Gradual Domain Adaptation in the Wild: When Intermediate Distributions are Absent
Authors: Samira Abnar
Rianne van den Berg
Golnaz Ghiasi
Mostafa Dehghani
Nal Kalchbrenner
Hanie Sedghi
Venue: ICLR 2022 Submitted (2022)
Keywords: gradual domain adaptation
self-training
gradual distribution shift
curriculum learning

Abstract: We focus on the problem of domain adaptation when the goal is shifting the model towards the target distribution, rather than learning domain invariant representations. It is shown that under the following two assumptions: (a) access to samples from intermediate distributions, and (b) samples being annotated with the amount of change from the source distribution; self-training can be successfully applied on gradually shifted samples to adapt the model toward the target distribution.  We hypothesize having (a) is enough to enable iterative self-training to slowly adapt the model to the target distribution, by making use of an implicit curriculum. In the case where (a) does not hold, we observe that iterative self-training falls short. We propose GIFT (Gradual Interpolation of Features toward Target), a method that creates virtual samples from intermediate distributions by interpolating representations of examples from source and target domains.
Our analysis of various synthetic distribution shifts shows that in the presence of (a) iterative self-training naturally forms a curriculum of samples which helps the model to adapt better to the target domain. Furthermore, we show that when (a) does not hold, more iterations hurt the performance of self-training, and in these settings GIFT is advantageous. Additionally, we evaluate self-training, iterative self-training and GIFT on two benchmarks with different types of natural distribution shifts and show that when applied on top of other domain adaptation methods, GIFT improves the performance of the model on the target dataset.

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GRADUAL DOMAIN ADAPTATION IN THE WILD: WHEN INTERMEDIATE DISTRIBUTIONS ARE ABSENT
Anonymous authors Paper under double-blind review
ABSTRACT
We focus on the problem of domain adaptation when the goal is shifting the model towards the target distribution rather than learning domain invariant representations. It is shown that under the following two assumptions: (i) access to samples from intermediate distributions, and (ii) samples being annotated with the amount of change from the source distribution, self-training can be successfully applied on gradually shifted samples to adapt the model toward the target distribution. We hypothesize having (i) is enough to enable iterative self-training to slowly adapt the model to the target distribution by making use of implicit curriculum. In the case where (i) does not hold, we observe that iterative self- trafntraining falls short. We propose GIFT (Gradual Interpolation of Features toward Target), method that creates virtual samples from intermediate distributions by interpolating representations of examples from source and target domains. Our analysis of various synthetic distribution shifts shows that in the presence of (i) iterative self- training naturally forms a curriculum of samples which helps the model adapt better to the target domain. Furthermore, we show that when (i) does not hold, more iterations hurt the performance of self-training, and in these settings, GIFT is advantageous. Additionally, we evaluate self- elf-training, iterative self self-training and GIFT on two benchmarks with different types of natural distribution shifts and show that when applied on top of other domain adaptation methods, GIFT improves the performance of the model on the target dataset.
INTRODUCTION
Learning algorithms are notorious for not being robust to changes in the environment, and their performance often drops when there is a shift in the data distribution (Taori et al.] [020 Hendrycks)) al. 202T Koh et al. 202T]. To be robust the changes in the distribution, learning algorithms either need to learn representations that are invariant to the shift, or they should update their parameters either setting, we are still far from a satisfactory solution. While unsupervised domain adaptation techniques commonly rely on learning domain invariant representations, our focus is on shifting the model towards the target distribution. We consider the unsupervised setting where do not have access labels the target domain. The setting we consider is similar to the setting suggested by Wang et al. (2021).
to more aligned with the new distribution.
We look at this problem through the lens of curriculum learning. Curriculum learning (Elman 1993 Sanger 1994 [engio et al., 2009) suggests presenting easier samples early on in the training process and gradually increasing the difficulty. In unsupervised domain adaptation, this is equivalent to gradually changing the distribution from the source domain to the target domain, i.e., getting the model adapt intermediate distributions before being exposed to the target domain, Kumar et al.) (2020) show that if learning algorithms are exposed to gradual changes in the data distribution under a self-training regime, the generalization gap (from source to target distribution) will be much lower. However, the problem remains unresolved when we do not have access to the intermediate steps of the distribution shift. Findings from Kumar et al. (220)) suggest that to be able to adapt the model by self-training, two conditions should be satisfied: (i) Access samples from intermediate distributions between source and target; (ii) Access to information about the amount of shift for each sample. While (ii) is hard to achieve in practice, (i) may be the case in many real-worle scenarios. We hypothesize that if (i) holds, i.c., the target distribution is diverse enough to include samples from intermediate distributions; iterative self-training (applying self-training iteratively) and filtering examples based

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on the confidence of the model, incorporates implicit curriculum and this curriculum helps the model to gradually adapt to the target domain. Furthermore, for cases where (i) does not hold, we propose GIFT (Gradual Interpolation of Features toward Target). GIFT creates virtual examples from intermediate distributions by linearly interpolating between source and target data in the input and feature space of a neural network. Note that such interpolations shown be meaningful in works that established the idea of mixing up representations (Verma et al. 2019a Mrouch 2020a). To gradually increase the difficulty of the virtual samples, we change the linear interpolation coefficient such that the samples start at the source distribution and gradually move towards the target distribution during training. