While the performance of deep learning has surpassed that of humans in a range of tasks, machine learning models perform best when learning objectives are narrowly defined. Practical realities however often require the learning of joint models over semantically different information. In this case, best performances are usually obtained by fitting a collection of models, with each model solving an individual sub-task. This is somewhat disappointing, seeing how humans and other biological systems are capable of flexibly adapting to a large number of scenarios.
Past solutions that address this problem tend to fall into some category of multi-domain learning, where – different from the broader multi-task scenario – a single loss function is shared across tasks. Multi-domain learning however relies firmly on the availability of domain annotations, for example used to control modules in domain-specific architectures(Rebuffi et al., 2018; Liu et al., 2019).
The reliance on domain annotations is however not limited to the multi-domain scenario, their presence is required in adversarial domain adaptation (Ganin et al., 2016), or multi-source domain adaptation (Xu et al., 2018; Peng et al., 2019a). Other examples of dependence on domain labels can be found in the continual learning literature, where task-specific memories guide the learning process (Lopez-Paz and Ranzato, 2017; Riemer et al., 2018), in domain generalization (Li et al., 2018, 2019b, 2019a), or meta learning (Finn et al., 2017).
The above approaches are successful when domain annotations are available. In the real world however, these can be difficult or expensive to obtain. Consider images that were scraped from the web. Existing multi-domain approaches would require that these scraped images are further annotated for the mixture of content types they will necessarily contain, such as real world images or studio photos (Saenko et al., 2010), clipart or sketches (Li et al., 2017).
In this paper we relax this requirement, and consider the alternative scenario of latent domain learning. This encompasses any task where we have reason to believe that some partitioning of the data would make sense, but we are uncertain about what a good partitioning might look like, or have inadequate resources to label all data. And as our experiments show, even when domain labels exist, there is no guarantee that these were chosen optimally, nor that learning them isn’t the better option.
Learning on latent domains poses a major problem for standard deep learning approaches, which have a strong tendency to overfit to large modes in data. This issue is displayed in Table 1: the first row shows performance of 9x ResNet26 architectures (He et al., 2016) individually finetuned to all datasets in Visual Decathlon (Rebuffi et al., 2017).111 Except ImageNet
Except ImageNet(Deng et al., 2009), which we omit due to its overweight. The second row shows the performance of a single ResNet26 jointly learned on all these tasks. While the overall loss in weighted accuracy appears modest (-2.69%), domain-conditional accuracies reveal that the single model achieves this feat by overaccounting for large datasets (Svhn, Omniglot, etc.), while disregarding smaller ones (Aircraft, Dtd, Ucf101).
We illustrate the difference between multi-domain and latent domain learning scenarios via graphical models in Figure 1, and further discuss this difference in Section 3.1. We subsequently propose novel mechanisms designed to address the central issues in latent domain learning: dynamic residual adapters (Section 3.3) allow us to achieve robust performance metrics on small domains, all without trading performance on larger ones (see experiments in Section 4). Our proposed module is efficient, can be incorporated and trained seamlessly with existing architectures, and is able to surpass the performance of domain-supervised approaches that rely on human-annotated data (Section 4.2).
2 Related work
Multi-domain learning relates most closely to our paper. The state-of-the-art introduces small convolutional corrections in residual networks to account for individual domains (Rebuffi et al., 2017, 2018). Stickland and Murray (2019) extend this approach to obtain efficient multi-task models for related language tasks. Other recent work makes use of task-specific attention mechanisms (Liu et al., 2019), attempts to scale task-specific losses (Kendall et al., 2018), or addresses tasks individually at the level of gradients (Chen et al., 2017).
A lack of domain annotations has recently attracted interest in unsupervised domain adaptation. Mancini et al. (2018)estimate batch statistics of domain adaptation layers with Gaussian mixture models using only few domain labels. Peng et al. (2019b) study the shift from some source domain to a target distribution that contains multiple latent domains. In our setting, there is no shift between source and target distributions, instead the focus lies on learning parameter efficient models that generalize well across multiple latent domains simultaneously.
