Disentangled Embedding through Style and Mutual Information for Domain Generalization
Authors: Noaman Mehmood
Kenneth Barner
Venue: Accepted by TMLR ()

Abstract: Deep neural networks often experience performance degradation when faced with distributional shifts between training and testing data, a challenge referred to as domain shift. Domain Generalization (DG) addresses this issue by training models on multiple source domains, enabling the development of invariant representations that generalize to unseen distributions. While existing DG methods have achieved success by minimizing variations across source domains within a shared feature space, recent advances inspired by representation disentanglement have demonstrated improved performance by separating latent features into domain-specific and domain-invariant components. We propose two novel frameworks: Disentangled Embedding through Mutual Information (DETMI) and Disentangled Embedding through Style Information (DETSI). DETMI enforces disentanglement by employing a mutual information estimator, minimizing the mutual dependence between domain-agnostic and domain-specific embeddings. DETSI, on the other hand, achieves disentanglement through style extraction and perturbation, facilitating the learning of domain-invariant and domain-specific representations. Extensive experiments on the PACS, Office-Home, and VLCS datasets show that both frameworks outperform several state-of-the-art DG techniques.

Published in Transactions on Machine Learning Research (06/2025)
Disentangled Embedding through Style and Mutual Infor- mation for Domain Generalization
Noaman Mehmood
nooman@udel.edt edu
Deportment of Electrical and Computer Engineering University of Delowore
Kenncth Barner
barner & uudel. edu
Deportmend of Electrical and Computer Engineering University of Delawore
Reviewed on OpenReview: https: // openreveew. net/ pert/formm id= 5w255666tedyyyb
Abstract
Doep neural networks often experience performance degradation when faced with distri- butional shifts between training and testing data, a challenge referred to as domain shift. Domaín Generalization (DG) addresses this issue by training models on multiple source domains, enabling the development of invariant representations that generalize to unseen distributions. Although existing DG methods have achieved success by minimizing vari- ations across source domains within shared feature space, recent advances inspired by representation disentanglement have demonstrated improved performance by separating la- lent features into domain-specific and domain-invariant components. We propose two novel frameworks: Disentangled Embedding through Mutual Information (DETMI) and Disen- tangled Embedding through Style Information (DETST). DETMI enforces disentanglement by employing a mutual information estimator, minimizing the mutual dependence between domain-agnostic and domain-specific embeddings. DETSI, the other hand, achieves dis- entanglement through style extraction and perturbation, facilitating the learning of domain- invariant and domain-specifi representations. Extensive experiments on the PACS, Office- Home, VLCS and Terrainc datasets show that both frameworks outperform several state-of-the-an DG techniques.
1
Introduction
Deep neural networks excel at learning discriminative features and achieve outstanding performance in computer vision tasks. However, their performance deteriorates significantly when tested on data with distribution different from the training data [en--avid et al. (2010). For instance, a network trained on images from an urban environment performs poorly when applied to rural environments. This performance drop results from the domain shift Sethhonero-Candele et al. (2022), which refers to the difference between the source and target data distributions. To address this issue, Domain Generalization (DG) was introduced in 2011 Blanchard et al. (2011). DG proposes training a model on multiple relevant source domains develop invariant representations that generalize new distributions not present during training.
During the past 12 years, numerous approaches have been proposed to address the challenge of DG. Among these, adversarial training has been widely explored to encourage domain-invariant feature lcarning in dif- ferent. domains Li et al. (2018ble c): Sinha et. al. (2017). Other stralegies have employed meta-learning Li et al. (2018a); Balaji et al. (2018) Zhao et al. (2021): Finn et al. (2017), which enables models to learn to generalize by simulating domain shifts during training. Ensemble learning Rame et al. (2022) is another popular method in domain generalization, where multiple models are trained with diverse data views, and their predictions aggregated to improve the robustness against domain changes.

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Data augmentation techniques have also emerged promising solutions, in which synthetic data is gener- ated to expose the model to a wider range of variations, helping it generalize to unseen domains Mehmood & Barner ) Volpi et al. (2018): Zhou et al. (2020a b). Furthermore, some methods focus on learning domain-invariant features, such as shape reprosentations, by minimizing the divergence between latent rep- resentations weeween domains, thereby improving generalization to new environments Zhou el al.] (2022); Lu ct al. (2022). These approaches represent key advances in DG, each contributing unique mechanisms to address the distributional shifts that lead to domain shifts.
Most of these methods discard domain-specific information (e.g, background, style) to minimize the diver- gence between the embeddings from different souree domains. Recently, inspired by disentangled represen- tation learning, the authors of POEM Jo & Yoon (2023) trained & model to learn domain-invariant and domain-specific information separately. In addition, to remove redundant information between these two feature spaces, cosine similarity was minimized, further enhancing disentanglement.
Inspired by disentangled embedding learning POEM Bui et al. (2021); Jo & Yoon 2023 Yu et al. (2024) for domain generalization (DG), we introduce two novel frameworks designed to effectively learn domain- agnostic embeddings by leveraging domain-specific information. These frameworks enable the model to explicitly factorize the representation space, allowing for more targeted learning of invariant features critical for out-of-distribution generalization. By decoupling the domain-specific noise and task-relevant, signal, we aim to enhance robustness and transferability across unseen domains.
In our first proposed framework, named DETMI, we leverage domain-spectte knowledge to decouple domain- invariant representations. To this end, we introduce domain-specific encoder and classifier alongside a task-specific encoder and classifier. To improve disentanglement, POEM Jo & Yoon 2023) employs co- sine similarity to promote linear independence between domain-specific and domain-aggostic feature spaces. However, cosine similarity does not account for higher-order dependencies, which can result in residual in- formation Icakage between the two spaces and compromise the effectiveness of the disentanglement. To overcome this limitation, we propose minimizing the mutual information between the two feature spaces. This strategy reduces higher-order correlations and facilitates the learning of more robust and statistically independent representations, thereby enhancing generalization to unseen domains. The DETMI framework goes beyond geometric constraints by offering a principled mechanism for enforcing independence, thereby enabling deeper statistical disentanglement of the underlying factors of variation.
