Beyond Boundaries: A Novel Data-Augmentation Discourse for Open Domain Generalization
Authors: Shirsha Bose
Ankit Jha
Hitesh Kandala
Biplab Banerjee
Venue: Accepted by TMLR ()

Abstract: The problem of Open Domain Generalization (ODG) is multifaceted, encompassing shifts in domains and labels across all source and target domains. Existing approaches have encountered challenges such as style bias towards training domains, insufficient feature-space disentanglement to highlight semantic features, and discriminativeness of the latent space. Additionally, they rely on a confidence-based target outlier detection approach, which can lead to misclassifications when target open samples visually align with the source domain data.
In response to these challenges, we present a solution named \textsc{ODG-Net}. We aim to create a direct open-set classifier within a \textit{discriminative}, \textit{unbiased}, and \textit{disentangled} semantic embedding space. To enrich data density and diversity, we introduce a generative augmentation framework that produces \textit{style-interpolated} novel domains for closed-set images and novel pseudo-open images by \textit{interpolating the contents of paired training images}. Our augmentation strategy skillfully utilizes \textit{disentangled style and content information} to synthesize images effectively.
Furthermore, we tackle the issue of style bias by representing all images in relation to all source domain properties, which effectively accentuates complementary visual features. Consequently, we train a multi-class semantic object classifier, incorporating both closed and open class classification capabilities, along with a style classifier to identify style primitives. The joint use of style and semantic classifiers facilitates the disentanglement of the latent space, thereby enhancing the generalization performance of the semantic classifier.
To ensure discriminativeness in both closed and open spaces, we optimize the semantic feature space using novel metric losses. The experimental results on six benchmark datasets convincingly demonstrate that \textsc{ODG-Net} surpasses the state-of-the-art by an impressive margin of $1-4\%$ in both open and closed-set DG scenarios.

Published in Transactions on Machine Learning Research (11/2023)
Beyond Boundaries: A Novel Data-Augmentation Dis- course for Open Domain Generalization
Shirsha Bose Technical University of Munich
shirshahosecs@ gmail.com
Ankit Jha
ankitjhal6@@ gmail.com
Indian Institute of Technology Bombay
Hitesh Kandala
khitesh2000 gmail.com
Indion Institute of T'Tchnology Bombay
Biplab Banerjee
getbiplab gmail.com
Indian Institute of Technology Bombay
Reviewed on OpenReview: http:////ppeeeeeeeaee////oootaaa lysl
Abstract
The problem of Open Domain Generalization (ODG) is multifaceted, encompassing shifts in do- mains and labels across all source and target domains. Existing approaches have encountered chal- lenges such as style bias towards training domains, insufficient feature-space disentanglement to highlight semantic features, and discriminativeness of the latent space. Additionally, they rely on a confidence-basse target outlier detection approach, which can lead to misclassifications when target open samples visually align with the source domain data. In response these challenges, present solution named ODG-NET. We aim create direct open-set classifier within discriminative, unbiased, and disentangled semantic embedding space. To enrich data density and diversity, introduce a generative augmentation framework that produces ryyle-interpolated novel domains for closed-set images and novel pseudo-open images by interpolating the contents of paired training images. Our augmentation strategy skillfully utilizes disentangled style and content information to synthesize images effectively. Furthermore, we tackle the issue of style bias by representing im- ages in relation to all source domain properties, which effectively accentuates complementary visual features. Consequently, we train multi-class semantic object classifier, incorporating both closed and open class classification capabilities, along with a style classifier identify style primitives. The joint use of style and semantic classifiers facilitates the disentanglement of the latent space, thereby enhancing the generalization performance of the semantic classifier. To ensure discriminativeness in both closed and open spaces, we optimize the semantic feature space using novel metric losses. The experimental results on six benchmark datasets convincingly demonstrate that ODG-NET surpasses the otate-of-the-arr by an impressive margin of 4% in both open and closed-set DG scenarios.
1 Introduction
Domain Generalization (DG), explored in the work of Zhou et al. (2022) aims to establish shared embedding space derived from labeled source domains, which can then be applied to unseen target domain. However, current DG methods are primarily tailored to closed-set scenarios, such as those seen in Zhou et al. (2020b) and Zhou et al. (2020a), where both source and target domains possess identical label sets. Nonetheless, this approach might not always be viable in dynamic worldw contexts, as exemplified by Robotics, where a navigating robot might encounter categories that are either common or unique its surroundings Zhao Shen (2022). This realization underscores the necessity of tackling the more pragmatic and intricate realm of Open Domain Generalization (ODG) Shu et al. (202)). which revolves around training on labeled source domains housing both shared and domain-specifer categories.

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Source Domain-1
Saurce Domain-2
D Domain-1
Pseudo Open Samples
Domain-2
Pscudo Domains
Unbiased Latent Feature Generation
Class-1
Class-2
Class-3
Class-4
Feature Disentenglement Eneuring Discriminativeenss
Open-set open-setCon Object Classifeer
Domain Clasesifier
Generative Domain
Class Augmentation
Figure 1: The working principle of ODG-NET. Given number of source domains with shared and private classes for each domain, our algorithm follows three simple stages to obtain effective semantic open-set object classifier.
In the context of ODG, the target domain consists of samples belonging to either familiar classes or novel classes exclusive to that particular domain, thereby introducing several noteworthy challenges. Firstly, a substantial data imbalance arises due the uneven representation of known classes within the source domains. Secondly, the task of establishing an embedding space that is both domain-agnostic and discriminatory becomes formidable in light of unregulated shifts in both domains and labels. Lastly, the absence of prior knowledge concerning the open space in the target domain adds to the complexity.
While one potential approach to addressing ODG could involve the fusion of pre-existing closed-set DG technique with a readily available open-set recognition (OSR) method, such as Openmax [eeddale & Bouli((2066)) this strategy may not yield optimal results. The DG technique could potentially be influenced by the domain-specific classes found in ODG, which are subject to significant under-representation.
Surprisingly, Open Domain Generalization (ODG) has garnered little attention in the Domain Generalization (DG) literature, with DAML (AauLShuuee et al. (202T) being the sole model explicitly designed for ODG. However, our extensive in- vestigation revealed three significant limitations in DAML's approach. Initially, DAML augments source domains via multi- molti-domain mix-up features, using a Dirichlet-distributin based weight scheme, where identical weight configura- tions correspond to labels for generated features. However, merging content and style details in the raw latent features might result in semantically inconsistent feature-label pairs. This was evidenced in a PACS dataset [i et al. (2017) experiment, where classifying the synthesized features yielded notably low accuracy. Additionally, DAML overlooks disentangling content features from domain attributes. potentially introducing biases towards specific styles, hindering adaptability across diverse visual domains. Furthermore, DAML's outlier rejection relies thresholding source do- main classifier responses, that can produce erroneous results, especially when target open samples visually align with certain source domain classes. These limitations underscore the imperative need for further exploration and refinement of ODG techniques, thereby unlocking their full potential and meaningfully addressing the inherent complexities.
overcome these challenges, we introduce an innovative approach for training a robust generalized semantic open-set classifier. This classifier can distinguish known and potential new samples in an unbiased and disentangled embed- ding space. However, we face a hurdle we lack representative open-space samples during training. To address this, we propose novel technique called "sample hallucination," which generates these essential samples, facilitating comprehensive classifier training. Additionally, we tackle the issue of class imbalance in ODG by diversifying the appearances of training classes. Our method emphasizes the importance of representing images in feature space un- affected by training domains. To achieve this, we advocate separating semantic features from style elements, revealing each image's 's true content. Ultimately, we ensure that the semantic space effectively discriminates between classes, enabling our classifier to make precise distinctions across various categories. These innovations pave the way for more effective and accurate open domain generalization.