Previous work that directly addresses latent domain learning can be found in Xu et al. (2014) which use exemplar SVMs to account for latent domains and thereby generalize to new ones, while Xiong et al. (2014) study the discovery of latent domains by clustering via maximization of mutual information.
Our work connects to multi-modal learning: Chang et al. (2018) propose an architecture for person reidentification that accounts for modality in distributions. Deecke et al. (2018) normalize data in separate batches to account for differences in feature distributions. Furthermore, our work is loosely related to learning universal representations (Bilen and Vedaldi, 2017), which Tamaazousti et al. (2019) use as a guiding principle in designing more transferable models.
Dynamic architectures have recently attracted considerable attention, with solutions from reinforcement learning(Zoph and Le, 2016; Pham et al., 2018) or using Bayesian optimization (Kandasamy et al., 2018). For differentiable dynamic architectures, two components are commonly used: Gumbel-softmax sampling (Jang et al., 2016)
, e.g. leveraged in dynamic computer vision architectures(Veit and Belongie, 2018; Sun et al., 2019), and mixtures of experts (Jacobs et al., 1991; Jordan and Jacobs, 1994), used to scale deep learning models to large problems spaces (Shazeer et al., 2017), and for universal object detection (Wang et al., 2019).
From the perspective of algorithmic fairness, a desirable property for models is to ensure consistent predictive equality across different identifiable subgroups in the data (Zemel et al., 2013; Hardt et al., 2016; Fish et al., 2016; Corbett-Davies et al., 2017). This relates to the central goal in latent domain learning, which is to ensure robustness on small latent domains.
3.1 Problem setting
In multi-domain learning, it is assumed that data is sampled i.i.d. from some mixture of domain distributions , with domain labels . Together, they constitute the underlying distribution as , where each domain is associated with a relative share , with the total number of samples, and those belonging to the ’th domain. The target space is usually made up of mutually exclusive classes of the underlying domains, i.e. . In multi-domain learning, the domain label is always available.
While the two are closely related, in the broader multi-task scenario the nature of underlying tasks is inherently different, and learning on each task distribution is associated with an individual loss function (for example, one task may be object classification, the other semantic segmentation). When the are equivalent across tasks, multi-task learning and multi-domain learning coincide.
Different from learning in a traditional multi-domain setting, in latent domain learning the information associating each sample to a domain is no longer available. As such, we cannot infer labels from sample-domain pairs and are instead forced to learn a single model only from .
A common baseline in multi-domain learning is to finetune a set of individual models, one for each domain. The task in the multi-domain literature is then to overcome this baseline (Rebuffi et al., 2018). We use this particular baseline throughout the paper, and show that in some cases, even when domain annotations were chosen carefully, a domain-unsupervised approach can surpass the performance of domain-supervised ones, see Section 4.2.1.
3.2 Residual adaptation
A widely adopted approach in multi-domain learning builds on the assumption that features from large pretraining tasks are universal, and only small convolutional transformations at each layer of the network are needed to correct for domain-specific differences. Rebuffi et al. (2017, 2018) use this insight to extend the layer-wise transformation of the widely adopted residual architecture (He et al., 2016):
where are the main convolutions of the residual network, and are light-weight (i.e. ) convolutional corrections. In this work access to is removed, resulting in two new challenges: we have no a priori information about the right number of corrections , and we cannot use to decide which one of these to apply. Throughout the next section, we present an alternative strategy of inspecting and choosing relevant corrections on the fly.
3.3 Dynamic residual adapters
While there is no access to domain labels in latent domain learning, we may still assume is constituted by several domain distributions . In order to account for these in a fully domain-unsupervised fashion, we propose the use of dynamic residual adapters (DRA): each incoming sample is first processed by a set of corrections , which we parametrize with light-weight 1x1 convolutions. Next, a noisy mixtures of experts (MoE) gating mechanism is responsible for weighing each correction , under which is then transformed. In the ’th layer of the network, the subsequent feature representation computes as
with the ’th component of the ’th gating function. For an illustration, see Figure 1 (c). While we motivate DRA from learning on latent domains, note that many additional factors (e.g. shape, pose, color) may enter the gate assignments as well. Extending networks with dynamic residual adapters exhibits strong performance on smaller modes, while retaining performance on larger ones, see our experiments in Section 4.
