We tackle unsupervised domain adaptation by accounting for the fact that different domains may need to be processed differently to arrive to a common feature representation effective for recognition. To this end, we introduce a deep learning framework where each domain undergoes a different sequence of operations, allowing some, possibly more complex, domains to go through more computations than others.
 This contrasts with  state-of-the-art domain adaptation techniques that force all domains to be processed with the same series of operations, even when using multi-stream architectures whose parameters are not shared.
 As evidenced by our experiments, the greater flexibility of our method translates to higher accuracy. Furthermore, it allows us to handle any number of domains simultaneously. While deep learning has ushered in great advances in automated image understanding, it still suffers from the same weaknesses as all other machine learning techniques: when trained with images obtained under specific conditions, deep networks typically perform poorly on images acquired under different ones. This is known as the domain shift problem: the changing conditions cause the statistical properties of the test, or target, data, to be different from those of the training, or source, data, and the network's performance degrades accordingly. Domain adaptation aims to address this problem, especially when annotating images from the target domain is difficult, expensive, or downright infeasible. The dominant trend is to map images to features that are immune to the domain shift, so that the classifier works equally well on the source and target domains (Fernando et al., 2013; Ganin & Lempitsky, 2015; . In the context of deep learning, the standard approach is to find those features using a single architecture for both domains (Tzeng et al., 2014; Ganin & Lempitsky, 2015; Yan et al., 2017; Zhang et al., 2018) . Intuitively, however, as the domains have different properties, it is not easy to find one network that does this effectively for both. A better approach is to allow domains to undergo different transformations to arrive at domain-invariant features. This has been the focus of recent work (Tzeng et al., 2017; Bermúdez-Chacón et al., 2018; Rozantsev et al., 2018; , where source and target data pass through two different networks with the same architecture but different weights, nonetheless related to each other. In this paper, we introduce a novel, even more flexible paradigm for domain adaptation, that allows the different domains to undergo different computations, not only in terms of layer weights but also in terms of number of operations, while selectively sharing subsets of these computations. This enables the network to automatically adapt to situations where, for example, one domain depicts simpler images, such as synthetic ones, which may not need as much processing power as those coming from more complex domains, such as images taken in-the-wild. Our formulation reflects the intuition that source and target domain networks should be similar because they solve closely related problems, but should also perform domain-specific computations to offset the domain shift. To turn this intuition into a working algorithm, we develop a multibranch architecture that sends the data through multiple network branches in parallel. What gives it the necessary flexibility are trainable gates that are tuned to modulate and combine the outputs of these branches, as shown in , each of which processes the data in parallel branches, whose outputs are then aggregated in a weighted manner by a gate to obtain a single response. To allow for domain-adaptive computations, each domain has its own set of gates, one for each computational unit, which combine the branches in different ways. As a result, some computations are shared across domains while others are domain-specific. computations should be carried out for each one. As an additional benefit, in contrast to previous strategies for untying the source and target streams (Rozantsev et al., 2018; , our formulation naturally extends to more than two domains. In other words, our contribution is a learning strategy that adaptively adjusts the specific computation to be performed for each domain. To demonstrate that it constitutes an effective approach to extracting domain-invariant features, we implement it in conjunction with the popular domain classifier-based method of Ganin & Lempitsky (2015) . Our experiments demonstrate that our Domain Adaptive Multibranch Networks, which we will refer to as DAMNets, not only outperform the original technique of Ganin & Lempitsky (2015) , but also the state-of-the-art strategy for untying the source and target weights of Rozantsev et al. (2019) , which relies on the same domain classifier. We will make our code publicly available upon acceptance of the paper. We have introduced a domain adaptation approach that allows for adaptive, separate computations for different domains. Our framework relies on computational units that aggregate the outputs of multiple parallel operations, and on a set of trainable domain-specific gates that adapt the aggregation process to each domain. Our experiments have demonstrated the benefits of this approach over the state-of-the-art weight untying strategy; the greater flexibility of our method translates into a consistently better accuracy. Although we only experimented with using the same branch architectures within a computational unit, our framework generalizes to arbitrary branch architectures, the only constraint being that their outputs are of commensurate shapes. An interesting avenue for future research would therefore be to automatically determine the best operation to perform for each domain, for example by combining our approach with neural architecture search strategies. Figure 1 : Multibranch LeNet. This architecture is a multibranch extension to the LeNet used by DANN (Ganin & Lempitsky, 2015 Figure 2 : Multibranch SVHNet. This architecture is a multibranch extension to the SVHNet used by DANN (Ganin & Lempitsky, 2015 (He et al., 2016) . We preserve the groupings described in the original paper (He et al., 2016) . N denotes the number of classes in the dataset.
A Multiflow Network is a dynamic architecture for domain adaptation that learns potentially different computational graphs per domain, so as to map them to a common representation where inference can be performed in a domain-agnostic fashion.
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