def instancenorm_4(x):
"""
Identify the pattern:
y = x * [gamma * rsqrt(variance + eps)] + (beta - mean * [gamma * rsqrt(variance + eps)])
This pattern corresponds to, should be fused as instance_norm.
All of the following must be satisty:
1) Input is rank 4 tensor
2) Reduce operates on spatial dimensions axes=[-2, -1], or axes=[-3, -2] (a
channel first to channel last transpose would be inserted in such case)
3) Gamma and beta are both shape (C,) after squeeze, where C is number of channels
|-----------|
| V
|------> mul_square1 -------------> sum1 -----> mul_mean1
| |
| V
x --> main_reduce --> mul_mean ==> mul_square --> sub_variance --> add_eps --> rsqrt
| | |
| | V
| | mul_gamma
| | |
| | |----------------|
| | | V
| |--------------------------------------------+-------------> mul2
| V |
|------------------------------------------------------------------> mul1 |
| V
| sub_beta --> add --> [...]
| ^
|---------------------------|
"""
mul_square1 = mb.mul(x=x, y=x, name="mul_square1")
main_reduce = mb.reduce_sum(x=x,
axes=[2, 3],
keep_dims=True,
name="main_reduce")
mul_mean = mb.mul(x=main_reduce, y=3.3333334e-05,
name="mul_mean") # dummy value here
mul_square = mb.mul(x=mul_mean, y=mul_mean, name="mul_square")
sum1 = mb.reduce_sum(x=mul_square1,
axes=[2, 3],
keep_dims=True,
name="sum1")
mul_mean1 = mb.mul(x=sum1, y=8.333333e-06,
name="mul_mean1") # dummy value here
sub_variance = mb.sub(x=mul_mean1, y=mul_square, name="sub_variance")
add_epsilon = mb.add(x=sub_variance, y=1e-5,
name="add_epsilon") # epsilon
rsqrt = mb.rsqrt(x=add_epsilon, name="rsqrt")
mul_gamma = mb.mul(x=rsqrt,
y=np.random.rand(1, 5, 1, 1),
name="mul_gamma")
mul1 = mb.mul(x=mul_gamma, y=x, name="mul1")
mul2 = mb.mul(x=mul_mean, y=mul_gamma, name="mul2")
sub_beta = mb.sub(x=np.random.rand(1, 5, 1, 1),
y=mul2,
name="sub_beta")
add = mb.add(x=mul1, y=sub_beta, name="add")
return add
def instancenorm_3(x):
"""
Detect InstanceNorm pattern in TensorFlow-Addons.
This pattern corresponds to, should be fused as instance_norm.
All of the following must be satisty:
1) Input is rank 4 tensor
2) Reduce operates on spatial dimensions axes=[-2, -1], or axes=[-3, -2] (a
channel first to channel last transpose would be inserted in such case)
3) Gamma and beta are absent. Default values for gamma and beta would be used.
|-------------------------------------------------------|
| |
| V
x --> main_reduce square --> mean1 --> add_eps --> rsqrt --> mul2 --> mul_sub
| | ^ | |
| V | | |
| --> sub -----------| | |
| V V
|--------------------------------------------------> mul1 -------------> add --> ...
"""
main_reduce = mb.reduce_mean(x=x, axes=[2, 3], keep_dims=True, name="main_reduce")
sub = mb.sub(x=x, y=main_reduce, name="sub")
square = mb.square(x=sub, name="square")
mean1 = mb.reduce_mean(x=square, axes=[2, 3], keep_dims=True, name="mean1")
add_epsilon = mb.add(x=mean1, y=1e-5, name="add_epsilon") # epsilon
rsqrt = mb.rsqrt(x=add_epsilon, name="rsqrt")
mul1 = mb.mul(x=rsqrt, y=x, name="mul1")
mul2 = mb.mul(x=main_reduce, y=rsqrt, name="mul2")
mul_sub = mb.mul(x=mul2, y=-1, name="mul_sub")
add = mb.add(x=mul1, y=mul_sub, name="add")
return add
def instancenorm_or_layernorm(x):
"""
Identify the pattern:
y = gamma * (x - mean) / sqrt(variance + epsilon) + beta
y = x * [gamma * rsqrt(variance + eps)] + (beta - mean * [gamma * rsqrt(variance + eps)])
x --> main_reduce --> sub --> square --> reduce_mean_2 --> add(epsilon) --> rsqrt
| | ^ |
| | | V
|----------------------- mul (gamma)
| | |
| | --------|---------
| | | |
| | | V
| |------------------------------------------------------------------> mul_3
| | |
| V |
|----------------------------------------------------------------> mul_2 |
| V
| sub (beta) --> add_2 --> [...]
| ^
|-------------------------------
This pattern corresponds to either layer_norm or instance_norm.
It is instance_norm if all of the following are true:
- input is rank 4
- axes of reduce_mean is [-2, -1] or [-3, -2]
(when [-3, -2], a channel first to channel last transpose would be inserted)
- gamma and beta are rank 1, after squeeze
It is layer_norm if all of the following are true:
- axes is either [-1] or [-1, -2] or [-1, -2, -3] and so on
- rank of gamma and beta is equal to the length of the axes
"""
main_reduce = mb.reduce_mean(x=x,
axes=[2, 3],
keep_dims=True,
name="main_reduce")
sub = mb.sub(x=x, y=main_reduce, name="sub")
square = mb.square(x=sub, name="square")
reduce_mean_2 = mb.reduce_mean(x=square,
axes=[2, 3],
keep_dims=True,
name="reduce_mean_2")
add_epsilon = mb.add(x=reduce_mean_2, y=1e-5, name="add_epsilon")
rsqrt = mb.rsqrt(x=add_epsilon, epsilon=1e-12, name="rsqrt")
mul_gamma = mb.mul(x=rsqrt,
y=np.random.rand(1, 5, 1, 1),
name="mul_gamma")
mul_2 = mb.mul(x=x, y=mul_gamma, name="mul_2")
mul_3 = mb.mul(x=main_reduce, y=mul_gamma, name="mul_3")
sub_beta = mb.sub(x=np.random.rand(1, 5, 1, 1),
y=mul_3,
name="sub_beta")
add_2 = mb.add(x=sub_beta, y=mul_2, name="add_2")
return add_2