. The only learnable parameters are those of a small linear transformation, resulting in a light-weight parametrization of the gates as
where is a projection onto the channel dimension that averages out height and width (average pooling), a channel-wise exploration noise.222Exploration noise is fixed at , zero otherwise. A final softmax ensures the gating mechanism corresponds to a valid categorical distribution over latent domains, i.e. and . How to choose is discussed in more detail in Section 4.1.1.
In practice, many other parametrizations of the gating function are possible. Self-attention gives rise to smooth assignments, allowing the weighted combination of different . Discrete assignments can be enforced through Gumbel-Softmax sampling (Jang et al., 2016)
. In practice, we found the latter approach to be too restrictive, and a smooth interpolation via MoE to be the more favorable option. We compare gate parametrizations in Table4 of the Appendix.
3.4 Style exchange augmentation
The central challenge in latent domain learning is the tendency of large domains in to suppress smaller ones. Besides accounting for this via dynamic residual adapters, we introduce an augmentation technique that encourages information exchange between domains.
We are motivated by the following example: assume two classes (say, cats and dogs) each with two latent domains (sketches and photos). Ideally, we would want to encourage the model to learn a domain-agnostic representation of , from which it may infer , invariant of . We achieve this here by augmenting with the style information of a second sample , drawn at random from (so potentially, but not necessarily crossing domains).
To ensure that this can be done with small computational overhead, we augment samples after they have been compressed into a dense representation, i.e. after the last convolutional layer of the network. Formally, we factorize the model (with convolutional parameters and
) and subsequent classifier into. As shorthand for a sample’s final representation we denote , and map the low-level feature representation of the pertubation onto the target via
borrowing from recent work in the style transfer literature (Huang and Belongie, 2017).
is introduced to scale the augmentation (higher values will augment more aggressively), momentsare estimated across channel, height and width of and , respectively.
In our experiments, we randomly pair samples in each mini batch. We find that modest values for work best, as augmenting to aggressively risks breaking the relationship between and its corresponding label , see Figure 4 in the Appendix. When learning on latent domains, exchanging feature-level style information between samples works much better in practice than applying other recently proposed generic approaches, e.g. MixUp (Zhang et al., 2017), c.f. the ablation in Table 4.
We consider two experimental settings to evaluate our proposed approaches: a traditional multi-domain scenario but without access to domain information (Section 4.1), and a single dataset that contains multiple latent domains (Section 4.2).
4.1 Latent multi-domain
The first trial combines nine datasets from the Visual Decathlon challenge (Rebuffi et al., 2017) that contain a variety of different images, with mutually exclusive labels, i.e. .333For SVHN and CIFAR-100, this would for example give rise to a 110-dimensional label space. Unlike in multi-domain learning however, in latent domain learning models may erroneously classify samples from CIFAR-100 to SVHN, and vice versa. Note the goal here is not to compare to the performance of domain-supervised approaches that Visual Decathlon was designed for, but to show that deep networks struggle with incorporating small latent domains when no domain annotations are provided.
Initial ResNet parameters were obtained from pretraining on ImageNet (Deng et al., 2009). For dynamic residual adapters, only gates and corrections are learned, the ResNet26 backbone remains fixed at its initial parameters. This requires less parameters to be learned (see Figure 2, left), while also benefiting performance (c.f. Table 4
). We followed the exact same optimization routine across models and experiments: we trained for 120 epochs using stochastic gradient descent (momentum parameter of 0.9), batch size of 128, weight decay of, and initial learning rate of 0.1 (reduced by 1/10 at epochs 80, 100). For dataset splits, we followed Rebuffi et al. (2017). Test accuracies displayed in tables were obtained by averaging over results from five random initializations.