Our proposed ODG-NET: In this paper, we introduce novel model, ODG-NET (depicted in Fig. D which addresses the aforementioned concerns comprehensively. ODG-NET consists of three pivotal modules, each devoted to addressing model bias, feature disentanglement, and the creation of a discriminative semantic feature space.
At the core of our research the aim to enrich the existing source domains using two types of synthesized images gen- erated by novel conditional GAN. These image types serve specific purposes: expanding the diversity of closed-set classes and creating representative pseudo-open images. The first image type, called domain or style mix-up images, involves sophisticated interpolation of style properties from source domains using Dirichlet distribution. This
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approach introduces new domains, diversifying the style of source images while preserving their inherent semantic object characteristics. The second type, known pseudo open-space images, results from skillful interpolation of both domain and class identifiers from source domain images, achieved through Dirichlet sampling. To ensure the creation of diverse and meaningful samples, we'v ve introduced diversification regularization to prevent potential mode collapse during the generation of domain or label-interpolated samples. Additionally, structural eycle consistency mechanism has been implemented to maintain the structural integrity of the generated images.
Our approach tackles a range of formidable challenges, spanning from class imbalance and limited style diversity to the absence of open-space prior. A unique aspect of our methodology lies in its capacity to unify label and domain mix-up concepts while offering customization in conditioning. This surpasses existing augmentation methods, which are limited to style or random image mix-ups Mancini et al. (2020a); Zhou et al. (2021). ODG-NET strives for an unbiased latent embedding space, devoid of source domain bias. We achieve this through an innovative approach involving the training of nomain-ssecifff classifiers, which adeptly capture domain-specific features from each source domain. Consequently, each image is represented as concatenation of features from all domain- -ppeifc models, creating a comprehensive and impartial embedding.
To disentangle domain-specife attributes from semantic object features in latent representations, train two snrentionddivenn classifiers: a domain classifier for domain label identification and an object classifier for recognizing class labels from the augmented domain set. This enriches our model's s grasp of object semantics while significantly mitigating the influence of domain- -epeifi- artifacts. For a highly discriminative semantic feature space, we introduce a contrastive loss among known classes, accentuating differences between various categories. Additionally, our en- tropy minimization objective strategically pushes pseudo outliers away from the known-class boundary, bolstering the model's s robustness.
We summarize our major contributions as:
[-] In this paper, we introduce ODG-NET, an end-to-end network that tackles the challenging ODG problem by jointly considering closed and open space domain augmentation, feature disentanglement, and semantic feature-space optimization.
[-] To synthesize augmented images that are diverse from the source domains, we propose a novel conditional GAN with a cycle consistency constraint and an anti-mode-collapse. regularizer that interpolates domain and category labels. We also adopt a classification-base approach for feature disentanglement. Finally, we ensure the separability of the semantic feature space for closed and open classes through novel metric objectives.
[-] We evaluate ODG-NET on six benchmark datasets in both open and closed DG settings. Our experiments demon- strate that ODG-NET consistently outperforms the literature. For instance, on ODG for Multi-dataset [Shu al.) (202T) and on closed DG for DomainNet [Peng al. (2019). ODG-NET outperforms the previous sfate-of-the-art by approximately 3%.
2 Related Works
Open-set learning and open-set domain adaptation: The Open-set Recognition (OSR) Bendale & Boult (2016c);
Kong & Ramanan (202T); Pal et al.) (2023b); Vaze et al. (2021) challenge involves effectively identifying novel, unknown-class samples during testing, leveraging training samples from known closed-set classes, However, OSR
doesn't 't account for any differences in distributions between the training and test sets. Another relevant problem is Open-set Domain Adaptation (OSDA) Panareda Busto Gall (2017): (Saito et al. (2018): Kundu et al.) al.] (2020); |Becii] et al. 2020), which addresses the scenario of labeled source domain and an unlabeled target domain. The target domain contains unlabeled samples from the same semantic classes as the source domain, along with novel-class samples unique to the target domain. OSDA operates in a transductive manner, where both source and target domains are simultaneously employed during training. In contrast, Open Domain Generalization (ODG) sets itself apart from OSR and OSDA. In ODG, the target domain remains unseen during training, making it distinct. Additionally, the multiple source domains consist of a combination of shared and private categories. This diversity of categories, including shared and domain-specific ones, renders ODG even more intricate than the other tasks.
(Open) DG: DG refers to the problem of learning a supervised learning model that generalizable across any target distribution without any prior knowledge. The initial studies in closed-set DG focused domain adaptation (DA) Li
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et al. (2020); ; Wang et al.
2021
; Li et al. (2021a) due the disparity in domain distributions. Several DG methods
have since been developed, such as supervuee learning Carlucci et al. (2019). ensemble learning Xu et al. (2014),
and meta-lcarning Patiiiinnngaaiiiaaa Patricia & Caputo (211)) Wang et al. (2020b); Li et al. (2019b 18: 2019)); Huang et al. (2020)
To address the domain disparity, the concept of domain augmentation Li et al. (2021c); Kang et al. (2022); Zhou et al.
(2020b) 202T>> : Zhang et al. (2022) was introduced, which involves generating pseudo-domains and adding them to the available pool of domains. Subsequently; the notion of ODG was introduced in [Shu et al. (202T). which based on domain-augmented meta-learning. To solve the single-source ODG problem. Zhu & Li (021) and Yang al. (2022)
further extended the idea of multi-source ODG. See Zhoou et al. (2022) for more discussions DG.
Our proposed ODG-NET represents a significant departure from DAML et al. (2027). Unlike their ae level mix-up stralegy, we introduce a more robust augmentation technique that leverages generative modeling to seam- lessly synthesize pseudo-open and closed-set image samples. Additionally, we take a direct approach to learning an open-set classifier in a meaningful and optimized semantic space, in contrast to the source classifier's confidence- driven inference used in Shu et al. 2021). As a result, ODG-NET is better suited to handling open samples of different granularities.
Augmentation in DG: Data augmentation is crucial technique in DG, and it can be implemented using various methods such as variational autoencoders. GANs, and mixing strategies Goodfellow et al. (2020); Kingma & Welling (2013) Zhang et al. (2017). For instance, Rehman el al. Rahman et al. (2019) used ComboGAN to generate new data and optimized ad hoc domain divergence measures to learn a domain- domain-generic space. Zhou et al. Zhou et al. (2020b) combined GAN-based image generation with optimal transport to synthesize images different from the source data, Gong et al. Gong et al. (2019) treated generation as an image-to-image translation process and extracted intermediate images given an image pair. Similarly, [i et al.. (202Tb) used adversarial training generate domains instead of samples. Mix-up, the other hand, generates new data by interpolating between a pair of samples and their labels, Recently, mi techniques Yun et al. (2019); Mancini et al. (2020a); Zhou et al. (2021) have become popular in the DG literature, applied to either the image or feature space.
The augmentation approach used by ODG-NET stands out from the existing literature by going beyond simple style or image mix-up. Our approach ensures that the object properties of images remain intact when using style mix-up, and we also have control over label mix-up to generate pseudo-open samples that can scatter the open space with varying levels of similarity to the source domains.