In our second approach, we introduce the DETSI framework, which also leverages domain-specific knowledge through a domain-specific encoder and classifier. Additionally, to improve disentanglement, it incorporates style information to separate domain-specifie and domain-agnostic embeddings. Inspired by [Huang & Be- longie (2017), which establishes a correlation between the domain of an image and its style, we apply style perturbation encourage the extraction of domsin-agnostic embeddings. These embeddings prioritize high-level features, such as object structure and semantic content, over domain-dependent attributes. This approach reduces the model's reliance on superficial cues and promotes the learning of features that generalize across domain shifts. Mcanwhile, for domain-specifie embeddings, DETSI captures style-spocific character- istics, including texture and arlistic style, rather than low-level ures like edges or pixel intensity. By explicitly modeling style-based attributes, DETSI effectively disentangles comainn-pecific components from domain-invariant ones and produces robust embeddings, thereby significantly enhancing generalization across diverse unseen domains.
We conducted extensive experiments on the PACS Li et al. (017)) ), OfficeHHome Venkateswara et al. (0117)
VLCS Torralba & Efros (2011), and TerraIncognita Beery et al. 2018 benchmarks. The results demon-
strate that the proposed approaches outperform several state-of-the-ar (SOTA) methods addressing Domain Generalization.
The remainder of this paper is organized as follows. Section 2 reviews related work, summarizing key methods developed to address the challenges of domain generalization. Section 3 details the proposed methodologies, including the techniques used to tackle domain generalization. Section 4 describes the experimental setup, covering datasets, implementation details, and the results of the proposed methods. Section 5 presents ablation studies, providing deeper insights into the contributions of individual components. Finally, Section 0 concludes the paper by summarizing the findings and discussing their implications.
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2
Related Work
Domain Generalization (DG) Zhou et al. (2020a) is an approach that trains models using labeled data from multiple source domains to generalize to an unseen target domain effectively. This problem arises naturally in applications such as medical imaging, autonomous driving, and visual recognition, where the distribution of data in the real world may differ significantly from that in the training set, leading to poor generalization performance. Over the past decade, numerous techniques have been proposed to tackle domain generaliza- tion, including domain--nnariann feature learning, which focuses extracting representations that remain consistent across domains; meta-learning, which leverages learning-to-leary paradigms for better adaptabil- ity; data augmentation, which generates diverse training examples to improve model robustness; adversarial learning, which introduces adversarial objectives to align distributions across domains; and disentangled emn bedding learning, which separates Nomain-speciff and domain invarininvariant factors enhance generalization. Each of these approaches is discussed in detail in the following subsections.
2.1 Domain-Invarian Representation Learning
One of the most popular strategies in domain generalization is to learn domain-invariant representations, where features are shared across different domains and remain stable under distributional shifts. Early works in this area have leveraged feature alignment techniques to ensure that representations different domains become indistinguishable in learned latent space. For example, Muandet et al. Muandet et al. (2013) introduced Domain-Invariant Component Analysis (DICA), where they aimed to learn feature transfor- mation that removes domain-specific variations while retaining the information necessary for classification. Similarly, Ghilary el al. proposed Scaller Component Analysis (SCA) Ghilary et al. (2016), method that projects data into a subspace where the variance between domains is minimized and the class separation is maximized.
Another approach uses distribution matching techniques like Maximum Mean Discrepancy (MMD) to align the feature distributions across domains. For example, Li al. Li et al. (2018b) proposed the Domain- Adversarial Neural Network (DANN) framework, where an adversarial loss is used to align feature dis- tributions between domains by confusing domain classifier that attempts to distinguish between source domains.
2.2 Meta-Learning
Meta-learning, often called "learning to learn," " has recently gained traction as a promising framework for domain generalization. Meta-learuing approaches Li et al. (2018a); Zhao et al. (2021); Finn et al. (2017) aim to train model to quickly adapt to new, unseen domains. In this method, data from source domains is divided into meta-train and meta-test segments, allowing the model to be trained specifically to excel on the meta-test data using the meta-train data, mimicking real-world applications where the model must adapt to completely new data.
Li el. al. [i et al. (2018a) introduced a meta-learning framework for domain generalization in which the model trained on multiple source domains to simulate the process of generalizing to new, unseen domains. Specifically, the model is trained in meta-learning loop, where each training iteration mimics the domain generalization process by exposing the model to different domain shifts, helping the model learn robust features that generalize well to unseen domains.
Another key work is by Balaji el al. Balaji et al. (2018), who proposed MetaReg, where a meta-regularization term learned to guide the model's parameters to be aggaoii.. These approaches focus on teaching the model to adapt quickly to new tasks by simulating domain shifts during training. Meta-learning ap- proaches have shown great promise in domain generalization due to their ability to simulate and adapt domain distributions in the training phase.
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2.3 Adversarial Learning
Adversarial learning has also been widely used in domain generalization to reduce the gap between source and unseen target domains. The core idea is to learn indistinguishable feature representations across domains using adversarial training techniques.
In one of the foundational works, Li et Li et al. (2018b) proposed an adversarial autoencoder (AAB), where the encoder is adversarially trained to produce features that are domain-invariant, while domain discriminator is trained to distinguish between features from different domains. The feature extractor tries to fool the domain discriminator, thus learning domain-invariant representations.
In another work, Li al. Li al. (2018c) train a conditional invariant adversarial network to learn domain-invariant representations by making the learned representations on different domains indistinguish- able through adversarial training.
Adversarial approaches have proven to be effective in learning representations that are robust to domain shifts, though they often require careful tuning the adversarial loss function.
2.4 Data Augmentation
In addition to improving DG, data augmentation techniques Zhou et al. (2020a by: Li et al. (2023) introduce more variety to training data by augmenting existing data pairs (x, 3). where x represents the imput and y the corresponding label. These techniques generate transformed pairs (A(z). y), where A(-) is a transformation that preserves the original label. This process helps to prepare the model to handle the diverse conditions encountered in the source domains.
Volpi et al. Volpi al. 2018) proposed an augmentation strategy based on adversarial perturbations, where synthetic examples are generated by perturbing the original data mimic potential unseen domains. The model can better handle domain shifts at test time by training on these perturbed examples.
Shankar et al. Shankar et al. (2018) introduced CrossGrad, an approach that uses the gradient of the domain classifier to perturb input examples. This ensures that the generated examples lie closer to the decision boundary of the domain classifier, forcing the model to learn domain-invariant features.
Zhou et al. Zhou al. (2020b) proposed data augmentation approach that utilizes a data generator to synthesize samples from pseudo-novel domains, effectively expanding the source domain with artificially generated data. By creating these domain variations, the model is exposed to wider range of potential domain shifts, enhancing its ability to generalize to unscen target domains.
In another work, Zhou et al. Zhou et al. (2020a) developed a Deep Domain-Adversarial Image Generation (DDAIG) network to generate more synthetic data using adversarial training, increasing domain diversity, and improving the generalization capabilitics the model. Other techniques like Domain Randomization (DR) Tobin et al. (2017) and image transformations, which adjust visual features such color, texture, and lighting, add further robustness.
