154
Applications in Computer Vision
where f(·) is the nearest-neighbor interpolation. Therefore, we formulate the learning ob-
jective for feature refinement as
arg min
aL,a∗
H
max
WD L F
Adv(aL, a∗
H, WD) + L F
MSE(aL, a∗
H) ∀i ∈N,
(6.13)
where L K
Adv(wi, bwi, αi, WD) is the adversarial loss as
L F
Adv(aL, a∗
H, WD) = log(D(a∗
H; WD)) + log(1 −D(aL; WD)),
(6.14)
where D(·) consists of several basic blocks, each with a fully connected layer and a
LeakyReLU layer. In addition, we adopt several discriminators to refine the features during
the binarization training process.
Moreover, L F
MSE(wi, bwi, αi) is the feature loss between the low-level and high-level
features, which is expressed by MSE as
L F
MSE(aL, a∗
H) = μ
2 ||aL −a∗
H||2
2,
(6.15)
where μ is a balancing hyperparameter.
6.2.4
Optimization
For a specific task, the conventional problem-dependent loss LS e.g., the cross entropy, is
considered, thus the learning objective is defined as
arg
min
wi,αi,pi = LS(wi, αi, pi) ∀i ∈N,
(6.16)
where pi denotes the other parameters of BNN, e.g, parameters of BN and PReLU. There-
fore, the general learning objective of BiRe-ID is Eqs. 6.79, 6.13, and 6.16. For each convo-
lutional layer, we sequentially update wi, αi and pi.
Updating wi: Consider δwi as the gradient of the real-valued kernels wi. Thus,
δwi = ∂L
∂wi
= ∂LS
∂wi
+ ∂L K
Adv
∂wi
+ ∂L F
Adv
∂wi
+ ∂L K
MSE
∂wi
+ ∂L F
MSE
∂wi
.
(6.17)
During the backpropagation of softmax loss LS(wi, αi, pi), the gradients go to bwi first
and then to wi. Thus, we formulate is as
∂LS
∂wi
= ∂LS
∂bwi
∂bwi
∂wi
,
(6.18)
where
∂bwi
∂wi
=
⎧
⎨
⎩
1.2 + 2wi,
−1 ≤wi < 0,
2 −2wi,
0 ≤wi < 1,
10,
otherwise,
(6.19)
which is an approximation of the 2×dirac-delta function [159]. Furthermore,
∂L K
Adv
∂wi
=
1
D(wi; WD)
∂D
∂wi
.
(6.20)
∂L K
MSE
∂wi
= λ(wi −αi ◦bwi) ◦αi,
(6.21)
∂L F
Adv
∂wi
= −
1
1 −D(ai; WD)
∂D
∂ai
∂ai
∂wi
I(i ∈L),
(6.22)