Among the existing augmentation strategies, Zhou et al. (2020b) and Gong el al. 2019 are the closest to our approach as they both use conditional GANs. However, there are several key differences between our method and theirs: (a) Gong et al.) (2019) requires paired training data to sample intermediate pseudo-stylized images, whereas we use conditional generation without the need for paired data; (b) Zhou et al. (2020b) uses extrapolation for domains, which is ill- ill-posed, while we use Dirichlet distributions to interpolate domains and classes; and (c) while both Zhou et al. (2020b) and et al. (2119) use style mix-up for closed-set data, we generate both closed and pseudo-open samples judiciously.
Disentangled representation learning. Disentangled feature learning refers to the process of modeling distinct and explanatory data variation factors. As per Dittadi et al. (220)). disentanglement can aid in out-of-distribution tasks. Previous efforts have focused on disentangling semantic and style latent variables in the original feature space using encoder-decoder models Wang et al.] (2022); [Cai et al. (2019), causality Ouyang et al. (002I), or in the Fourier space Wang et al. 2022). These models are complex and require sophisticated knowledge to improvement the feature learning of the models. In contrast, ODG-NET proposes to use simple implement yel effective, attention-based classifiers, separate the style and semantic primitives from the latent visual representations.
3 Problem Definition and Proposed Methodology
In the context of ODG, we have access multiple source domains denoted as D (Di, D2, these domains has different distributions and contains combination of domainn-spcciin and shared categories. During nh where yo E Y, is the label for x, E Xg. The training, use labeled samples from each domain D. = (a', v=)== total number of classes in D is denoted by C. The target domain Dy = { has a distribution that is different from that of D. It consists of unlabeled samples that belong to one of the source classes present in D or novel classes
Ds). Each of
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that not seen during training. The objective is model a common classifier that can reject outliers while properly recognizing the known class samples given 'D and then evaluate its performance on Dy.
Open and Closed Set Sample Generation
Tr
Fim im
0.6
0.1
Pseudo Domain Vector
F
Vdd
0
Domain Vector
L Drec
Generator
y/
Class Vector
F
y
0.1
0.4
08 as
Interpolated Class Vector
FG
2
72 77
F
Noise
Unbiased Discriminative Disentangled Feature Space Learning
F
Domain Classifier
Fea
Domain labels
Ad
08/0r cs
I
Domain-speccfic Attention
F
Fdisc
Fg
Brec
Fer
Discriminator
12 C..C C+11
Semanttcc-seccin Attention
Fo
ClosedDuttio
classesclasses
Feo
F
Ao
F
Local Domain Specific Network
Open-set Classifier
Figure A depiction of the ODG-NET architecture. It shows the model components: the embedding networks: (Fim,Fy. F,). cGAN consisting of Fdise) the local domain-specific classifiers {Fi = Fi) and the global domain and semantic classifiers Fo) with corresponding attention blocks Aa and Ag. respectively, Colors indicate the flow of information for different data items.
In our formulation, each domain/style D represented using an S-dimensional one-hot vector va. In contrast, a pseudo-domain (synthesized style) is represented by 02. which sampled from Dirichlet distribution with parameter a and has the same length as va- For instance, S 3, source domain can be represented as a three-dimensional one-hot vector (e.g., [0, 0, 1)), while êa could be [0.2, 0.3, 0.5].
Similarly, we denote the label y C-dimensional one-hot vector. On the other hand, interpolated label space is represented by J. which is sampled in the same way as 0g. A real image-label pair from D is denoted as (xr, v). In contrast, a cGAN synthesized image denoted by (2'² y) or ( depending on whether it represents a style- interpolated closed-set image with label y or joint style and label interpolated pseudo-open image with label ②. respectively. Finally, aid in open-set classification, we introduce a label space ğ RC+1, The first C indices are reserved for closed-class samples, while the C + 1-th index is used for pseudo-outlier samples.
3.1 Architecture and training overview for ODG-NET
Our objective is to craft direct open-set classifier operating within disentangled, discriminative, and unbiased semantic feature space. Additionally, we introduce method for generating training samples for the open space by proposing the creation of pseudo-open samples through a generative module.
accomplish our aims, we introduce ODG-NET, composed of four modules (illustrated in Fig. 2 First and foremost, ODG-NET employs generative augmentation strategy, utilizing conditional GAN equipped with U-Net-based generator denoted Fo and a binary discriminator referred as Faisc- We condition Fe on four variables: the domain label va/Oa, the class label y/ū, an input image z./n6f /rff. and noise tensor mn /1p///
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sampled from predefined distributions. To ensure the proper combination of these conditioning variables, we propose the use of separate embedding networks Fu: Fy. Fr)) to encode the image, domain label, class label, and noise into meaningful latent representations. We train FG to generate two types of images: (i) (xf*, y) when conditioned on (zr, 0d. y. Th ). where x7" retains the class label y/ of z,, while the style changes according to 6g. and (ii) (ar?", 9) when conditioned on (xy, vi// Dd: D: 1/2),, thereby modifying the semantic and stylistie characteristics of xt according to á and va/Oa in ay. We employ a standard min-max formulation to train the conditional GAN and introduce regularizer to ensure that the generated samples do not closely resemble the data from D (as expressed in Eq. D.. Furthermore, we introduce cycle consistency loss to maintain the semantic consisteney of the generated images (as indicated in Eq. To achieve an unbiased latent feature space, we propose representing all images with respect to the feature space of all source domains. We introduce S local source-domain specitic networks, which comprise a feature backbone and a classification module, denoted as Ff = (Fle, Fi,) and are trained on D.. We aggregate feature responses from all F% to obtain the latent representation (z) = Fbi Fiss for a given image x (as described in Eq. 3). To disentangle domain-dependen properties from semantic object features within (x) we introduce global domain and semantic object classifiers, denoted as Fa with S output nodes and F., with C C+1 1 output nodes (expressed in 4 5 which are shared across domains. We employ spectral-spatial self-attention modules Ar and A. to highlight domain and semantic object features from Fet, resulting in Fea and Fe.. We aim to ensure the discriminative quality of the semantic embedding space (outputs of the feature encoder of Fo, denoted as F.)) through novel metric losses, which encourage the separation of all closed and pseudo-open class samples (as indicated in Eq. 6 In the following sections, we delve into the details of the proposed loss functions.
Eq.
3.2 Loss functions, training, and inference
Regularized cGAN objectives with structural cycle consistency for image synthesis: As previously mentioned, we employ a cGAN model to generate potential open-space images. Within this framework, FG and Faisc engage in min-max adversarial game. The primary objective of Fdise is to accurately discern between real and synthesized images, while Fa endeavors to deceive Faisc- To prevent the generated images from being too similar to those D, we introduce regularization term denoted as W. This regularization term penalizes scenarios in which the real and synthesized images, represented by their respective features (x,)) and Fe become indistinguishable for slightly different values of (va, 0a) or (ya. 9a). Here, å represents the cosine similarity, and is a small constant. Es- sentially, even if ō(va, 0a) or (ya. 9u) tends toward 1, W enforces ((Fei(x))FFettt (e((z)//0)) to approach O, minimizing the loss. The comprehensive loss formulation is presented below.
8 8(Fer(z)). Fei(s,) (1/ +e
Lean
E Pp. Poo/o// noive
(Fs((asee + log(1 FFaso (Fell (0/0)))) + B 6(va, 0a) + ō(ya. Da) +
(1)
w
In this context, PD. Preise. and pos generate closed-set and open-set samples, respectively. We set Pos = (O, I), and pos Pross = NO, o). where o is large value. Our goal is to limit the space of generated closed-set images so that they represent similar semantic concepts while allowing for more scattering in the pseudo-open space, aiding in learning robust open-set classifier.
noise denote the data distribution of the source domains in D and the noise used to
To maintain the structural robustness of Fa against variations in style or label, we propose a method for reconstructing Fr. We take into account the embeddings of the synthesized x io the actual class label y, the domain identifier va. and a noise vector i7s (O, I) inputs Fo: 2F Fa Vd y, ms). By following the path x, -> x rec we ensure that , cs/os represents a meaningful image rather than noisy data.
cs
To compute the loss, we use the standard & distance between the original real domain images and the remapped images ree,, given by:
Ly
(o.) [||=, - x, [[.]