Data augmentation methods have been particularly effective when the goal is to simulate diverse, unseen domains during training. However, a challenge with these methods is ensuring that the generated augmen- tations accurately reflect the domain shifts encountered in practice.
2.5 Disentangled Embeddings Learning
Inspired by representation learning, recent advances in disentangled embedding learning for domain general- ization have increasingly focused on partitioning the latent space into domain-invariant and domain-specific embeddings. Researchers, including Bui el al. (2021) and Jo & Yoon 2023). ; minimize metrics such as co- variance or cosine similarity between these spaces to enforce greater independence. Using a similar intuition, Yu al. (2024), minimize KL divergence loss to learn domain-agnostic and domain-speeific emboddings through a single encoder. This separation enhances the model's generalization ability across diverse and unseen domains.
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Our proposed frameworks tackle DG by disentangling latent representations into domain- and domain- invariant components. We leverage domain-specifie information to aid in the learning of domain-invariant semantic features, ensuring a more robust representation. We leverage mutual information and style infor- mation in DETMI and DETSI, respectively, to effectively capture both domain-related and domain-agnostic embeddings. Through this disentanglement, our proposed approaches improve the model's s ability to learn well-separated representations, leading to improved generalization across diverse domains.
3 Proposed Method
The feature and label spaces are represented by X' C CRP and y C R, respectively. A domain is represented by a joint distribution Pay Pxxx,, where Pxxx denotes the set of joint probability distributions on X' x V. In DG, we have access to K similar but distinct souree domains as S (2) o ( each associated with a joint distribution p(&) where (n:(a, , ~ Pay and N(k) denote the total number of data points particular domain k. The goal of DG is to learn a model f X + y using data from the source domain that it can generalize well to an unseen larget domain I having a joint distribution Pry
(k) (
())
The next two subsections introduce frameworks for discntangling embeddings to improve domain general- ization. The first subsection, Disentangled Embedding Through Mutual Information (DETMI), presents a framework that leverages mutual information between domain-specific and domain-invariant components to achieve learning of generalizable features. The second subsection, Disentangled Embedding Through Style Information (DETSI), proposes a complementary strategy that uses style information, such as feature statistics and Gram matrices, to isolate domain-specífie and domain-agnostic features. This framework pro- motes the separation of domain-relevant components by focusing on content and style perturbations, further improving the model's ability to generalize across unseen domains.
3.1 Disentangled Embedding through Mutual Information (DETMI)
DG assumes the invariance between X' and y. Existing methodologics primarily focus on acquiring invariant features from available source domains, anticipating that these invariant features can be exlended to predict the target domains unseen during training. However, these approaches remain susceptible to erroncous predictions because of their inability to handle variations caused by data bias. Domain-specific features such as background, style variation, and location introduce data bias that adversely affects the prediction performance of a model. Drawing inspiration from disentangled embedding learning Bengio et al. (2013). we leverage these domain-specific cues disentangle domain-agnostic representations and extract more generalizable features. By separating domain-specifie information from domain-invariant components, our approach enhances the model's ability to generalize to unseen target domains.
To this end, we propose the Disentangled Embeddings Through Mutual Information (DETMI) framework illustrated in Fig. [ In the framework, we train two encoders, E, and Ea, to learn calegory-related and domain-specific characteristics denoted as Z. and Za, respectively. We also employ two classifiers, C' and č, to predict class labels and domain labels, respectively. The class and domain classifiers are trainod using cross-entropy losses Le and La, defined as:
L. 3 log (a (C())(u);0.);65.)) )
(1)
L. = d log (o (C(Ea(a,; 02):
(2)
where y and di denote the class and domain labels, respectively. The parameters 8e, Sa. d., and Os correspond to the classifiers C, Õ, and the encoders F,, and Eat, respectively. The function denotes the sigmoid activation.
The optimization objective function for learning domain-agnostic feature space through the leverage of domain-specific information is:
La = Lo + Ai
(3)
where d1 is the weighting coefficient.
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Label Classifier
Feature Extractor E.
I(Ze: Zg)
Estimator Ng
Domain Classifler
Ld
Feature Extractor E
Figure 1: DETMI: Disentangled Embedding Through Mutual Information
Although leverage domain-spocific features to learn only domain-agnostic features, this constraint is insufficient to remove all domain-relevant information. A recent utu Jo & Yoon (2023) tackled this challenge by employing cosine similarity to encourage geometric independence between these feature spaces, thus improving disentanglement. Our approach minimizes mutual information between Ze and Za to enforce independence, addressing higher-order correlations beyond the mere spatial arrangement.
3.1.1 Independence through Mutual Information
Let X and Y be two random variables. Mutual information T(X;Y) measures the statistical dependence between two variables.
Theorem 1. If I(X;Y) = o, then X and Y are statistically independent.
Proof. The mutual information between two random variables and is given by:
((x:)) - // P(z.v) log P(r)
P(x.y) dx dy.
(4)
IT Y(X;Y) then:
log P(r,y) 0 P(x,v) P(x)
(5)
P(x)
In light of Theorem 1, well-known result in information theory, reducing I(X;Y) brings P(x, y) closer to Pyr) promoting statistical independence. This facilitates the learning of semantically meaningful disentangled embeddings, enhancing the extraction of generalizable fcatures for improved domain adaptation.
The mutual information between Ze and Za is given by:
T(2:; 7d) = // 2) log
p(2. 2) p(2)p(2)
da d2
(6)
where p(E,2) 2) the joint probability density function of Z, and Za, and p(E) and p(8) are the marginal probability density functions of Ze and Za, respectively. For high-dimensional variables, the calculation of the double integrals is quite complex.

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MINE Belghazi al. (0188). utilizes the Donsker-Varadhan
Varadhan representation of the Kullback-Leibler (KL)
divergence to provide lower bound mutual information and optimize it using neural network.
Using Lonsker-Varadhar representation, the Kullback-Leibler (KL) divergence between two probability dis- tributions P and Q is given by:
DKL (PIQ) = sup Ep(T] log Role"]. T:Q-RR
(7)
where the supremum taken over all functions for which both expectations remain finite.
The mutual information I( between two random variables and Y is defined using the Kullback- Leibler (KL) divergence
T(X;Y)- ((.((P(X))))((()XX)))
(8)
where P(X, Y) is the joint probability distribution of X and Y. P(X)P(Y) represents the product of marginal distributions.
Following MINE, we employ neural network No to estimate the lower bound of I(Zc: Za):
T(Ze Za) 2 TZze; Za) sup E) [No] log logl [e No.
