core). You may also need to change SEQUENTIAL_BLAS_LIB if you don't want to use OpenBLAS.

You may then build the project with the following commands:

$ mkdir build
$ cd build
$ cmake ../quick-adc
$ make -j4 # Build on 4 cores

Usage

List of executables:

  • db_add Add vectors to an existing database
  • db_query Query an existing database (indexed or flat) using the conventional ADC procedure.
  • db_query_4 Query an existing database (indexed of flat) using Quick ADC.
  • flatdb_create Create a flat database (without an inverted index) of vectors
  • indexdb_create1 Create an indexed database of vectors (Step 1)
  • indexdb_create2 Create an indexed database of vectors (Step 2)

All executables display a short help message when they are invoked without arguments:

$ ./db_add 
Usage: db_add [db_file] [base_file]

These executables take input files in .fvecs, .ivecs or .bvecs format. The SIFT1M, GIST1M, Deep1M and SIFT1B datasets used in our experiments all contain a learning set, a base set and a query set in .fvecs or .bvecs format. The ground truth is also provided as an .ivecs file.

Building databases

The Quick ADC project allows building flat (without an inverted index) databases and indexed databases.

Building flat datbases

(1) Learn a Product Quantizer (PQ), or an Optimized Product Quantizer (OPQ)

We do not provide scripts or executables to learn product quantizers or optimized product quantizers. Our executables expect product quantizers or optimized product quantizers to be stored in the file format described in the Product quantizer file formats section.

You may use the Quantizations project to learn product quantizers or optimized product quantizers. To learn a product quantizer, you may use the learnCodebooksPQ function, as follows:

learnCodebooksPQ(
    '../sift/sift_learn.fvecs', # learning set
    128, # dimension of vectors
    8,  # number of sub-quantizers
    256, # number of centroids per sub-quantizer 
    # (8-bit quantizer, 256 centroids)
    100000, # number of vectors in the learning set
    'SIFT1M.8x8.pq.pickle', # output file
    iterCount=50 # number of iterations
)

To learn an optimized product quantizer, you may use the learnCodebookOPQ function, as follows:

learnCodebooksOPQ(
    '../sift/sift_learn.fvecs',
    100000, # number of vectors in the learning set
    128, # dimensionality of vectors
    8, # number of sub-quantizers
    256, # number of centroids per sub-quantizer
    'SIFT1M.8x8.opq.pickle', # output file
    ninit=50 # number of iterations
)

The product quantizer and optimized product quantizer files output by these functions do not match the file format our executable expect. We provide a script to convert to this format:

$ python convert-quantizer.py pq SIFT1M.8x8.pq.pickle SIFT1M.8x8.pq.data
$ python convert-quantizer.py opq SIFT1M.8x8.opq.pickle SIFT1M.8x8.opq.data

(2) Create database

To create the database SIFT1M.8x8.opq.flat.db with the OPQ stored in SIFT1M.8x8.opq.data:

$ ./flatdb_create SIFT1M.8x8.opq.data SIFT1M.8x8.opq.flat.db

(3) Add vectors of the base set to the database

To add vectors of the base set ../sift/sift_base.fvecs to the database SIFT1M.8x8.opq.flat.db:

$ ./db_add SIFT1M.8x8.opq.flat.db ../sift/sift_base.fvecs

Building indexed databases

(1) Build the quantizer for the inverted index (Step 1)

To create an indexed database with K=256 cells using the learning set ../sift/sift_learn.fvecs:

$ ./indexdb_create1 256 ../sift/sift_learn.fvecs \
    SIFT1M.256.empty.index.db SIFT1M.256.residuals.fvecs 
    # inverted index with 256 cells

The database is output to SIFT1M.256.empty.index.db and the residuals are output to SIFT1M.256.residuals.fvecs

(2) Learn a Product Quantizer (PQ), or an Optimized Product Quantizer (OPQ) on the set of residuals

learnCodebooksOPQ(
    'SIFT1M.256.residuals.fvecs',
    100000, # number of vectors in the learning set
    128, # dimensionality of vectors
    8, # number of sub-quantizers
    256, # number of centroids per sub-quantizer
    'SIFT1M.256.8x8.opq.pickle', # output file
    ninit=50 # number of iterations
)

$ python convert-quantizer.py opq SIFT1M.256.8x8.opq.pickle \
    SIFT1M.256.8x8.opq.data

(3) Create the database (Step 2)

To complete the creation of the database SIFT1M.256.empty.index.db with the OPQ SIFT1M.256.8x8.opq.data and output the result to SIFT1M.256.8x8.opq.index.db:

$ ./indexdb_create2 SIFT1M.256.empty.index.db SIFT1M.256.8x8.opq.data \
    SIFT1M.256.8x8.opq.index.db

(4) Add vectors of the base set to the database

$ ./db_add SIFT1M.256.8x8.opq.index.db ../sift/sift_base.fvecs

Querying databases

We provide two executables to query databases:

  • db_query to query databases using the conventional ADC method
  • db_query_4 to query databases using Quick ADC

Both theses executables can be used to query flat databases and indexed databases.