We experimented with different values for the amount of style exchange. While a range of values improve over having no augmentation, the best results were obtained by limiting this to a modest amount (results shown use throughout), see Figure 4. Setting provides the network with corrections (where denotes the number of layers), which was sufficient to achieve robust performance across latent domains. There is a small but limited performance gain from increasing further, see Section 4.2.
|RA (Rebuffi et al., 2018)||✓||2.6 mil||86.47||92.37||95.15||94.61||92.51|
|4x ResNet26||✓||24.8 mil||88.77||95.97||95.95||95.83||94.44|
|MLFN (Chang et al., 2018)||✗||7.6 mil||78.50||91.29||89.97||93.20||89.20|
For a domain-supervised baseline, we finetune 9x ResNet26 (He et al., 2016) (four layers in each block; channel widths of 64, 128, 256), one individual model for each latent domain . We then use the exact same model to learn a joint classifier on . Next, we couple dynamic residual adapters with the very same ResNet26. For further comparison, we also include a significantly deeper ResNet56. Results are shown in Table 2.
Loosing access to domain labels significantly harms performance (9x ResNet26 versus ResNet26). While performance on larger domains is not impacted, the performance on smaller domains (Dtd, Ucf101, Vgg-Flowers) suffers considerably.
This problem is not addressed by simply increasing the depth of the network: while weighted accuracy increases slightly, a ResNet56 suffers the same issues, leaking performance on small domains. Without ever having access to domain annotations, the flexible assignments of convolutional corrections in our dynamic residual adapters close a large portion of this gap. For further analysis on how this is achieved, see Section 4.2.2 and 4.2.3.
4.1.3 Memory requirements
Adding corrections to the residual network results in additional memory requirements.444At each layer learnable parameters are needed to parametrize gates and corrections, respectively. We show in Figure 2 (left) that these are very modest. In particular when comparing the number of learnable parameters, dynamic residual adapters have a significant advantage: the pretrained convolutions of the ResNet stay fixed throughout, only the gates and corrections have to be learned, amounting to less than 20% of parameters in the network.
4.2 Joint label space
The second trial examines performance on a dataset called PACS (Li et al., 2017), standing for its four constituting domains (art painting, cartoon, photo, sketch; examples shown in Figure 3, right). Each domain contains samples of equivalent classes (“giraffe”, “guitar”, etc.). The domains are unbalanced (see in Table 3).
We reserved 20% of samples for evaluation, leaving the remainder for training. Splits were computed at random, as we assume no a priori knowledge of domain memberships. We make no changes to the optimization described in Section 4.1.1.
The results in Table 3 show that dynamic residual adapters improve considerably over a single ResNet26 baseline. While the largest domain sketch is handled well by the traditional model, dynamic residual adapters can much better account for the small domains that also constitute .
To the best of our knowledge, latent domain learning has not been targeted through customized deep learning architectures. A related baseline is MLFN (Chang et al., 2018), which builds on ResNeXt (Xie et al., 2017) to define a latent-factor architecture that accounts for multi-modality in data. Crucially, where we share small convolutional corrections at every layer, MLFN instead enables and disables entire network blocks. Arguably, our more fine-grained approach to parameter sharing allows us to outperform MLFN.
We also evaluate domain-supervised residual adapters (Rebuffi et al., 2018). While these have been shown to work extremely well in the multi-domain scenario, their performance here was sub-par. This is likely a result of its per-domain corrections , which exhibit no cross-domain sharing of parameters. Dynamic residual adapters share parameters natively across domains: this substantially benefits performance on domains like art painting (92.15% versus 84.42%), which shares a lot of visual information with photo (c.f. Figure 3, left).
Lastly, we finetune 4x individual ResNet26 to each PACS domain for a strong domain-supervised baseline. Unsurprisingly, this outperforms the single ResNet26 trained jointly on all domains. While requiring only a fraction of learnable parameters (mil versus mil), DRA however surpasses the performance of the fully domain-supervised ensemble by sharing model parameters across domains.
We further examine the benefit of introducing larger numbers of residual corrections . While the performance edges up slightly, the sequential nature of the network arguably already allows complicated partitionings of the residual corrections for , making larger unnecessary.