(9)
The expectations in are computed using the approach MINE, Accordingly,
1 Σ 2(,,2. log Ma) = n1
Σ exp (EL
(10)
where (2, 2) is obtained through the joint probability density function p(2, 2) and ă is obtained through the marginal distribution p(2) by random shuflle.
By minimizing i(Zo: Za), we force the learned embeddings Z, and Za to satisfy:
P(Z., Za) Re P(Z.)
(11)
This prevents information leakage from Za into Ze, ensuring proper disentanglement. The final optimiza- tion objective function for learning domain-agnostic feature space through the leverage of domain-related information is:
La== = L. + A + Az Za).
(12)
where A and X2 are the weighting coefficients.
Algorithm Training procedure for DETMI
Input: K domains data samples; Eacoders Fa, Faa; Classifiers C, C Mutual information estimator No:
Batch size B
Output: Optimized Encoder E, and Classifier C
3: Using MINE, Update Mutual information estimator No by maximizing 10 until convergence.
4: for i = epochs do
5: Sample a mini-batch (xr
, Mi ( S*
6: Compute the objective function
7: La = Le + La + (Z, Za).
Update En, Ea, C, Č
end for
10: Return Optimized Encoder E, and Classifier C

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3.2 Disentangled Embedding through Style Information (DETSI)
We propose DETSI, an alternative approach for learning domain-agnostic embeddings by leveraging domain- specific information. DETSI leverages style information to learn domain-agnosse and domain-specifie em- beddings, denoted as Ze and Za- Building on the work of Huang & Belongic (2017). which establishes the close relationship between style and instance-level feature statistics, and recognizing the strong corre- lation between image style and visual domains, we employ style perturbation encourage content-focused learning for domain-agnostin embeddings. Additionally, we extract style features enhance the learning of domain-specific information, enabling more effective separation of domain-specific and domain-invarian. invariant components.
3.2.1 Preliminaries
Huang Belongie (2017) demonstrated that CNN convolutional features maps statistics i.e. channel-wise and variance, effectively characterize image style. Building this insight, [Uyanov al. (2016) proposed Instance Normalization (IN) to normalize these style statistics and mitigate style variations in style transfer models.
For a given input image x, its feature maps are represented as fa E CC where C' denotes the number of channels, and H and W correspond to the spatial dimensions. The formulation of Instance Normalization (IN) is expressed
IN(Ja) = fn uf + 8,
(13)
of
where 7, E RC correspond to learnable afline transformation parameters, and Kf:0f E RRC correspond to the channel-wiss wise mean and standard deviation.
H
W
fehkwr
(14)
HW h=11
and
W
Σ
(Jan - p2)2 te,
(15)
HW
where a small constant e is added avoid numerical instability.
Furthermore, leveraging these style statistics, Huang & Belongie (0117) introduced Adaptive Instance Nor- malization (AdaIN), which transfers image's 's style to target style by replacing the alline parameters with corresponding style-specific statistics (H,, AdalN is defined as:
fz f=- 1f
AdaIN(fz; =
+ Us.
(16)
0s
In this paper, we introduce perturbations to the channel-wise mean and standard deviation of each feature map to introduce style randomization. Furthermore, we utilize AdaIN to substitute the original style infor- mation with randomly generated style statistics, enhancing style invariance in our feature representations.
3.2.2 Content-focused Learning
We achieve content-focused learning by introducing style perturbation, which alters the feature statistics at the instance level of the training images. These feature statistics, closely tied to style, are perturbed to encourage the model to focus on content rather than stylistic variations. The process is formally defined by:
Prew {p(s(!) (1 {)p(f(
(17)
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and
new = )))
(18)
where À ~ U(0, 1). Here, f! represents specific batch of feature maps at a layer of the encoder Ee, and fe is derived by shuffling fe randomly across the batch dimension.
Following the method outlined by Huang & Belongie 2017], we then reconstruct the new feature maps using the perturbed feature statistics:
( + Knew-
( = new
(19)
off!))
The perturbed feature maps are used to drive content-focused learning, thereby aiding in learning domain- agnostic embeddings.
3.2.3 Domain-focused Learning
Recognizing the strong correlation between image style and its domain, prioritize extracting style features over traditional low-level features in the initial layers of the domain-specific encoder Ed- This approach aims to enhance the learning of domain-specific embeddings. To achieve this, we employ two widely used methods for style feature exttacoon.
Style Perturbation
Label Classifier
Ze
Feature Extractor E
Za
Domain Classifier
Ca
Feature Extractor E
Style Extraction (Instance-level
statistics)
Figure 2: DETSI: Disentangled Embedding Through Style Information, leveraging instance-level feature statistios for style feature extraction to enable domain-focused learning.
Instance-Level Feature Statistics (Mean and Variance) We compute instance-level feature statis- tics, such as the mean and variance of feature activations, to represent an image's 's style. To capture style information, we utilize these instance-level statistics and modify the current feature maps following the methodology introduced by Huang & Belongie (001))
(1) Sty
Psty + Ssty I
10)
(20)

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where / represents a specifie batch of feature maps at a layer I of the encoder Ed, and Usty and csty denote the style characteristics of the feature maps f(i) Instead of directly using f(l) the domain-specific embedding Za is computed using fly
This approach enhances domain-specific learning and strengthens the disentanglement of domain-specific and domain-invariant components. By improving this separation, we enhance the model's ability to generalize to unseen domains. Fig. 2 illustrates the DETSI framework, which leverages instance-level feature statistics for style extraction to enable focuee- learning.
Gram Matrix-Based Approach This work also considers another popular method introduced by Gatys et al. (2016) to capture the style using Gram matrices, which compute the correlations between feature chan- nels CNN. The Gram matrix encodes second-order statistics (feature correlations), effectively capturing texture and style information. The Gram matrix is formally defined as:
GO
(1)
(1)
(21)
where (() represents specific batch of feature maps layer of the encoder Ea. To extract style informa- tion, Gram matrices are computed from the early layers of the domain-specilic encoder E.. Adapl ive average pooling is applied to the Gram matrices to reduce complexity while retaining critical information, producing resized feature vectors denoted fuy These vectors combined and passed through fully connected layers to learn the domain-specifie embedding Za.
The DETSI framework leverages Gram matrices for style feature extraction to enable domain-focused learn- ing, as illustrated in Fig. 3
The performance analysis of both methods for style extraction detailed in Section Details about the network structure are provided in the following section.
