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Benchmarking USearch

Hyper-parameters

All major HNSW implementation share an identical list of hyper-parameters:

  • connectivity (often called M),
  • expansion on additions (often called efConstruction),
  • expansion on search (often called ef).

The default values vary drastically.

Library Connectivity EF @ A EF @ S
hnswlib 16 200 10
FAISS 32 40 16
USearch 16 128 64

Below are the performance numbers for a benchmark running on the 64 cores of AWS c7g.metal "Graviton 3"-based instances. The main columns are:

  • Add: Number of insertion Queries Per Second.
  • Search: Number search Queries Per Second.
  • Recall @1: How often does approximate search yield the exact best match?

Different "connectivity"

Vectors Connectivity EF @ A EF @ S Add, QPS Search, QPS Recall @1
f32 x256 16 128 64 75'640 131'654 99.3%
f32 x256 12 128 64 81'747 149'728 99.0%
f32 x256 32 128 64 64'368 104'050 99.4%

Different "expansion factors"

Vectors Connectivity EF @ A EF @ S Add, QPS Search, QPS Recall @1
f32 x256 16 128 64 75'640 131'654 99.3%
f32 x256 16 64 32 128'644 228'422 97.2%
f32 x256 16 256 128 39'981 69'065 99.2%

Different vectors "quantization"

Vectors Connectivity EF @ A EF @ S Add, QPS Search, QPS Recall @1
f32 x256 16 128 64 87'995 171'856 99.1%
f16 x256 16 128 64 87'270 153'788 98.4%
f16 x256 ✳️ 16 128 64 71'454 132'673 98.4%
i8 x256 16 128 64 115'923 274'653 98.9%

As seen on the chart, for f16 quantization, performance may differ depending on native hardware support for that numeric type. Also worth noting, 8-bit quantization results in almost no quantization loss and may perform better than f16.

Utilities

Within this repository you will find two commonly used utilities:

  • cpp/bench.cpp the produces the bench_cpp binary for broad USearch benchmarks.
  • python/bench.py and python/bench.ipynb for interactive charts against FAISS.

To achieve best highest results we suggest compiling locally for the target architecture.

cmake -USEARCH_BUILD_BENCH_CPP=1 -DUSEARCH_BUILD_TEST_C=1 -DUSEARCH_USE_OPENMP=1 -DUSEARCH_USE_SIMSIMD=1 -DCMAKE_BUILD_TYPE=RelWithDebInfo -B build_profile
cmake --build build_profile --config RelWithDebInfo -j
build_profile/bench_cpp --help

Which would print the following instructions.

SYNOPSIS
        build_profile/bench_cpp [--vectors <path>] [--queries <path>] [--neighbors <path>] [-b] [-j
                                <integer>] [-c <integer>] [--expansion-add <integer>]
                                [--expansion-search <integer>] [--native|--f16quant|--i8quant]
                                [--ip|--l2sq|--cos|--haversine] [-h]

OPTIONS
        --vectors <path>
                    .fbin file path to construct the index

        --queries <path>
                    .fbin file path to query the index

        --neighbors <path>
                    .ibin file path with ground truth

        -b, --big   Will switch to uint40_t for neighbors lists with over 4B entries
        -j, --threads <integer>
                    Uses all available cores by default

        -c, --connectivity <integer>
                    Index granularity

        --expansion-add <integer>
                    Affects indexing depth

        --expansion-search <integer>
                    Affects search depth

        --native    Use raw templates instead of type-punned classes
        --f16quant  Enable `f16_t` quantization
        --i8quant   Enable `int8_t` quantization
        --ip        Choose Inner Product metric
        --l2sq      Choose L2 Euclidean metric
        --cos       Choose Angular metric
        --haversine Choose Haversine metric
        -h, --help  Print this help information on this tool and exit

Here is an example of running the C++ benchmark:

build_profile/bench_cpp \
    --vectors datasets/wiki_1M/base.1M.fbin \
    --queries datasets/wiki_1M/query.public.100K.fbin \
    --neighbors datasets/wiki_1M/groundtruth.public.100K.ibin

build_profile/bench_cpp \
    --vectors datasets/t2i_1B/base.1B.fbin \
    --queries datasets/t2i_1B/query.public.100K.fbin \
    --neighbors datasets/t2i_1B/groundtruth.public.100K.ibin \
    --output datasets/t2i_1B/index.usearch \
    --cos

Optional parameters include connectivity, expansion_add, expansion_search.

For Python, jut open the Jupyter Notebook and start playing around.