Learning style agnostic latent representations for all the images: Subsequently, our aim is to guarantee that the latent feature embeddings of images remain impartial and not skewed toward any particular training source domain. To mitigate the risk of overfitting to any specific source domain, we introduce a method wherein input images are represented based on the characteristics of all source domains, leveraging the feature representation (x) This approach constructs multi-view representation space that encompasses diverse and complementary perspectives of the images.

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To achieve this, train Fi using D. where belongs to (1.2. S}. We consider S multiclass cross-entropy losses (LeE) for this purpose (as shown in Eq. 3). where Pi represents the data distribution for the 8th source domain.
Lloeal
E
S
Disentangling latent features of the images to highlight the semantic contents through global classifiers: Si- multaneously, our objective is to disentangle Coomain-speciine attributes from the semantic object features within the previously derived latent representations. This disentanglement facilitates the object classifier in focusing exclusively on the semantic content, thereby enhancing its generalizability across novel target domains.
In this context, the global domain classifier, denoted as Fa. is tasked with identifying domain identifiers based on the attended features, which are defined as Fea(z) = (z) @ Ad + Fe((z). This is achieved through the use of a multiclass cross-entropy loss. It is worth noting that Fa implicitly ensures that Fc generates images in accordance with the specified conditioning domain identifiers. The corresponding loss function is delineated below.
Ldaam
E
(FFeFaF )) va) LLR(Fa(Feall (ea()) 0,))))
(4)
Pespos woise
domain
domain Fenturre
In contrast, the open-set classifier, Fo. is trained to accurately identify all samples belonging known classes while disregarding the generated pseudo-outliers by labeling them as C C++ 1, from Fe.(z) = Fei @ Ao Fe( This is achieved using multiclass cross-entropy loss. Similar Fa, F, also aids Fo in producing high-quality synthesized images and supplements Lree-
Letass
E Poapoo moise
[For FFo((r))))))))))))))())))))))F ),0) + (FFol((Fe Ø)]
object features.
object features
Fa and Fo work together on Fe((x), and seek to learn the domain-speciff and semantic features separately, suggesting that fact that both the networks are devoted to disentangling the latent features wisely.
Algorithm ODG-NET training algorithm
Require: Initialized Fc, Fim, Fn, Fdiec: [F])
1: while Not Converged do
Sample batch of (zr, y, va) from D and m N(O,, 1), m N(0,o), ~ NO0, is the noise variance for generating the pseudo-open samples. Generate éu and ÿs using Dirichlet(a). a is the parameter of the distribution.
3:
4: Obtain batch of 5 Fa Ga; y, 71)-
Obtain batch of 24 = Fo Ua/ fa/0a, 0. 72))
Obtain x:, = Fc cs/os Vd: V, 77))
7:
Obtain Fer, the latent representation corresponding to (Ir, 27 : ; x xxee).
8:
Obtain Fes, the attended domain features, and Fe.. the attended semantic features from Fer. Solve: argmin argmax LGan + WreeL + Wiocal A
9:
Fom Fu. Faise
(F1)
10: Solve: argmin [dom + Lelass + w Loemm
FayFa
11: end while
Ensuring discrininativenes. of the semantic feature space. The inherent diversity within multi-domain data poses challenge for F. in creating an optimized semantic feature space based on Fb. In this space, it's expected that closed-set classes from the augmented domains should form distinct clusters, while pseudo-open-se samples should be effectively pushed away from the support region of the closed set. enhance the discriminative qualities, we propose the utilization of a contrastive loss for closed-set samples across the augmented domain set. Simultaneously, we aim minimize the entropy (E) of F, predictions for pseudo-open samples. Minimizing the entropy effectively acts weighting mechanism for F. when handling pseudo-open samples. This weighting strategy increases the posterior probability p(y = C + 1 f / for pseudo-open samples while reducing the posteriors associated with the known-class indices (1 C). This approach contributes to the overall objective creating a more discriminative semantic feature space, which is crucial for the successful separation of classes and pseudo-open samples.
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To implement the contrastive loss, Leon+ select anchor sample, Tas and randomly obtain a positive sample, 4++ which shares the same class label as Za. as well as a set of negative samples, {xm {xm) Im=1, where no restrictions are imposed on the styles of the samples. The goal is to maximize the cosine similarity, ö, for (E while minimizing it for all possible pairs of (Ta, x=)) The semantic feature space optimization loss can be expressed as follows:
yym
B Pp. paafe
((Fo(Feo(a)) Teon
(6)
where Leon is defined as follows.
exp(6(F((z)), (xa). (xpp
Lyon
log
(7)
> m=1
Total loss and training. We follow an alternate optimization strategy in each training episode for ODG-NET, men- In the vanilla training stage, we train the embedding networks Fu. Fr), GAN modules Fa, disce and the local domain-specific networks {Fi given the fixed (Fa. to produce meaningful images. ws represent the loss contributions and we set them the value 1 in all our experiments.
tioned in Algorithm [
argmin
argmax WWan Lean WrecIrec Wlocat Aocal)
Fuin Fo Fa. Jasse (5))
Subsequently, we train Fo and Fa obtain the optimized semantic classifier keeping other parameters fixed.
arg min
[Lown + Letass + w Lum]]-
Fo.Fa
Testing, During inference, images from Dy are provided as input to (F The class labels with the highest softmax probability scores are predicted according to Fo.
4 Experimental Evaluations
Datasets. We present our results on six widely used benchmark datasets for DG. Specifically, we follow the approach of Shu al. (021) and use the following datasets: (1) Office-Home Venkateswara al. (2017), (2) PACS Li et al.)
(2017). (3) Multi-Dataset (Shu al. (2021). In addition, we introduce the experimental setup of ODG for two ad- ditional DG datasets, namely VLCS Fang et al. (2013) and Digits-DG Zhou et al. (2020b) in this paper. For our closed-set DG experiment, we also utilize the large-scale DomainNet Peng et al. (2019).
Implementation details: To ensure clarity, we use a ResNet-18 based backbone He et al. 2016) for Fo consistently, while we adopt standard architectures per benchmark for closed-DG tasks, following established literature Zhou et al.) (2000)). Our attention modules (A) are composed of pair of spatial and spectral attention modules, imple- mented using the query-key-value processing-based approach Han et al. (2022). In total, ODG-NET comprises 48 million parameters for S = 3. and the training stage requires 65 GFLOPS.
Training protocol and model selection. We employ standardized training protocol across all datasets. During each training iteration, we first optimize Eq. using the Adam optimizer Kingma & Ba (014)) 4). with a learning rate of 2e 2 - and betas of (0.5, 0.99). We then minimize Eq. using Adam with a learning rate of 2e 2 and betas of (0.9, 0.99). Our batch size is typically set to 64, and we train for 30 epochs, except for DomainNet, where we use a batch size of 128 and train for 40 epochs. We follow a cross-validation approach to estimate the loss weights, holding out 10% of samples per domain and using held-out pseudo-open-sel validation samples obtained through cumix Mancini et al.) (2020b), that the model has not seen to select the best- rest-performing model. In this regard, the mixup samples do not have clear semantic meaning as they are generated by randomly combining two images. Hence, they can be considered representative open samples. We further consider 3 0.5 to put W soft constraint in LGAN- A large / instigates the generation of ambiguous images in order to make them different from D. Besides, we set a 0.5 following Shu et al. (202T).
