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belongs to as follows,

C MS (x

S )







p y

= 1|xi

p y

= 2|xi

p y

= K|xi







=1 e

u j







eu1

eu2

euK







(2)

where u j

= MS (xi

S ) j is the j-th value of MS (x

S ),

=1 e

u j is a normalized term, and p y

= j|MS (xi

S )

represent the distribution of the class j ∈ {1, 2, ..., K} given the input MS (x

S ). Give the source

domain data DS , the parameters of the source feature extractor MS can be derived by maximizing

the following supervised loss,

max

Lcls(DS )

1{y

S = j} logC MS (x

S )

(3)

where 1{yi

S = j

} is an indicator function, whose value is 1 if yi

S = j, otherwise is 0.

Target feature extractor MT . Based on ”How to parametrize the target feature extractor”, the

approaches of most published adversarial adaptation works can be summarized into two cate-

gories: symmetric transformation and asymmetric transformation. For many prior symmetric

transformation methods [39, 40], all layers are constrained, thus enforcing exact source and tar-

get mapping consistency. Although learning a symmetric transformation can reduce the number

of parameters in the model, this may make the optimization poorly conditioned, since the same

network must handle samples from two separate domains [41]. The intuitive idea behind the

asymmetric transformation is to constrain a subset of the layers. Rozantsev et al. [42] showed

that partially shared weights can lead to e

ﬀective adaptation in both supervised and unsupervised

settings. We choose to learn parameters of the target feature extractor MT by partially untying

layers between source and target mappings. As shown in Figure 1, solid lines indicate tied layers,

and dashed lines indicate adaptive layers. Given that the target domain is unlabeled, we initialize

the parameters of the target feature extractor MT with the source feature extractor MS .

Domain discriminator D. For an instance xi

S (resp. x

T ), the output feature vector MS (x

S ) (resp.

MT (x

T )) mapped by the feature extractor MS (resp. MT ), pseudo-labeled with a domain label

= 0 (resp. di = 1), is the input of the domain discriminator D. The domain discriminator

is a multi-layer perceptron (MLP), which is composed of several fully-connected layers (e.g.

input →

500 → 500 → 1). The domain discriminator is in the binary classiﬁcation setting. With

the logistic regression model, its loss takes the form below,

max

Ladv

D =

logD

(MS (x

S )) +

log

(1 − D(MT (x

T )) .

(4)

In order to obtain domain-invariant features, we seek the parameters of the target feature

extractor MT to fool the domain discriminator D by maximizing the following loss function

Ladv

MT with inverted domain labels [36],

max

Ladv

MT =

logD

(MT (x

T )) .

(5)

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