Algorithm Training procedure for DETSI
Input: K domains data samples; Encoders E.s Ea; Classifiers C, Č Output: Optimized Encoder E. and Classifier C
for i= 1: epochs do
( Sample a mini-batch (or(²,, :hi "h E S*
5( (
5:
6:
f (x(at)
fer Shuffle (1
(1) StylePerturbattonn (()))
8:
ssy StyleExtraction (f())
10:
Compute the objective function.
11:
Las = Le + A1 Lad
12: Update Ec, Ea, C, Ò
13: end for
14: Return Optimized Encoder Fg and Classifier
4 Experimental Setup and Evaluation
This section details the experimental setup, including the datasets, implementation specifics, and network architectures, to evaluate the proposed methods for DG. We utilize four widely recognized benchmarks, PACS, VLCS, Office-Home,, and Terralncoguita, each designed to test the robustness of DG models across diverse domains and styles. The implementation details describe the training protocols, hyperparameter configurations, and data preprocessing techniques, ensuring reproducibility.
Finally, we outline the architecture of the feature extractors, predictors, and auxiliary networks used in our experiments, emphasizing their roles in learning disentangled embeddings and leveraging style and mutual
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Style Perturbation
Feature Extractor E
Z
Label Classifier
Le
Feature Extractor
Za
Domain Classifier
La
Figure 3: DETSI: Disentangled Embedding Through Style Information, utilizing Gram Matrix for style feature extraction to enable domain-focused learning.
information for improved generalization. These components collectively validate the effectiveness of our framework in addressing the challenges posed by DG.
4.1 Datasets
PACS PACS is a benchmark for object recognition DG tasks, It includes four domains named Photo, Art-painting, Cartoon, and Skotch, each characterized by significant variations image styles. The dataset contains 9,991 images
classes: dog, elephant, girafle, guitar, horse, house, and person. This study uses the official training valiing-alld split.
VLCS VLCS is another object recognition dataset comprising 10,729 images in five categories. It includes four domains: VOC 2007 (Pascal), LabelMe, Caltech, and Sun. The training and validation split follows the methodology described
et al. (2018b).
Office-Home is designed for DG and features 15,500 images spanning 65 categories. It includes four domains: Art, Clipart, Product, and Real-world with variations in viewpoints and image styles. The training and validation split adheres to the approach outlined in Xu et al. 2021
Office-Homme Home
Terrainc TerraIncognita is a wildlife image dataset designed for domain generalization, containing 24,788 images in animal categories. The data set includes four domains corresponding to camera trap locations, L38, L43, L100, and L46. These domains exhibit significant visual variability due differences background, lighting, and environment. Following the protocol in Cha al. (2022), we use 80% of the data from the source domain for training and reserve the remaining 20% for validation.
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Target
Source
Figure 4: Training Vs.
Inference Samples
4.2 Implementation Details
We follow the standard approach for domain generalization (DG) illustrated in Fig. In this setup, domain is designated as the target domain for testing, while the training and validation splits of the remaining domains are used to train the model and select the best-performing configuration, respectively.
The model is trained using mini-batch stochastic gradient descent (SGD) with a batch size of 32 for the PACS, Office-Home, VLCS, and and Terralncognita datasets. The training process spans 50 epochs, with weight decay of 54 and an initial learning rate of 0.001. The learning rate reduced by factor of 0.1 after every 40 epochs. The weighting coefficients A₁ and A2 are set 1. Standard data augmentation tochniques applied, including color jittering, horizontal flipping, and random resized cropping. All input images resized to 224x224 to ensure consistency during training.
4.3 Structure of Networks
Feature Extractors We utilize pre-trained ResNet50 He et al. (2016) the feature encoders E, and Ea for all datasets. The encoder E. extracts domain-agnostic features, denoted Ze, while Eg extracts domain-specific features, denoted as Zu-
Predictors The class label predictor consists of a single fully connected linear classifier C with an input dimension of 2048. We use classifier Ö to predict domain labels comprising an input layer of size 2048, two hidden layers, and an output. layer. The dimensions of the hidden layers identical to the input layer, and ReLU activation function follows each hidden layer. The output dimensions of both classifiers correspond to the number of object classes and domains in the training data.
Network for Mutual Information Estimation The mutual information estimator, Ng, a neural network with two fully connected layers. The hidden layer outputs a feature vector of size 512, and the network produces a single scalar value that represents the estimated mutual information between Zo and Za.
Network for Style Extraction in DETSI In the DETSI framework, the style information is extracted using Gram matrices computed from the three layers of the encoder Eg. Experimental results indicate that the first layer captures the most significant style information compared to the subsequent layers. To optimize computational efficiency while preserving critical information, the Gram matrices initially sized x56x256 (layer 1), 512x512 (layer 2), and 1024 (layer 3) are resized uniform dimension of 64x64 using adaptive average pooling. The resized Gram matrices flattened and passed through fully connected
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network with ReLU activation. The resulting features fed into the domain classifier C₁ ensuring balance between computational efficiency and effective use of style information for disentanglement.
4.4 Results and Discussion
We employ Empirical Risk Minimization (ERM) Vapuik (0013) as a baseline, which trains single model across all source domains by minimizing the average classification loss. In our experiments, we train the ERM model using labeled data from all available source domains and evaluate it. on the unseen target domain without access to target supervision. We use ResNct-50 as the embodding encoder for the PACS, OfficeHomee, VLCS, and TerraIncognita datasets. The corresponding results are presented in respectively. The results demonstrate that the proposed frameworks, DETMI and DETSI, outperiorm several state-of-the-art (SOTA) approaches in terms of average accuracy across these standard benchmarks. Fig. and show the t-SNE Van der Maaten & Hinton (0088) visualization of domain-agnostic embeddings learned using the DETMI and DETSI frameworks, respectively.
and
Class Separation
Domain Aligrment
brd
Source catech
Source: lebelme
chai-
Source: sun
dog
pescal
pesson
20
-20
-20-
-40-
-40
Figure 5: t-SNE plots of embeddings learned by the DETMI framework using the VLCS benchmark. (Left) Points are colored by class label to show semantic separation. (Right) Points are colored by domain to illustrate source-targer alignment.
Closs Soparation
Domain Alignment
50
Brdd
60
Source: lebelme
Source: caheer
chai
Source: oun
dop
Target peccal
60 perton
40
20
-20
-20-
Figure 6: t-SNE plots of embeddings learned by the DETSI framework using the VLCS benchmark. (Left) Points are colored by class label to show semantic separation. (Right) Points are colored by domain to illustrate source-target alignment.