Evaluation protocol. For ODG experiments, we report the top-1 accuracy for closed-set set samples (Acc) and the H- score for closed and open samples. For closed-set set DG experiments, we consider the top-1 performance. We report the mean + std. over three runs.
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Published in Transactions on Machine Learning Research (11/2023)
4.1 Results on open DG tasks
Baselines. Our baseline method, AGG, involves merging the source domains with different label sets and training unified classifier on all the classes. In comparison, we evaluate the performance of ODG-NET against traditional DG
methods that are less sensitive to label changes between different source domains, as outlined in Shu et al.
(2021)
These include state-of-the-art meta-learning-basse Mancini et al. (2020a); Zhou et al. (202I); Shi et al. (202T); Rame et al. (2022), heterogencous DG Li et al.
and augmentation-baat
DG methods [i et al. (2018a
2019a)
2019b)
and methods that produce discriminative and generic embedding spaces Wang al.] (2020b); Huang et al.
(2020):
Zhang et al. (2022). As per [Shu et al. (00TT) we employ confidence- based classifier for our competitors. Here, sample classified as unknown if the class probabilities
below a predefined threshold. Alternativel,, we also compare against the only existing ODG technique. DAML,Shu et al. (2021) and consider a variant where we combine
DAML with Openmax Bendale & Boult (2016b) based OSR. Finally, we report the results of two open-set recognition baselines, Openmax Bendale & Boult 6016b) and MORGAN Pal et al. (2023b)
Table I: Comparative analysis for PACS on ODG, (In %)
Art
Sketch
Photo
Cartoon
Avg
Methods
H-score
Ace
H-score
Acc
H-score
Ace
H-score
Ace
H-score
AGG
51.35
38.87
49.75
47.09
53.15
44.19
66.43
48.98
55.17
44.78
OpenMax Bendale & Boolt 2016b 2016b
53,33
40.83
55.45
54.18
73.76
53.29
73.39
53.87
63.98
50.54
MORGAN Par all 20255
44.56
35.78
52.31
51.49
70.29
49.55
66.31
48.69
58.37
46.37
MLDG 201ha
44.59
31.54
51.29
49.91
43.35
71.64
55.20
57.43
45,00
Ll 201 96
51.12
39.01
51.15
49.28
60.94
45.79
69.32
52.67
58.13
46.69
Epi-CC
2019g
54.16
41.16
46.35
46.14
70.03
48.38
72.00
58.19
60.64
48.47
Wang et
20/00
52.97
39.21
53.62
52.00
51.86
36.53
67.77
52.05
56.56
44,95
RSC Huang
2000
50.47
38.43
50.17
44.59
67.53
49.82
67.51
47.35
58.92
45,05
CuMix Mancuni al. 22000a
53.85
38.67
37.70
28.71
65.67
49.28
14.16
47.53
$7.85
41.00 .0
Fish Shi el 2012
52.22
39.54
55.54
54.28
69.41
48.87
69.85
$1.75
61.75
48.61
Discitanglkeneni Zhiang al. 2022
53.18
56,39
53.36
71.99
70.54
50.63
63.02
47.42
Mixstyle at 2021
53.41
39.33
56, 10
54.44
72.37
47.21
71.54
52.22
63.35
48,30
DAML Shu ot al. 2021
54.10
43.02
58.50
56.73
75.69
53.29
73.65
54.47
65.49
$1.88
DAMI. OpenMax Hendale Boult 2016a
52.73
57.81
56.82
74.55
54.55
75.84
55.96
65.23
52.15
ODG-NET
57.21
46.19
61.85
59.25
78.76
56.67
77.39
61.11
68.80
55.81
Table 2: Comparative analysis for Office-Home on ODG. (In %)
Clipart
Real- World
Product
Methods
Acc
H-score
Acc
H-score
Acc
H-score
Acc
Hescore
Acc
H-score
AGG
42,83
44.98
62.40
53.67
54.27
50.11
42.22
40.87
50.43
47.41
OpenMax Bendale & Boult
2016b
43.29
43.67
62.45
59.86
56.71
52.29
48.76
47.54
52.81
50,84
MORGAN ot a. 20258
39.68
59.87
59.76
55.33
52.19
43.33
42.87
49.55
49,00
MLDG 2018a
41.82
41.26
62.98
55.84
56.89
52.25
42.58
40.97
51.U7
47.58
FC ef 20196
41,80
41.65
63.79
55.16
54.41
$2.02
44.13
43, 25
51.03
48.02
Fp
2019a
37.13
42.05
62.60
54.73
54.95
52.68
46.33
50.25
PAR Wang ci
20.26
41.27
41.77
65.98
$7.60
55.37
$4.13
42,40
42.62
51.26
49,03
RSC luang el al
2120
38.60
38.39
60.85
53.73
54.61
$4.66
44.19
44.77
49.56
47,89
CuMix Mancini et
41.54
43.07
64.63
58.02
57.74
55.79
42.76
40.72
51.67
49.40
Fish Shi
43.76
44.38
65.25
58.74
57.86
57.33
49.78
46.57
54,16
51.75
Disentanglement /hang et
2022
44,89
42.87
63.18
59.51
58.88
55.44
45.49
43.43
53.16
50.31
Mixstyle Zhou al (0021)
42.28
41.15
61.78
60.23
59.92
53.97
50.11
42,78
53.52
49.53
DAML 2012
45.13
43.12
65.99
60.13
61.54
59.00
53.13
$1.11
56.45
53,34
DAML- OpenMax Bendale & Boult
2016a
45.51
44.25
60.33
61.46
60.71
59.67
51.34
52.34
54.47
54.43
ODG-NET
49.81
48.39
68.45
63.33
63.29
61.51
$6.05
53.52
59.40
$6.69
Quantitative and qualitative analysis. Tables 1 present a performance comparison of ODG-NET with the literature on five datasets. ODG-NET consistently outperforms others in terms of Acc and H-score for all domain combinations and the average leave-one-out case where all the domains except one are used during training and the model is validated on the held-out target domain. For example, on PACS, ODG-NE: achieves an Acc of 68. 80% and an H-score of 55.81%, beats the previous best of DAML+OpenMax which obtained 65.23% and 52.155 12.15, respectively. Our method outperforms et al. (2021) by As 3% for Office-Home and 5% for VLCS and Dig in H-score. For the Multi-
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Published in Transactions on Machine Learning Research (11/2023)
Table 3: Comparative analysis for VLCS on ODG, (In %)
Caltech
LabelMe
Methods
Ácc
H-seore
Acc
H-score
Acc
H-Score
H-score
H-score
Acc
AGG
65.49
62,39
46.15
42.78
48.29
44.31
44.48
40.67
51.10
47.58
OpenMax Bendale
47.77
MORGAN
20233
61.59
59.87
43,33
40.98
46.71
40.08
42.22
41.16
48.46
45.52
MLDG al 20
66.91
63.11
45.65
41.76
48.37
42.71
44.29
42.22
51.30
47.45
FC al. 2019b
65.59
60.48
45.23
44.22
49.23
45.89
45.32
44.45
51.34
48.76
EPEECR
66.81
62.98
47.83
45.35
50.22
45.56
46.03
44.32
52.72
49.55
PAR Wang al 20406
65.78
61.25
46.21
42,54
50.11
46.33
45.39
43.65
51.87
48. 44
[SCnn et al.
