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# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
#
# This source code is licensed under the BSD license found in the
# LICENSE file in the root directory of this source tree.
import math
import pytest
import torch
from xformers.components.attention import FavorAttention, ScaledDotProduct
from xformers.components.attention.feature_maps import (
FeatureMapType,
NormDistribution,
SMHyperbolic,
SMOrf,
SMReg,
)
_device = torch.device("cuda") if torch.cuda.is_available() else torch.device("cpu")
@pytest.mark.parametrize("features", [SMOrf, SMHyperbolic, SMReg])
def test_random_matrix(features):
torch.random.manual_seed(0)
DRAWS = 100
DIM = 10
for _ in range(DRAWS):
q = features._get_random_ortho_matrix(
1, DIM, device=_device, norm_distribution=NormDistribution.Xi
).squeeze(0)
# Check that the matrix is indeed orthonormal
torch.allclose(
torch.diag(q @ q.transpose(0, 1)),
torch.diag(torch.ones(10, device=_device)),
)
# Check that the row norm is in the right ballpark (sqrt(dim))
assert abs(torch.mean(torch.norm(q, dim=1)).item() - math.sqrt(DIM)) < 1.0
def _plot_distribution(ortho_feature_map):
# Debug helper, check the uniformity of the random matrix draws
DRAWS = 1000
DIM = 50
q = ortho_feature_map._get_random_ortho_matrix(DRAWS, DIM, device=_device)
x, y = [], []
for qq in q:
# For every matrix, look at the real and imaginary eigen value
e = torch.linalg.eigvals(qq)
x.append(e.real)
y.append(e.imag)
# Ideally the repartition of the real and imaginary eigenvalues
# should build a circle in the complex plane
import matplotlib.pyplot as plt
import seaborn as sns
sns.kdeplot(x=torch.cat(x).cpu().numpy(), y=torch.cat(y).cpu().numpy())
plt.axis("equal")
plt.savefig("kde.png")
def _get_rng_data(device):
emb = 10
batch_size = 2
seq_len = 20
num_heads = 1
shape = (batch_size * num_heads, seq_len, emb)
return torch.randn(shape, device=device)
def test_feature_map_shape():
# Check the delayed initialization of the feature map
nb_random_features = 1000
batch = _get_rng_data(_device)
att = FavorAttention(
dropout=0.0,
dim_features=nb_random_features,
feature_map_type=FeatureMapType.SMOrf,
)
_ = att(batch, batch, batch)
assert att.feature_map.features.shape[0] == batch.shape[-1]
assert att.feature_map.features.shape[1] == nb_random_features
def test_feature_map_redraw():
# Check the delayed initialization of the feature map
nb_random_features = 1000
batch = _get_rng_data(_device)
def check(should_redraw: bool):
att = FavorAttention(
dropout=0.0,
dim_features=nb_random_features,
feature_map_type=FeatureMapType.SMOrf,
iter_before_redraw=1 if should_redraw else 100,
)
v0 = att(batch, batch, batch)
assert att.feature_map is not None
f0 = att.feature_map.features
v1 = att(batch, batch, batch)
f1 = att.feature_map.features
# There should not have been a redraw after v0
assert should_redraw != torch.allclose(v0, v1)
assert should_redraw != torch.allclose(f0, f1) # type: ignore
check(should_redraw=True)
check(should_redraw=False)
@pytest.mark.parametrize("feature", ["sm_orf", "sm_hyp", "sm_reg"])
@pytest.mark.parametrize("causal", [True, False])
@pytest.mark.parametrize("normalize_inputs", [True, False])
@pytest.mark.parametrize("device", [_device])
def test_favor_approximation_accuracy(feature, causal, normalize_inputs, device):
# Run two attentions in parallel, the normal scaled dot product and the favor approximation
torch.random.manual_seed(0)
query, key, value = (
_get_rng_data(device),
_get_rng_data(device),
_get_rng_data(device),
)
for x in (query, key, value):
x.requires_grad = True
# Build the two attention heads
sdp_attention = ScaledDotProduct(dropout=0.0, causal=causal).to(device)
approx_attention = FavorAttention(
dropout=0.0,
causal=causal,
dim_head=10,
feature_map_type=FeatureMapType(feature),
normalize_inputs=normalize_inputs,
).to(device)
with torch.cuda.amp.autocast(enabled=_device.type == "cuda"):
standard_attention_result = sdp_attention(query, key, value)
approx_attention_result = approx_attention(query, key, value)
mismatch = torch.mean(
(standard_attention_result - approx_attention_result) ** 2
).item()
if causal:
# FIXME(@lefaudeux) the causal case seems significantly worse, not obvious why,
# could be worth investigating
assert mismatch < 0.6
else:
assert mismatch < 0.23
# Check trainability
torch.sum(approx_attention_result).backward()
if __name__ == "__main__":
_plot_distribution(SMOrf)
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