(12)

(13)

(14)

(15)

The overall back-translation loss is given as

Note that Lsrc
consistency loss proposed for unpaired image-to-image translation Zhu et al. [2017].

Lback-translation = Lsrc2tgt
(16)
spec( ˆSt, St), which is a part of Lback-translation, can be viewed as a cycle

back-translation + Ltgt2src

spec( ˆSs, Ss) + Lsrc

back-translation.

4.2.4 Overall Loss

For the reconstruction phase, the loss is given by

Lrecon-phase = Lrecon + LMUSE(Ss) + LMUSE(St).

(17)
In the back-translation phase, the optimization of both the back-translation loss, represented as
Lback-translation, and the reconstruction loss, represented as Lrecon-phase, is carried out to ensure that the
encoder output produces a multilingual embedding. The overall loss is given by

LBT-phase = Lback-translation + Lrecon-phase.

(18)

5 Experiments and Results
Translatotron3