2020
64.43
61.39
45.61
43.71
60
42.65
45.76
42.71
51.10
47.61
Fish Shi ct 2021
65.82
62.29
47.66
46.52
50.11
45.53
45.54
43.33
52.28
49.41
Disentanglemsss Zhang et
2022
63.27
61,86
48.65
45.39
50.53
43.22
46.72
45.76
52.29
49.05
Mixstylo Zhou al (2221
66.11
63.19
46.72
46.22
49.75
46.19
46,62
46.87
52.30
50.61
DAMI, Shu Shu
2021
69.18
64.65
48.22
47.71
49.87
47.22
46.87
46.78
53.53
51.59
DAML + OpenMax Bendale & Boult 2016a
68.24
66.51
46.43
46.18
$2.49
47.00
47.43
47.71
53.64
51.85
ODG-NET
73.42
69.93
51.89
51.56
53.44
$2.75
50.21
50.14
57.24
56.09
Table 4: Comparative analysis for Digit- on ODG, (In %)
MNIST
MNIST_M M
SVHN
SYN
AVG
Methods
Acc
H-score
Acc
H-score
Acc
H-Score
Acc
H-score
Acc
H-score
AGG
69.45
63,28
43.51
42.15
50.26
46.89
61.87
56.31
56.27
52.15
OpenMax Bendale & Boull
20166
73.87
65.39
46.71
44.63
53.87
48.21
65.55
61.63
60.00
54.96
MORGAN
72.45
63.59
41.78
43.32
50.67
48.77
54.29
MLDG
20180
71.33
69.22
43,19
41.78
48.73
45.37
61,28
58.22
56.13
33.64
FC ct 9019
71.29
66.29
41.22
40.67
47.72
44.41
59.33
55.67
54.89
51.76
PAR Wang
40206
70.88
67.47
44.62
42.65
49.34
45.72
60,23
57.11
56.26
53.23
RSC luang ml. 2020
72.77
66.34
42.27
41.43
48.32
45.59
62.41
$7.26
56.44
52.65
CuMix Mancini al.
2020s
72.10
67.52
45.88
43.74
52.22
47.22
62.33
58.33
58.13
54.20
Fish Shi
74.43
66.89
42.65
44.45
52.31
46.71
64.76
58.73
58.53
54.19
Disentangiementi Zhhnng et
2022
71.29
68.83
45.38
41.59
50.16
42.71
65.66
60.33
58.12
53.36
Mixstyle Zhon (202
76.56
70.56
47.81
45.66
54.97
47.24
61.80
61.96
60.23
56.35
DAML
2021
73.98
DAML OpenMax Bendall & Boult 2016a
75.77
71.38
48.51
47.49
55.61
49.69
65.49
62.77
61.34
$7.83
ODG-NET
78.56
75.75
50.52
50.22
57.81
$2.62
68.94
65.33
63.85
60.98
6
6
6
(DuRAR 4E5000 UOINUA 9/
Siye Variation
Figure 3: (a) Depiction of the generated pseudo-open-set samples by ODG-NET. (b) Depiction of the pseudo-stylized
images (columns 2-4) generated by ODG-NET w.r.t. the input images mentioned in column 1. (c) Results of the intermediate images (two images for both casee.)showing the transition between pair of domain/label.
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Table Comparative analysis for Multi-Dataset on ODG. (In %)
Clipart
Real
Painting
Sketch
Avg
Methods
Acc
H-score
Acc
H-score
Acc
H-Score
Acc
H-score
Acc
H-score
AGO
29.78
34,06
65.33
64.72
44.30
51.04
27.59
35.41
41.75
46.31
OpenMax Bendale & Boult 2010b
36.72
34,41
63,29
62.88
44.19
50.75
34.51
32.29
44.67
45.08
MORGAN Pal 202330
29.45
28.59
59.97
62,22
43.75
47.53
31.19
30.04
41,09
42.09
MLDG Li a
80
29.66
35,
65.37
54,40
44.04
50.53
26.83
34,57
41,48
43.65
FC et 2019h
29.91
35.42
64.77
63.65
44.13
50.07
28.56
34.10
41.84
45.81
Cp
2019a
27.70
37.62
60.31
64.95
39.57
33.74
38.59
46.64
PAR Wang of
20200b
29.29
39.99
64,09
62.59
42.36
46.37
30,21
39.96
41,49
47.23
RSC Huang ot a.
2020
27.57
34,98
60.36
60.02
37.76
42.21
26.21
30.44
37.98
41.91
CuMix Mancini al
2020a
30.03
40.18
64.61
65.07
44.37
48.70
29.72
33.70
42.18
46.91
Fish Shi at
32.78
35.42
65.43
67.77
45,37
48.81
32.35
32.45
43.98
46.11
Disentang/ement Zhäng et
2022
28.76
33.33
64.48
64.44
42.29
50.05
30.65
35.87
41.54
45.92
Mixsly Zhou el
Y2021 2021
30.03
40.18
64.61
65.07
44.37
48.70
29.72
33.70
42.18
46.91
DAML Shu
37.62
44.27
66.54
67.80
52.93
34,48
51.71
DAML + OpenMax Bendale & Boult 1016a
2016a
38.55
45.51
66.87
68.89
48.51
53.12
35.61
42.56
47,38
52.52
ODG-NET
40.75
47.54
69.49
71.22
50.11
55.39
37.58
44.10
49.48
54.56
dataset, ODG-NET achieves an Acc of 49.48% and an H-score of 54.56%, which is improvement of more than 3% than (Shu et al. (021). Visually, the T-SNE| Van der Maaten & Hinton (2008) Fig. 4(a) confirms the discriminative and domain-independee nature of the semantic space given the augmented source data.
Moreover, we present a collection of synthetically created images produced by our novel ODG-NET. As illustrated in Figure 3 (a) displays the generated pseudo-open-set examples, while (b) exhibits the pseudo-stylized pictures (columns 2-4) derived from their corresponding input images (column 1). This comparison highlights the evident transformation from the original input images to the synthesized pscudo images. Additionally, in (c), we demonstrate two aspects: first, the variation in artistic style of the input image, such from sketch painting: second, the combined shift in both style and label, exemplified by the transition from "dog" class image to a "bag" class image.
4.2 Results on closed DG tasks
In the context of closed-set DG tasks, we compare the performance of ODG-NET against the existing literature, focus- ing supervised pre-training methods that use meta-learning, regularization, and domain augmentation techniques
Zhou et al. 2020bb 2021);; Chen et al. (2021): b: Kang et al. (2022); Chattopadhyay et al. (2020): ; Xu al. 2021 Shu
al. 22221 Shi et al. (2021 Du et al. (2020); Zhao et al. (2020). among others.
As shown in Table 6 for the five benchmark DG datasets, ODG-NET outperforms all comparative techniques in the average leave-one-out DG evaluations, despite these techniques being designed explicitly for closed-set DG. We observe an improvement of least - 4% across all datasets. For DomainNet, ODG-NET achieves an average accuracy of 50.16%, which is 4% better than the previous state-of-the-ar method SWAD Cha et al. (2021). likely due to the more diversified training set which ODG-NET is trained. Finally, in closed-set DG experiments, ODG-NET outperforms DAML Shu et al. 2021 by significant margin of at least 5 - 7%.
4.3 Ablation analysis
Model and loss ablation. In Table we present the effects of different components of the ODG-NET model and the loss functions for PACS and Office-Home datasets. We confirmed that embedding networks are crucial for learning latent conditioning information in a meaningful way. The model without embedding layers resulted in a performance drop of approximately 5 - 6% in the H-score. Similarly, attention modules helped to highlight the style and semantic features better, and using (Aa, Ao) resulted in a --% improvement in the H-score for both datasets. Additionally, we experimented with using a common backbone for the source domains instead of (Fi)s This approach significantly reduced the H-score by 4% and 6% for both datasets, indicating the importance of multi-view features learned by the domain-specine backbones.