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For the PACS benchmark, both approaches achieve comparable performance compared to several SOTA methods, with average accuracy improvements of +0.74%. In particular, in the sketch domain, characterized by its reliance on domain-invariant features, DETSI significantly outperforms DETMI and other SOTA methods, demonstrating its effectiveness in learning discntangled embeddings for improved performance.
For the VL.CS dataset, DETMI and DETSI also demonstrate notable improvements over the SOTA methods, achieving average accuracy gains of +0.67% and +1.01%, respectively.
For the OfficeHome dataset, known for its complexity due to the large number of classes, methods outperform several existing SOTA approaches, including POEM.
For the Terralncognita dataset, which is considered challenging due to severe domain shifts caused by varying camera trap locations, backgrounds, lighting conditions, and class imbalance, our methods outperform exist- ing SOTA approaches, achieving improvements +0.94% and +0.38% in the average accuracy for DETMI and DETSI, respectively.
These results underscore the effectiveness of our methods in learning domain-agnostic embeddings, signifi- cantly enhancing the generalization capabilities of our framework to previously unseen target domains.
Table 1: Leave-one-domnin-ouu results on PACS. The best and second-best results are bolded and underlined respectively.
Methods
Art
Cartoon
Photo
Sketch
Avg.
ResNet-50
ERM
86.18
78.58
97.24
73.55
83.88
SagNet (CVRR 21)
87.40
80.70
97.10
80.00
86.30
MatchDG (ICML 21)
85.61
82.12
97.94
78.76
86.11
mDSDI (NeurIPS 21)
88.10
81.10
98.40
79.60
86.80
SWAD (NeurIPS 21)
89.30
83.40
97.30
82.50
88.10
DIWA (NeurIPS 22)
90.60
83.40
98.20
83.80
89.00
MIRO (ECCV 22)
85.04
POEM (AAAI 23)
86.90
CCFP (ICCV 23)
86.60
INSURE (TIP 24)
90.20
85.30
97.90
83.80
89.30
CMCL (TNNLS 25)
87.57
83.60
96.03
83.73
87.73
DETMI (Ours)
88.76
85.70
98.08
82.08
88.65
DETSI (Ours)
90.18
84.85
98.20
86.94
90.04
5
Ablation Studies
This section presents ablation studies conducted to evaluate the DETMI and DETSI frameworks. The studies analyze key components and design choices within the frameworks to assess their impact on performance and generalization.
The first study evaluates the impact of disentangling domain-specific and domain-invariant characteristics by leveraging domain-specific knowledge and minimizing mutual information between domain-specific (Za) and domain-invariant (Zc) representations. The goal is to assess how this disentanglement contributes to improved generalization performance of DETMI on unseen domains.
The second study examines the residual interaction between the domain-specific (Za) and domain domain-invarian invariant (Z.) fcature spaces of DETSI by incorporating mutual information estimator. This estimator quantifics any remaining mutual information between the two embedding spaces, providing information on the effectiveness of the disentanglement process.
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Table 2: Leave-one-domiinoott results on VLCS. The best and second-best results are bolded and underlined
respectively.
Methods
Caltech
Labelme
Pascal
Sun
Avg.
ResNet-50
ERM
98.58
64.53
75.23
71.51
77.46
SagNet (CVRR 21)
97.90
64.50
77.50
71.40
77.80
mDSDI (NeurIPS 21)
97.60
66.40
77.80
74.00
79.00
SWAD (NeurIPS 21)
98.80
63.30
79.20
75.30
79.10
DiWA (NeurIPS 22)
98.90
62.40
73.90
78.90
78.52
MIRO (ECCV 22)
79.00
POEM (AAAI 23)
79.80
CCFP (ICCV 23)
79.20
INSURE (TIP 24)
98.80
63.80
81.04
72.20
79.01
DETMI (Ours)
98.65
68.22
78.70
76.32
80.47
DETSI (Ours)
99.15
68.67
78.34
77.08
80.81
Table 3: Leave-one-domain-on results on OfficeHome. underlined respectively.
The best and second-best results are bolded and
Methods
Art
Clipart
Product
Real
Avg.
ResNet-50
ERM
67.30
55.80
78.98
79.06
70.28
SagNet (CVRR 21)
63.40
54.80
75.80
78.30
68.10
mDSDI (NeurIPS 21)
68.40
52.50
76.20
80.60
69.42
DiWA (NeurIPS 22)
69.20
59.00
80.60
82.20
72.75
HIB (AAAI 22)
68.60
MIRO (ECCV 22)
70.90
POEM (AAAT 23)
68.20
CCFP (ICCV 23)
68.90
CMCL (TNNLS 25)
67.22
57.88
78.47
79.79
70.84
DETMI (Ours)
68.58
58.28
79.22
81.27
71.83
DETSI (Ours)
67.30
60.29
78.30
80.03
71.48
Table 4: Leave-one-domain-ont results on Terralncognita. underlined respectively.
The best and second-best results are bolded and
Methods
L100
L38
L43
L46
Avg.
ResNet-50
ERM
55.93
44.56
54.02
38.66
48.29
SagNet (CVRR 21)
53.00
43.00
57.90
40.40
48.60
mDSDT (NeurIPS 21)
53.20
43.30
56.70
39.20
48.10
SWAD (NeurIPS 21)
55.40
44.90
59.70
39.90
50.00
DiWA (NeurIPS 22)
57.20
50.10
60.30
39.80
51.85
TBB (AAAT 22)
47.20
MIRO (ECCV 22)
50.40
POEM (AAAI 23)
50.10
CCFP (ICCV 23)
49.00
INSURE (TIP 24)
58.80
46.40
61.70
45.50
53.10
DETMI (Ours)
60.13
51.53
57.98
46.50
54.04
DETSI (Ours)
62.24
50.99
56.41
44.29
53.48
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features, which ultimately leads to improved generalization performance on Published in Transactions on Machine Learning Research (06/2025)
The third study evaluates the impact of different style extraction techniques in DETSI to learn domain- specific embeddings (Za). It compares the performance of Gram matrices and instance-level feature statistios, with style perturbation applied solely through instance-level feature statistics across various layers.
The fourth study investigates the effect of style perturbation in the task-specific encoder and style extraction in the domain-specific encoder across different layers. The findings highlight the critical role of early encoder layers in achieving effective disentanglement.
Finally, the last study explores the independent contributions of style perturbation for task-specific em- beddings, domain-specfic embeddings, and style extraction for domain-specific embeddings. This analysis underscores their complementary roles in facilitating robust disentanglement and enhancing generalization across domains.
