# Bootstrapped SSL CycleGAN for Asymmetric Domain Transfer
## 3 Proposed Approach
### Improving the Learning Process by BTS Strategy  
As the second part of the proposed learning procedure, we employ the bootstrapping (BTS) strategy based on the internal structures already available in the CycleGAN model. Since the domain \(\mathcal{X}\) is assumed to be scarce, during the training discriminator \(D_{X}\) at its disposal has a significantly smaller pool of unlabeled training samples in comparison to the discriminator \(D_{Y}\) in the domain \(\mathcal{Y}\). Therefore, the aim of the proposed BTS strategy is to overcome this imbalance, by artificially expanding the size of the unlabeled training pool of the discriminator \(D_{X}\). This is illustrated in the left part of Figure 3.  
This is achieved by exploiting the already learned mapping \(F\), shown in the right part of Figure 1, i.e., the GAN implementing the generator function \(G_{Y\to X}\). Under the term \"already learned\", it is assumed that in the initial phase of the training procedure, parameters of the CycleGAN model are first initially optimized for some time using the previously described SSL strategy from Section 3.1. Only after this \"initial training\" phase, the \(G_{Y\to X}\) structure from the CycleGAN model should be considered as reliable enough to be used as the bootstrapping data sampler for the training pool of the discriminator \(D_{X}\) residing in the scarce domain \(\mathcal{X}\). Of course, the decribed BTS strategy could also be applied independently from the SSL one, but in the assumed scarce \(\mathcal{X}\) scenarios such approach would not result in the same level of performance, as in the \"SSL+BTS\" case, when these two strategies are synergistically combined together. The only requirement is that semi-supervision is feasible, i.e., that there exists a small amount of paired data in  
Figure 3: Bootstrapping of the statistics of the discriminator \(D_{X}\) in the scarce domain \(\mathcal{X}\), by adding a set of novel examples \(X_{BTS}\) to the original pool of unlabeled training data \(X\). Bootstrapped samples are randomly generated by \(G_{Y\to X}\). set \(\mathcal{P}_{data}\) with \(M_{SSL}\) matched samples from both domains, as described in Section 3.1 and illustrated in Figure 2.  
BTS of the \(D_{X}\)'s training pool, i.e., BTS of its statistics, is periodically repeated during the whole learning procedure in order to exploit the improved versions of the utilized generator \(G_{Y\to X}\) each time. Furthermore, available set of paired, i.e., labeled samples \(\mathcal{P}_{data}\) is used alongside the larger unlabeled training sets \(X\) and \(Y\), from both \(\mathcal{X}\) and \(\mathcal{Y}\) domains, during the whole training procedure. This means that even after the initial SSL is already accomplished, i.e., after the proposed BTS strategy is invoked for the first time during the training, \(\mathcal{P}_{data}\) samples are continued to be used in the SSL objective, Equation (12). In such a way, the initial constraints that are expressing the closeness between the \"transformed\" and the \"true\" samples in Figure 2, i.e., expressing the quality of generators \(G_{Y\to X}\) and \(G_{X\to Y}\) in some training iteration \(k\), are also preserved in the future - after the BTS of \(D_{X}\) statistics is periodically performed, and the training pool of \(D_{X}\) is re-expanded again. In Figure 1, the proposed periodical bootstrapping of the \(D_{X}\)'s statistics, which is achieved by \(G_{Y\to X}\) GAN that is transferring examples from the full into the scarce domain, is illustrated by an additional third arrow, oriented from \(\mathcal{Y}\) towards \(\mathcal{X}\) and centrally positioned in the functional diagram of the SSL CycleGAN architecture, in the right part of Figure 1. The same process is also illustrated in Figure 3, where it can be seen that the \(X_{BTS}\) denotes the set of novel unlabeled training samples that are added to \(D_{X}\)'s training pool. The samples are randomly generated based on the parameters of the generator \(G_{Y\to X}\) that have been learned up to that moment.