Furthermore, Fa helped to discriminate the domain and semantic properties of Fer(x), and the omission of Fa reduced performance by almost 5%. We also removed both F, and the local classifiers (Fi )= simultancously. resulting in a performance drop of over 6%. When we trained F, from scratch instead of using a pre-trained ResNet-18 backbone, we observed performance drop of around 3%. The pre-trained ResNet- 18 backbone already rich in discriminative information, which helps our DG tasks. Concerning the loss function of feature optimization, it is evident that both
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Published in Transactions on Machine Learning Research (11/2023)
Average leave one oou accuracy
(Class
Real (Class 2)
Generated (Class 2]
(Class
(Class
Real (Class
Generated (Class 4]
Class
35
25
Cumix
ODGNET
(h)
Average leave one out accuracy
60
Close (withoul diversity loss)
Open (willhout diversity loss) Open (with diversity
Close diversity loss)
300
40
200
20
100
0
Mixstyle L2A-OT
ODG-NET
PACS
VLcs
Office-Home Multi-dataset
Digits DG
(c)
(d)
Figure 4: (a) T-SNE of real and cGAN synthesized images the semantic feature space F for PACS dataset. (b) Accuracy comparison between ODG-NET and Cumix Mancini et al. (2020a) based pseudo-open sample generation. (c) Accuracy comparison between ODG-NET and Mixstyle Zhou et al. [2021) and 1.2A-OT Zhou et al.) (2020b) based closed-set sample generation. (d) The Frechet distance Dowson & Landau (1982) between real data and the closed and pseudo-open images generated, with and without the consideration of W in LGan-
168.7
54.00
150
150.2
50
Average H-score
Distance
109.7
114.5
104.5
40
100
94.7
91.9
83.1
AGG
50
DAML
20
DAML
ODG-Net Dom, classifier
10
ODG-Net w/o entropy min
ODG-Net
ODG-Net
Ar-Rw
Pr-Rw
Cl-Rw
10
20
of
No. of unknown classes
(a)
(b)
Figure 5: (a) Frechet distance between the source and target domains for the closed-set classes. (b) Openness analysis.
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Published in Transactions on Machine Learning Research (11/2023)
Table Results PACS, VLCCS, Office-Home, Digits-DG and DomainNet datasets under close-set DG. (In %)
Methods
PACS
VLCS
Office-Home
Digits-DG
DomainNet
CCSA Motiian et al.
2017
79.40
70.20
64.90
74.50
SFA-A Lr al. (202
81.70
74.00
79.60
MetaReg Balay al.
2018
81.70
43.62
MixStyle Zhou
2021
83.70
65.50
34.0
JiGin Carlucci Mariica et
2019
80.51
73.19
61.20
76.20
SagNet Wa al.
83.25
62.34
40,30
RSC Huang et
2120
85.15
75.43
63.12
38.90
DDATG Zhou
20
83.10
65.50
77.58
L2A-O1 Zhou al.
2020b
82.80
78.10
FACT et [02]
84.51
81.55
STEAM Chen cl al. [2021
86.60
66.80
83.13
Style Neo.
Kang cl all
2022
85.47
65.89
44.60
Liu ct al.
Liu ct al. 202T
76.48
67.85
80.02
MMD-AAE
20188) 8b
77.00
72.30
62.70
74.60
Cross Cross-Grad Shankar al.
2018
80.70
64.40
75.83
MASF Dou et 2019
81.03
74.11
BISNet Wang 2020
2020a
82.15
74.65
MctaViB Du
74.54
DGER Zhao
2020
74.38
MixUp Zhang el 2017
DMG Chatiopadhyyy et 2020
43.63
SWAD al. 2021
88.10
79.10
70.60
46.50
Fish Shi ct 2021
85.50
77.80
68.60
42.70
DAML Shu ct al. (021)
82.70
72.95
67.71
79.89
ODG-NET
90.66
79.85
72.92
86.75
50.16
Table 7: Model and loss ablation analysis PACS & Office-Home datasets. (In %)
PACS
Office-Home
Model variants of ODG-NET
Ace
H-score
Acc
H-score
w/o (Fom: Fu. Fy.
63.43
50.82
53.07
50.55
w/o Ai and A.
66.01
52.93
56.58
53.53
w/o (JT)S but common backbone for the domains
63.73
$1.53
53.14
50.50
Fd
64.98
$2.09
55.55
52.69
w/o F.J and (FF)
62.38
49.67
51.95
49.02
w/o Entropy loss
66.81
53.15
57.35
54.36
w/o T-on
65.36
51.73
55.40
51,60
w/o Isem
64.74
51.12
54.57
51.11
w/o F, and {FT) and Tem
59.07
47.07
48.91
45.56
with training J, from scratch
65.96
$2.86
56.38
53.33
w/o in LCAN
66.26
53.96
58.38
54.93
Sensitivity to noise variance of GAN synthesizing closed and pseudo-open samples
poe
noise
NOO.. 1); pos NNO.,
noise
65.30
52.51
55.38
52.53
pes
AE 1); pos NN(0
66.35
53.32
56.44
53.40
pes (O, 1): pos
((0,3)
67.29
54.21
57.18
54.49
naise
pes (O, 1);
pos
NO0., 4)
67.98
55.14
58.29
55.52
naise
moise
naise (10, 1): Pos
noise
Ni1. 10)
68.22
55.37
58.72
56.11
Pes
noise
(0,
Pos
())
67.13
54.22
55.65
52.24
ODG-NET(P2S
NoO. 1);
pos
68.80
55.81
59.40
56.69
boise
the closed-set contrastive and open-space entropy regularizer assists in generating a more discriminative feature space. The model without any of these losses or the full Lsem led to performance degradation by approximately 4%. Finally, we removed the diversity regularization W in LçAN- Although, as per Fig. [(d) W induces diversity the generated images, empirically, we observed nominal change in the accuracy 1.5%) the presence of W.
Comparison of our augmentation with methods from the literature. Our augmentation technique enables more
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controlled style and label mix-up, and compared it against two types of augmentation techniques from the liter- ature: existing style diversification approaches /hhou et al. (2020b 202T) for closed-set classes, and Cumix Mancini ct (2020a), which performs random image mix-up so that the generated images can be proxy for open-space. Our results in Fig. 4(b) [c) demonstrate that ODG-NET performs better with our proposed augmentation. Our method is interpolation- based,, which allows us to generate more style primitives than Zhou et al. (2020b). Since our method is image-based as opposed to the naatrr-bbsed method of ZZhou et al. (2021) we can handle the semanties better, Similarly, for pseudo-open samples, we can generate more meaningful images with varied similarities the closed classes than the random mix-up of Mancini et al. (2200a).
Sensitivity to variances of pue/ee. In this experiment, we tune the a parameter of Roose while fixing noise for Fa As shown in 7 7 we observe that as we increase from I to 5, the model performance continuously improves from 52.51% 1 to 55.81 % for PACS and from 52.53% to 56.69% for Office- Home. With high variance, the open samples are sparsely distributed, better covering the open space. However, the performance improvements are found to saturate beyond o- 5. On the other hand, increasing the variance of P significantly affects the performance, leading to drop of at least 3%. This occurs because the generated images may deviate from the original semantic concepts, degrading the quality of the generated images.