5.1 Impact of Domain-Speciffe Knowledge and Mutual Information Minimization in DETMI
To evaluate the contribution of each component in the DETMI framework, we conduct a study that focuses on the role of domain-specific knowledge controlled through x1 and mutual information between domain- specific (Za) and domain-invariant (Ze) representations controlled through 22 in T2 Our results, presented in Table demonstrate that leveraging domain-specific information plays critical role in promoting the disenlanglerment of domain-invariant and domain-specific representations. This structural separation enables the model to more effectively isolate invariant features that generalize across domains. Furthermore, incor- porating mutual information minimization between the two feature spaces further strengthens this disentan- glement by suppressing higher-order dependencies, thereby reducing redundancy. This encourages learning of more robust unseen domains.
Table 5: Impact of Domain-Specific Knowledge and Mutual Information Minimization
Methods
Art
Cartoon
Photo
Sketch
Avg.
ResNet-50
ERM
86.18
78.58
97.24
73.55
83.88
11==0
87.93
82.59
97.72
79.48
86.93
(A -
88.76
85.70
98.08
82.08
88.65
5.2 Validating Implicit Disentanglement in DETSI
We integrated a mutual information estimator into the DETSI framework to evaluate the residual interaction betweon domain-specific (Zz) and domain-invariant (Z.) fcature spaces. This integration enabled us to quantify any remaining mutual information between the two embedding spaces. The results, summarized performance with the addition of mutual
in Table G. indicate that there is no significant improvement information estimation. These findings confirm that the inherent design of DETSI effectively achieves robust disentanglement without the need for additional mutual information measures.
Table 6: Validating Implicit Disentanglement in DETSI using the PACS Dataset.
Methods
Art.
Cartoon Photo
Sketch
Avg.
ResNet-50
DETSI
90.18
84.85
98.20
86.94
90.04
DETSI with MI
89.79
84.72
98.32
86.43
89.82
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5.3 Impact of Style Extraction Techniques Learning Domain-Specifte Embeddings in DETSI
This subsection presents the experimental results that evaluate the impact of different style extraction techniques on the learning of domain-specific embeddings (Za). As shown in Table 7 Gram matrix-based style extraction consistently outperforms methods based on instance-level feature statistics.
The superior performance of Gram matrices stems from their ability to encode second-order statistics, which capture correlations between feature maps across the entire image. These correlations effectively represent texture patterns, color distributions, and structural styles, all of which are critical components of an im- age's overall style. In contrast, instance-level feature statistics primarily focus low-level details, such brightness and contrast, but fail to capture global style attributes, including texture patterns, artistic brush- strokes, and structural relationships. These limitations make instance-level feature statistics less effective for representing domain-specific style information.
Table 7: Impact of Style Extraction Techniques Learning Domain-Specith Embeddings Za the PACS Datasct.
Methods
Art
Cartoon
Photo
Sketch
Avg.
ResNet-50
Instance-level Statistics
86.69
84.25
98.08
85.72
89.43
Gram Matrix
90.18
84.85
98.20
86.94
90.04
5.4 Effect of Style Perturbation and Extraction Across Layers in DETSI
This study examines the impact of style extraction and perturbation across the early layers of encoders in the DETSI framcwork, using instanco-level feature statistics to learn domain-specific embeddings.
The results, summarized in Table g reveal that the application of style extraction and perturbation within the first three layers the domain-specific encoders achieves superior performance compared to other layer combinations. These findings align with the established understanding that carly encoder layers primarily caplure low-level features, such as textures and palterns, which are closely associated with style.
Interestingly, the fourth layer, which primarily encodes high-level semantic features rather than style at- tributes, was excluded from this analysis. This exclusion underscores the critical rolc of carly encoder layers in style manipulation to enhance the disentanglement of domain-specific and domain angnosic embeddings in the DETSI framework.
Table 8: Evaluation of Style Feature Extraction and Perturbation Across Different Layers of DETSI on the PACS Dataset
Methods
Art
Cartoon
Photo
Sketch
Avg.
ResNet-50
((L1),,E(LL) (L12), Ea(2)))
89.79
84.51
98.08
82.92
88.82
89.59
84.00
98.32
84.72
89.15
(L(21))), Ea(1123)
89.69
84.25
98.08
85.72
89.43
5.5 Evaluation of DETSI Components on Domain Generalization Benchmarks
This ablation study examines the impact of style perturbation on lask-specific embeddings, domain-specific embeddings, and style extraction on domain-specific embeddings within the DETSI framework. As shown in Table g cach component contributes the performance gains, and the combined application yiclds significant improvement. These results highlight the roles of style perturbation and style extraction enhance feature disentanglement. Ultimately, the framework increases generalization across unseen domains.
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Table 9: Evaluation of DETSI Components on Domain Generalization Benchmarks
Methods
PACS
VLCS
OfficeHome
ERM
83.88
77.46
70.28
+Style Pert. in Ee
85.20
77.90
60.40
Style Pert. in E. + +Ea
89.58
79.76
70.71
+Style Pert. in E. + Style Extr. in Es
90.04
80.81
71.48
Result adopted from Zhou et al. 2024 due to matching configuration.
6
Conclusion
This paper addresses the challenge of domain shift in Domain Generalization (DG) by introducing two novel frameworks: Disentangled Embedding through Mutual Information (DETMT) and Disentangled Embedding through Style Information (DETSI). These frameworks effectively leverage domain-specifie information to disentangle the latent feature space into domain-specifee and domain-invariant components, enabling the extraction of class-relevant features and enhancing generalization to unseen domains.
DETMI utilizes a mutual information estimator to promote feature disentanglement, while DETSI achieves disentanglereent through leveraging style information. Both frameworks perform better than stale-of-the-art DG techniques, promoting domain invariance and improving generalization. Furthermore, DETSI achieves comparable results with reduced complexity, making it a practical and efficient solution for scenarios with limited computational resources.
The proposed frameworks advance the state-of-the-art in DG and highlight the critical role of leveraging domain-specific information alongside domain-invarianl features. These findings underscore the potent ial of disentanglement- based approaches to effectively address domain shift and provide a foundation for developing more efficient and robust DG methods the future.