Domain-supervised approaches can be incorporated into DRA by setting , and fixing gate assignments to across the network. This also encompasses any potential clustering of domains, which introduces a different, but fixed set of global gate activations. Evident from the results shown here, such global assignments are not always optimal, even when domains have been assigned as carefully as in PACS. Dynamic residual adapters remove the need to decide a priori what constitutes good domain separations, and instead dynamically share or separate features at every layer. We analyze how this occurs in additional detail in the next two sections, by looking at activation paths across the network.
4.2.2 Gate activations
In Figure 2 (right) we show average per-layer activations of the gating mechanism. Different domains activate gates at different depths of the network, while visually similar domains (such as art painting and photo, c.f. examples in Figure 3, left) tend to activate together. At some layers there is little need for multiple corrections . In this case, dynamic residual adapters simply relax to a uniform gate: the activation becomes , joining the unit into a single residual correction .
4.2.3 Gate pathways
Intuitively, one might expect the gating mechanism to assign different convolutional corrections to the different human-annotated domains in PACS. The visualization of gate activations in Figure 2 (right) seems to suggest the opposite: the purity (share of maximum activation relative to all activations) is relatively low across the network.
Arguably, the above intuition oversimplifies how the network processes different samples, and is further contradicted by the performance loss that results from enforcing discreteness (c.f. Gumbel-softmax in Table 4). To understand better how partitioning occurs, it is helpful to inspect what happens across the entirety of the network, and compare sets of feature activations throughout their processing. For a sample , we define its ’th activation path across the -layered network as
If samples have similar activations paths, this means they also share a large amount of parameters. As a group of samples with low pairwise distances in Figure 3
(right) shows, similar gate activations are indicative of visual similarity: pose, color or edges of samples that group together are visibly related, compare in particular the pose of elephants from thephoto and sketch domains.
We collected gate activation paths for (an equal number) of samples from all domains, and visualize their principal components in Figure 3 (left). This reveals an intuitive clustering of domains: visually similar domains art painting and photo (•,•) share a region. The manifold describing sketches (•) is arguably more primitive than those of the other domains, and indeed only maps to a small region. Cartoon (•) lies somewhere between sketches and real world imagery. Under visual inspection (c.f. examples in Figure 3, right) this makes perfect sense: a cartoon is, more or less, just a colored sketch. We highlight one particular elephant that resides amongst the cartoon domain, but has been annotated as photo in the PACS dataset. The ground-truth annotation is incorrect, but different from domain-supervised approaches, dynamic residual adapters are not irritated by this.
Recent work in multi-domain learning has been chiefly focused on a setting where domain annotations are assumed to be routinely available. As this requires careful curation of datasets, in real world scenarios this assumption can often be of limited merit. Dynamic residual adapters help inject adaptivity into networks, preventing them from overfitting to the largest domains in distributions, a common failure mode of traditional models. Not only does our approach successfully close a large amount of the performance gap to domain-supervised solutions, but in some scenarios – even when domains have been assigned very carefully – exceeds their performance.
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The ablations in Table 4 show that latent domain learning benefits from both the addition of multiple dynamic residual adapters (i.e. ) as well as style exchange augmentation between the feature maps of samples ().
While adding a single residual adapter () helps the model with smaller modes, it registers performance losses on medium and larger ones. In line with what Rebuffi et al.  report, when not fixing parameters of the ResNet convolutions, this leads to problems with overfitting.
With no augmentation via style exchange (), performance drops visibly. MixUp [Zhang et al., 2017], an alternative augmentation that interpolates between samples, is not equally well suited for latent domain learning. Results for additional choices of are shown in Figure 4: modest values for work best, as augmenting too aggressively risks breaking the relationship between image-label pairs.
Replacing mixtures of experts with Gumbel-softmax sampling negatively impacted performance: while some domains (CIFAR-100, Omniglot) are handled well, discrete gates struggle particularly with smaller ones. Performance for soft and straight-through Gumbel-softmax sampling was on par, and we report straight-through sampling here.