Freéhet distance for domain alignment. To assess the domain independence of Fo we calculate the Frechet distance Dowson Landau (1982) between the closed-set classes of the source and target domains for Office-Homm Home, with the target domain being Real-world. In Fig. [(a)] we show the Freéhet distance of the baseline AGG, DAML, and two variants of ODG-NER -ET, with and without the domain classifier Fa. The full ODG-NET produces the minimum Frechet distance, indicating that it performs the best domain alignment among the compared models. The model without Fa performs poorly compared to the full ODG-NET, suggesting that the use of Fa helps disentangle features better, mak- ing F less affected by domain properties and focus on shared components.
Sensitivity to number of target open classes. Since there is no restriction on the number of open classes in the target domain, we are interested in assessing whether ODG-NET can handle different numbers of open classes during inference. Here, we considered the average leave-one-out H-score for Office-Home and simulated three scenarios with different numbers of open classes in the target: 10, 20, and 30. In Figure [ ODG-NET consistently outperforms DAML et al. (2021) by at least 3% for different openness factors. The entropy minimization component of Lyem widens the gap between open and closed spaces, which is helpful in this regard. We validate this by removing the entropy component of Lsem and re-running the experiments, in which case we find that performance drops by 2 - -3%. Performance comparison when the source domains have a disjoint set of classes. Here, we present a novel exper- imental scenario in ODG, where the source domains have completely different sets of classes, and the target domain consists of all the classes from the sources, plus previously unknown class samples. We compare the performance of ODG-NET with that of DAML Shu et al. (202T) for this setup in Table g We find that ODG-NET outperforms DAML by around 3%, demonstrating its robustness to extreme domain and label shifts within the source domains.
Table 8: Comparison between DAML Shu et al. 2021 and ODG-NET when the source domains have mutually disjoint classes on Office-Home dataset in terms of H-score. (In %)
Domain
Clipart
RealWorld
Product
Art
Average
DAMI Shu et al. 2021
40.12
58.72
54.85
47.25
50.23
ODG-NET
45.69
62.77
56.95
49.86
53.81
5 Takeaways
In this paper, we present ODG-NET, solution to the challenging problem of open domain generalization. This task combines domain generalization, open-set learning, and class imbalance in common setting. One of the key features of ODG-NET is the novel generative augmentation, which enables continuous domain and label conditional image synthesis through interpolation of conditioning variables. This augmented training set is utilized to learn a discrimina- tive and unbiased semantic space for an open-set classifier while minimizing the effects of domain- -deendde artifacts. In our experiments, ODG-NET achieves state-of the-an art performance for both open-set and closed set domain gen- eralization on six benchmark datasets. We plan to extend our evaluation to more safety-critics applications in the future.
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Reviews:
[{"review_id": "4iGZ5nSwsp", "reviewer": "Reviewer_wqPp", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strength\n\n- This paper proposes a new network structure called ODG-NET to address the Open Domain Generalization problem.\n\n- ODG-NET constructs an open-set classifier by acquiring discriminative, unbiased, and disentangled semantic embedding spaces. \n\n- To synthesize diverse augmented images from the source domain, this paper proposes a novel conditional GAN with cycle consistency constraints to interpolate domain and category labels and regularization to avoid modal collapses.\n\n- Experimental results on six benchmark datasets show that ODG-NET outperforms the baseline method.\n\nWeaknessess\n\n- The network as a whole is admittedly new. On the other hand, many of the individual methods are techniques that have already been used for domain generalization and domain adaptation, and have marginal novelty.\n\n- The network structure is complex in order to incorporate different properties.\n\n- Similarly, many loss functions are combined, and the methods lack simplicity.\n\n- Many hyperparameters, such as \\alpha, \\beta, \\epsilon, and different weights w for loss functions, which are difficult to tune.\n\n- Large performance variations depending on the noise parameters.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "To address the challenge of Open Domain Generalization (ODG), this paper proposes a model called ODG-NET. The model introduces a generative augmentation framework that generates new domains of style-interpolated closed-set images and new pseudo-open images by interpolating the content of paired training images. It also addresses the problem of style bias by representing all images in terms of all source domain properties. As a result, a multi-class semantic object classifier incorporating both closed and open class classification features is trained, along with a style classifier to identify style primitives.  Experimental results on six benchmark datasets show that ODG-NET outperforms the baseline method.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- The text in Figure 2 is too small and should be made easier to read. Also, it would be better to describe the function of each module in the figure.\n\n- In Figure 2, \\mathcal{F}^b_{1S} should be \\mathcal{F}^b_{l1} and \\mathcal{F}^c_{1S} should be \\mathcal{F}^c_{l1}.\n\n- Right brackets are missing in the denominator and numerator of equation (7).", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "ZXbOVXfFtc", "reviewer": "Reviewer_NZiC", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1. Extensive experiments are employed to validate the effectiveness of the proposed method.\n\n2. The proposed method achieves promising results for open and closed-set domain generalization.\n\nWeaknesses\n\n1. The authors should thoroughly review the writing to ensure it is easily comprehensible to a broader audience.\n\n2. The clarity of the depiction in Figure 2 should be enhanced, and it is advisable for the authors to provide a more lucid illustration of the proposed method.\n\n3. The proposed method appears complex due to its numerous objectives, with some not being adequately explained in the method section.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper introduces ODG-NET, a solution for open domain generalization, combining domain generalization, open-set learning, and class imbalance. \nODG-NET employs generative augmentation for continuous domain and label conditional image synthesis, enhancing open-set classification while reducing domain-related artifacts. \nIt achieves state-of-the-art performance on six benchmark datasets for both open-set and closed-set domain generalization.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "As mentioned earlier, it is recommended that the authors enhance the clarity of their writing. This includes providing more comprehensive explanations for each component of the final objective and elucidating the underlying motivations, with the aim of improving the paper's overall accessibility to readers.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "RXMUPJICay", "reviewer": "Reviewer_U3Gw", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengthens\n1. a novel and interesting problem. (I like this problem)\n\n2, an effective method\n\nWeaknesses\n1. Poor writing (please polish it again)\n2. Please consider some baselines in OOD detection\n3. I expect you to explore whether generalization can benefit detection and detection can benefit generalization.\n4. Missing references:\nsome reference related to OOD detection, open set domain adaptation and domain generalisation, e.g.,\n1. Is out-of distribution detection learnable?\n2. Moderately Distributional Exploration for Domain Generalization\nand so on", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper considers a novel issue  Open Domain Generalization, which aims to give open classifier to generalize well when we have multiple source domains.\n\nTechniques:\n1. a novel conditional GAN with a cycle consistency constraint\n2. an anti-mode-collapse regularizer that interpolates domain and category labels\n\nExperiments show a good performance of the proposed method ODG-NET.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please see the weaknesses", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: Reviewers requested further polishing and improvement of the text. Moreover, the paper needs some polishing also with respect to figure and table spacing and sizes - it seems that the paper was compressed in that regard to fit the 12 page limit. Please: 
- Make sure that there is enough space around figures (e.g. Fig2 would be better on the top of the page, with extra margins,  Fig 4 is also hard to read, enlarging the figures and placing them in a 2 by 2 grid would be better, etc)
- Make sure that the fonts in the tables are not much smaller than actual text - tables are now very hard to read.  Tab1 and Tab2 can be split into two each, ie one per dataset, Tab3,4 and 5 can cover more width so that they are readable. Also please use \citep{} for all paper references in the Tables (ie so that the reference is in a parenthesis)

It is ok of the paper ends up being slightly longer than 12 pages, as long as it is readable.
Decision: Accept (poster)