To query the database SIFT1M.8x8.opq.flat.db using the query set ../sift/sift_query.fvecs, and the groundtruth in ../sift/sift_groundtruth.ivecs:

$ ./db_query -r100 -b32 SIFT1M.8x8.opq.flat.db ../sift/sift_query.fvecs ../sift/sift_groundtruth.ivecs
[...]
r,recall,ma,adc_type,index_us,rotate_us,table_us,scan_us
100,0.9419,1,adc,0,1,2,2594

Queries are processed by batches of 32 (-b32), and the Recall@100 is computed (-r100). The command outputs important metrics as CSV values:

r, the r parameter passed on the command line
recall, the Recall@r
ma, the multiple assignement (always 1 for flat databases, may be selected for indexed databases)
adc_type, the ADC method used: adc for the conventional ADC method, and qadc for Quick ADC.
index_us: time spent in the inverted index (microseconds, always 0 for flat databases)
rotate_us: time spent rotating the vector (microseconds)
table_us: time spent computing distance tables (microseconds)
scan_us: time spent scanning short codes (microseconds)

When querying indexed databases, the -m switch can be used to specify the multiple assignement. For instance for a multiple assignement of 24:

$ ./db_query -r100 -b32 -m24 SIFT1M.256.8x8.opq.index.db ../sift/sift_query.fvecs \ 
    ../sift/sift_groundtruth.ivecs
[...]
r,recall,ma,adc_type,index_us,rotate_us,table_us,scan_us
100,0.9646,24,adc,7,12,46,323

The db_query_4 executable can only be used with databases using PQ or OPQ with 4-bit quantizers (16 centroids per quantizer). This is because Quick ADC requires 4-bit quantizers. For instance, to build an indexed database compatible with db_query_4:

learnCodebooksOPQ(
    '/home/fabien/postdoc/pq/build-qadc/SIFT1M.256.residuals.fvecs',
    100000,
    128,
    16,
    16,
    'SIFT1M.256.16x4.opq.pickle',
    ninit=50
)

$ python convert-quantizer.py opq SIFT1M.256.16x4.opq.pickle SIFT1M.256.16x4.opq.data

$ ./indexdb_create2 SIFT1M.256.empty.index.db SIFT1M.256.16x4.opq.data \
    SIFT1M.256.16x4.opq.index.db

$ ./db_add SIFT1M.256.16x4.opq.index.db  ../sift/sift_base.fvecs

This database can then be queried using db_query_4:

$ ./db_query_4 -r100 -m24 -k0.213 -b32 SIFT1M.256.16x4.opq.index.db ../sift/sift_query.fvecs \
    ../sift/sift_groundtruth.ivecs
r,recall,ma,adc_type,keep,index_us,rotate_us,table_us,scan_us
100,0.9426,24,qadc,0.00213,7,13,14,86

The scan time is much lower (86us) when using Quick ADC, than when using the conventional ADC method (323us), as shown in the publication.

Compared to db_query, db_query_4 requires an additional parameter: keep passed via the -k switch, which is the percentage of codes scanned NOT using SIMD in each partition before using Quick ADC.This parameter is linked to the init parameter mentionned in the publication, keep=(init*K)/(ma*N), where K is the number of partitions in the dababase, ma the multiple assignement and N, the totalnumber of codes in the database. In practice, we have found values between keep=0.05% and keep=1% to provide the best accuracy-speed ratio.

Product quantizer file formats

Product quantizers or optimized product quantizers should be stored as binary files, as follows:

Product Quantizer

int32_t dimension; // Dimensionality of vectors
int32_t m; // Number of sub-quantizers
int32_t b; // Number of bits per sub-quantizer
float[m*2^b*dimension/m] codebooks; // Codebooks, stored as a contiguous array

Optimized Product Quantizer

int32_t dimension; // Dimensionality of vectors
int32_t m; // Number of sub-quantizers
int32_t b; // Number of bits per sub-quantizer
float[m*2^b*dimension/m] codebooks; // Codebooks, stored as a contiguous array
float[dimension*dimension] rotation; // Rotation matrix

Notes about the source code

To process queries, db_query and db_query_4 use an instance of an nns_engine (or nns_engine_batch, the only difference between the two is that the nns_engine_batch processes queries by batches). The nns_engine assigns query vectors to partitions (or cells) of the inverted index, and computes distance tables. The nns_engine then uses a "scanner" to scan the short codes in the partitions. The class scanner_simple (used by db_query) is an implementation of the conventional ADC method, while scanner_4 (used by db_query_4) is an implementation of Quick ADC. The scan functions used by scanner_4 are defined in scan_simd.hpp. The current implementation of db_query_4 uses the scan_avx_4 function (which calls AVX intrinsics). We have left an earlier implementation of the scan function named scan_sse_16_4, which uses only SSE, in the scan_simd.hpp file. You may modify db_query_4.cpp to use the older scan_sse_16_4 instead of scan_avx_4.

License

This project is licensed under the terms of BSD 3-clause Clear license. by downloading this program, you commit to comply with the license as stated in the LICENSE.md file.