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20


Reviews:
[{"review_id": "xIoHbglUD9", "reviewer": "Reviewer_vwZz", "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": "\\+ The presentation of the paper is clean and easy to understand\n\n\\+ The proposed approaches are meaningful and compelling\n\n\\- The experimental evaluation is weak. In domain generalization is based on domainbed (Gulrajani et al.2020), which includes PACS, VLCS, office-Home, but also TerraIncognita and DomainNet. Those two are larger datasets and seem more challenging and I think it is important to validate the proposed methods on those datasets. In addition, there are methods based on ensembling (Lakshminarayanan et al. 2017 and Rame et al. 2022), which are quite competitive and not included in the evaluation.\n\n\\- Even if the presentation of the paper is simple, there are several points that need to be improved. In many equations (e.g. eq. 1 and 2), there are several variables that are not defined (\\delta, \\sigma). The same image is used multiple times for the different approaches. There could be a better way to present that without showing multiple times the same image, which seems a bit repetitive.\n\n\\- The introduction does not motivate much the proposed contributions. It looks more like an additional related works.\n\n\\- The proposed methods are not new (MINE, AdaIN). The novelty stems form the application of the methods to domain generalization. While, this is interesting, the contribution is limited. \n\n\\- In the introduction, the authors talk about domain generalization which tries to improve generalization. In my understanding this is misleading, as in domain adaptation the aim is not to generalize, but to adapt a model to perform well on the target dataset, without caring about the performance on other domains.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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 presents two methods to improve image classification when training with multiple domains and testing on another unknown domain, which is normally referred as domain generalization. Both approaches are based on separating the model representation in two complementary parts, the first is domain invariant and the second is domain specific. The first approach is based on minimizing the mutual information between the two representations (domain-invariant and domain-specific) using MINE. \nThe second approach is based on style disentaglement, in which the style of an image is substituted with the style of another image using AdaIN, such that the model would learn to focus on content and overlook style.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "\\- Add missing datasets: TerraIncognita and DomainNet\n\n\\- Include methods based on ensembling\n\n\\- Improve presentation of the paper as explained in the previous section\n\n\\- Explain and motivate more concretely what are the contributions of this paper\n\n\\- Correct the statements about domain adaptation in the intro or explain your way of understanding that", "broader_impact_concerns": "I do not see any concerns about ethical implications of the work.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "4RnkRM7f5s", "reviewer": "Reviewer_6KZa", "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": "**Pros**:\n+ This paper is generally well-written and easy to follow. \n+ The experiments can verify some of the key parts of the proposed method, like the Gram Matrix style extraction scheme \n+ Both the DETMI and DETSI achieve better or comparable performance to state-of-the-art methods.\n\n**Cons**:\n\n1. There are many related works to be comprehensively compared to highlight the differences between the proposed methods and the existing ones.\nFirstly, the basic idea of the feature disentanglement used in this paper is not new because it has been explored in POEM (Jo & Yoon, 2023). \nSecondly, mutual information has been used in domain generalization [A] and unsupervised domain adaptation [B]. Please compare the DETMI with these methods.\nThirdly, the content-focused learning in Sec. 3.2.2 is very similar to MixStyle [C]. Please clarify their differences and compare their performance.\n\n[A] Junbum Cha et. al. Domain Generalization by Mutual-Information Regularization with Pre-trained Models. ECCV 2022\n\n[B] Jiahong Chen et. al. Preserving domain private information via mutual information maximization. Neural Networks 2024.\n\n[C] Kaiyang Zhou et. al. MixStyle Neural Networks for Domain Generalization and Adaptation. IJCV, 2023\n\n2. I do not understand why this paper first proposes DETMI with mutual information and then presents DETSI which is not compatible with mutual information (evidenced by the result in Tab. 4). Please explain why these two incompatible strategies are introduced in the same paper.\n\n3. In Ln. 3 of Alg. 1, please explain why and how the mutual information estimator $N_\\theta$ is updated by maximizing Eq (5). Eq. (5) states the case when I(X, Y)=0, so it seems not an objective function.\n\n4. Please evaluate the sensitivity of lambda_1 and lambda_2. Particularly, the results of lambda_2=0 vs. lambda_2!=0 are necessary to verify the effectiveness of the mutual information design in DETMI.\n\n5. In Tab. 7, the style perturbation, or MixStyle, has been verified effective in previous work. The proposed style extraction only improves it by 0.46% on the small-scale dataset, PACS. Such improvement can hardly be considered as \"significant\" as it can even be caused by different random seeds. Besides, if the style extraction is based on the Instance-level Statistics, there will be no improvement.\n\n6. Please visualize the feature embeddings of the DETMI and DETSI.\n\n**Minor concerns**:\n\n7. Please prove that \"by reducing higher-order correlations, DETMI ensures statistical independence\". It is not easy to understand that reducing higher-order correlations can \"ensure\" statistical independence because the mutual information can hardly be 0.\n\n8. To facilitate comparison, please include the baseline results in Tab. 4.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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 proposes a Disentangled Embedding through Mutual Information (DETMI) and a Disentangled Embedding through Style Information (DETSI) for domain generalization, both inspired by recent advances in representation disentanglement. DETMI disentangles domain-agnostic and domain-specific embeddings by employing a mutual information estimator, while DETSI achieves this by style extraction and perturbation. Experiments on the PACS, Office-Home, and VLCS datasets show that both frameworks achieve state-of-the-art DG performance.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please address the questions in Cons and revise the manuscript accordingly.", "broader_impact_concerns": "There is no concerns on the ethical implications.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "h083YUEDdJ", "reviewer": "Reviewer_TXmC", "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\nThe paper is quite easy to follow, with a comprehensive survey of related work.\n\nThe experimental design is clear, and it demonstrates the effectiveness of the proposed methods on the three benchmarks.\n\n\n**Weakness:**\n\n-   Incremental Novelty: the dual-encoder setup with a domain classifier and a label classifier is common for DG. DG by mutual information is also explored (for example MIRO). Adding a mutual-information term to encourage independence between learned embeddings, while shows promising results in the paper, is a relatively straightforward extension rather than a paradigm shift. Likewise, instance normalization and Gram are both explored.\n\n-   Limited Evaluation Scope: while PACS, Office-Home, and VLCS used to be popular DG benchmarks, they feature only a few domains with pronounced style differences. It remains unclear how the proposed methods scale to more challenging benchmarks such as DomainNet, or to real-world distribution shifts such as  WILDS-FMoW or TerraIncognita.", "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 presents two frameworks, namely Disentangled Embedding through Mutual Information (DETMI) and Disentangled Embedding through Style Information (DETSI), to separate domain-invariant and domain-specific features. DETMI minimizes the mutual information between learned embeddings, while DETSI extracts style statistics (instance-level feature statistics & Gram) and introduces style perturbation. Both approaches deliver strong results on PACS, Office-Home, and VLCS.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Please see weakness part.\n\nAdditionally, I feel like the framework figures in the paper are quite similar to each other, which can be somewhat distracting in their current form. It may be more effective to present them side by side for a clearer comparison and overall clarity.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)