/
local_response_normalization.py
164 lines (136 loc) · 5.39 KB
/
local_response_normalization.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
import numpy
import six
from chainer.backends import cuda
from chainer.backends import intel64
from chainer import function
from chainer.utils import type_check
def _cu_conv_sum(y, x, n):
# Convolutional sum
# TODO(beam2d): Use scan computation
rdim = x.size // (x.shape[0] * x.shape[1])
cuda.elementwise(
'raw T x, int32 rdim, int32 N, int32 n_', 'raw T y',
'''
int half_n = n_ / 2;
int offset = i / rdim * N * rdim + i % rdim;
float sum_part = 0;
for (int j = 0; j < N + half_n; ++j) {
if (j < N) {
sum_part += x[offset + j * rdim];
}
if (j >= n_) {
sum_part -= x[offset + (j - n_) * rdim];
}
if (j >= half_n) {
y[offset + (j - half_n) * rdim] = sum_part;
}
}
''', 'lrn_conv_sum')(x, rdim, x.shape[1], n, y,
size=x.shape[0] * rdim)
class LocalResponseNormalization(function.Function):
"""Cross-channel normalization function used in AlexNet."""
_use_ideep = False
def __init__(self, n=5, k=2, alpha=1e-4, beta=.75):
self.n = n
self.k = k
self.alpha = alpha
self.beta = beta
def check_type_forward(self, in_types):
type_check.expect(in_types.size() == 1)
x_type, = in_types
type_check.expect(
x_type.dtype.kind == 'f',
x_type.ndim >= 2,
)
def forward_cpu(self, x):
if (intel64.should_use_ideep('>=auto')
and intel64.inputs_all_ready(x, (4,))):
self._use_ideep = True
return self._forward_ideep(x)
half_n = self.n // 2
x2 = numpy.square(x[0])
sum_part = x2.copy()
for i in six.moves.range(1, half_n + 1):
sum_part[:, i:] += x2[:, :-i]
sum_part[:, :-i] += x2[:, i:]
self.unit_scale = self.k + self.alpha * sum_part
self.scale = self.unit_scale ** -self.beta
self.y = x[0] * self.scale
return self.y,
def _forward_ideep(self, x):
param = intel64.ideep.localResponseNormalizationParam(
self.n, self.k, self.n * self.alpha, self.beta,
intel64.ideep.localResponseNormalizationParam.lrn_across_channels)
y, indexes = intel64.ideep.localResponseNormalization.Forward(
intel64.ideep.array(x[0]), param)
self.y = y
self.indexes = indexes
return self.y,
def backward_cpu(self, x, gy):
if self._use_ideep:
return self._backward_ideep(x, gy)
half_n = self.n // 2
summand = self.y * gy[0] / self.unit_scale
sum_part = summand.copy()
for i in six.moves.range(1, half_n + 1):
sum_part[:, i:] += summand[:, :-i]
sum_part[:, :-i] += summand[:, i:]
gx = gy[0] * self.scale - 2 * self.alpha * self.beta * x[0] * sum_part
return gx,
def _backward_ideep(self, x, gy):
param = intel64.ideep.localResponseNormalizationParam(
self.n, self.k, self.n * self.alpha, self.beta,
intel64.ideep.localResponseNormalizationParam.lrn_across_channels
)
gx = intel64.ideep.localResponseNormalization.Backward(
intel64.ideep.array(x[0]),
intel64.ideep.array(gy[0]),
self.indexes,
param)
return gx,
def forward_gpu(self, x):
self.y = cuda.cupy.square(x[0]) # temporary
self.scale = cuda.cupy.empty_like(self.y)
_cu_conv_sum(self.scale, self.y, self.n)
cuda.elementwise(
'T x, T k, T alpha, T beta',
'T y, T scale',
'''scale = k + alpha * scale;
y = x * pow(scale, -beta);''',
'lrn_fwd')(x[0], self.k, self.alpha, self.beta,
self.y, self.scale)
return self.y,
def backward_gpu(self, x, gy):
summand = cuda.elementwise(
'T scale, T y, T gy', 'T summand',
'summand = y * gy / scale',
'lrn_bwd_summand')(self.scale, self.y, gy[0])
gx = cuda.cupy.empty_like(x[0])
_cu_conv_sum(gx, summand, self.n)
cuda.elementwise(
' T x, T gy, T scale, T beta, T coeff', 'T gx',
'gx = pow(scale, -beta) * gy - coeff * x * gx',
'lrn_bwd')(x[0], gy[0], self.scale,
self.beta, 2 * self.alpha * self.beta, gx)
return gx,
def local_response_normalization(x, n=5, k=2, alpha=1e-4, beta=.75):
"""Local response normalization across neighboring channels.
This function implements normalization across channels. Let :math:`x` an
input image with :math:`N` channels. Then, this function computes an output
image :math:`y` by following formula:
.. math::
y_i = {x_i \\over \\left( k + \\
\\alpha \\sum_{j=\\max{1, i - n/2}}^{\\min{N, i + n/2}} \\
x_j^2 \\right)^\\beta}.
Args:
x (Variable): Input variable.
n (int): Normalization window width.
k (float): Smoothing parameter.
alpha (float): Normalizer scaling parameter.
beta (float): Normalizer power parameter.
Returns:
Variable: Output variable.
See: Section 3.3 of `ImageNet Classification with Deep Convolutional \\
Neural Networks <https://www.cs.toronto.edu/~fritz/absps/imagenet.pdf>`_
"""
return LocalResponseNormalization(n, k, alpha, beta)(x)