Datasets

BigANN benchmark is a good starting point, if you are searching for large collections of high-dimensional vectors. Those often come with precomputed ground-truth neighbors, which is handy for recall evaluation.

Dataset Scalar Type Dimensions Metric Size
Unum UForm Creative Captions float32 256 IP 3 GB
Unum UForm Wiki float32 256 IP 1 GB
Yandex Text-to-Image Sample float32 200 Cos 1 GB
Microsoft SPACEV int8 100 L2 93 GB
Microsoft Turing-ANNS float32 100 L2 373 GB
Yandex Deep1B float32 96 L2 358 GB
Yandex Text-to-Image float32 200 Cos 750 GB
ViT-L/12 LAION float32 2048 Cos 2 - 10 TB

Luckily, smaller samples of those datasets are available.

Unum UForm Wiki

mkdir -p datasets/wiki_1M/ && \
    wget -nc https://huggingface.co/datasets/unum-cloud/ann-wiki-1m/resolve/main/base.1M.fbin -P datasets/wiki_1M/ &&
    wget -nc https://huggingface.co/datasets/unum-cloud/ann-wiki-1m/resolve/main/query.public.100K.fbin -P datasets/wiki_1M/ &&
    wget -nc https://huggingface.co/datasets/unum-cloud/ann-wiki-1m/resolve/main/groundtruth.public.100K.ibin -P datasets/wiki_1M/

Yandex Text-to-Image

mkdir -p datasets/t2i_1B/ && \
    wget -nc https://storage.yandexcloud.net/yandex-research/ann-datasets/T2I/base.1B.fbin -P datasets/t2i_1B/ &&
    wget -nc https://storage.yandexcloud.net/yandex-research/ann-datasets/T2I/base.1M.fbin -P datasets/t2i_1B/ &&
    wget -nc https://storage.yandexcloud.net/yandex-research/ann-datasets/T2I/query.public.100K.fbin -P datasets/t2i_1B/ &&
    wget -nc https://storage.yandexcloud.net/yandex-research/ann-datasets/T2I/groundtruth.public.100K.ibin -P datasets/t2i_1B/

Yandex Deep1B

mkdir -p datasets/deep_1B/ && \
    wget -nc https://storage.yandexcloud.net/yandex-research/ann-datasets/DEEP/base.1B.fbin -P datasets/deep_1B/ &&
    wget -nc https://storage.yandexcloud.net/yandex-research/ann-datasets/DEEP/base.10M.fbin -P datasets/deep_1B/ &&
    wget -nc https://storage.yandexcloud.net/yandex-research/ann-datasets/DEEP/query.public.10K.fbin -P datasets/deep_1B/ &&
    wget -nc https://storage.yandexcloud.net/yandex-research/ann-datasets/DEEP/groundtruth.public.10K.ibin -P datasets/deep_1B/

Arxiv with E5

mkdir -p datasets/arxiv_2M/ && \
    wget -nc https://huggingface.co/datasets/unum-cloud/ann-arxiv-2m/resolve/main/abstract.e5-base-v2.fbin -P datasets/arxiv_2M/ &&
    wget -nc https://huggingface.co/datasets/unum-cloud/ann-arxiv-2m/resolve/main/title.e5-base-v2.fbin -P datasets/arxiv_2M/

Profiling

With perf:

# Pass environment variables with `-E`, and `-d` for details
sudo -E perf stat -d build_profile/bench_cpp ...
sudo -E perf mem -d build_profile/bench_cpp ...
# Sample on-CPU functions for the specified command, at 1 Kilo Hertz:
sudo -E perf record -F 1000 build_profile/bench_cpp ...
perf record -d -e arm_spe// -- build_profile/bench_cpp ..

Caches

sudo perf stat -e 'faults,dTLB-loads,dTLB-load-misses,cache-misses,cache-references' build_profile/bench_cpp ...

Typical output on a 1M vectors dataset is:

            255426      faults                                                      
      305988813388      dTLB-loads                                                  
        8845723783      dTLB-load-misses          #    2.89% of all dTLB cache accesses
       20094264206      cache-misses              #    6.567 % of all cache refs    
      305988812745      cache-references                                            

       8.285148010 seconds time elapsed

     500.705967000 seconds user
       1.371118000 seconds sys

If you notice problems and the stalls are closer to 90%, it might be a good reason to consider enabling Huge Pages and tuning allocations alignment. To enable Huge Pages:

sudo cat /proc/sys/vm/nr_hugepages
sudo sysctl -w vm.nr_hugepages=2048
sudo reboot
sudo cat /proc/sys/vm/nr_hugepages