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Gerard Moreno-Torres Bertran
db9ba35118
Summary: Pull Request resolved: https://github.com/facebookresearch/faiss/pull/4856 Using a Hadamard transformation is very similar to using a random rotation matrix, but we can calculate it in `d log d` time instead of `d ^ 2`. I initially started exploring this using a fast fourier transform which does outperform a random rotation, but a Hadamard transformation has the same computation complexity as FFT and in practice it is much easier to implement. Also because it is an orthonormal transformation, the recall is identical to a random rotation matrix. I added a benchmark to compare both. Reviewed By: mdouze Differential Revision: D94658424 fbshipit-source-id: bb2f9dc0ab5a41ce58874a1e72a3e85c22e58ea2
91 lines
2.6 KiB
Python
91 lines
2.6 KiB
Python
# Copyright (c) Meta Platforms, Inc. and affiliates.
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#
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# This source code is licensed under the MIT license found in the
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# LICENSE file in the root directory of this source tree.
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"""Benchmark HadamardRotation (HD3 FWHT) vs RandomRotationMatrix (BLAS sgemm).
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Measures:
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1. Speed: wall-clock time for transform.apply(x)
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2. Recall@1: nearest-neighbor recall after pre-transform + Flat index
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"""
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import faiss
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import numpy as np
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import time
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n = 10000
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nq = 200
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n_trials = 15
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print(f'n={n} vectors, nq={nq} queries, {n_trials} speed trials')
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# --- Speed benchmark ---
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print('\n=== Speed ===')
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print(f'{"dim":>6s} {"HR (ms)":>10s} {"RRM (ms)":>10s} {"speedup":>8s}')
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print('-' * 42)
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dims = [64, 128, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192]
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for d in dims:
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np.random.seed(42)
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x = np.random.randn(n, d).astype('float32')
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hr = faiss.HadamardRotation(d, 42)
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hr.apply(x[:100]) # warmup
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times_hr = []
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for _ in range(n_trials):
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t0 = time.perf_counter()
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hr.apply(x)
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t1 = time.perf_counter()
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times_hr.append((t1 - t0) * 1000)
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hr_ms = sorted(times_hr)[1]
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rr = faiss.RandomRotationMatrix(d, d)
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rr.train(x[:100])
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rr.apply(x[:100]) # warmup
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times_rr = []
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for _ in range(n_trials):
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t0 = time.perf_counter()
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rr.apply(x)
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t1 = time.perf_counter()
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times_rr.append((t1 - t0) * 1000)
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rr_ms = sorted(times_rr)[1]
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speedup = rr_ms / hr_ms
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print(f'{d:6d} {hr_ms:10.2f} {rr_ms:10.2f} {speedup:7.1f}x')
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# --- Recall benchmark with IVF (where rotation actually matters) ---
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print(f'\n=== Recall@1 with IVF (L2, n={n}, nq={nq}, k=1) ===')
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print(f'{"dim":>6s} {"HR R@1":>8s} {"RRM R@1":>8s} {"none R@1":>8s}')
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print('-' * 40)
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for d in [64, 128, 256, 768, 1024, 2048, 4096]:
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np.random.seed(42)
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xb = np.random.randn(n, d).astype('float32')
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xq = np.random.randn(nq, d).astype('float32')
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# Ground truth (brute force, no transform)
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gt_index = faiss.IndexFlatL2(d)
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gt_index.add(xb)
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_, gt_I = gt_index.search(xq, 1)
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nlist = 64
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recalls = {}
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for label, factory_str in [
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('HR', f'HR,IVF{nlist},Flat'),
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('RRM', f'RR,IVF{nlist},Flat'),
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('none', f'IVF{nlist},Flat'),
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]:
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index = faiss.index_factory(d, factory_str)
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index.train(xb)
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index.add(xb)
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faiss.extract_index_ivf(index).nprobe = 8
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_, I = index.search(xq, 1)
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recall = (I[:, 0] == gt_I[:, 0]).mean()
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recalls[label] = recall
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print(
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f'{d:6d} {recalls["HR"]:8.4f}'
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f' {recalls["RRM"]:8.4f} {recalls["none"]:8.4f}'
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)
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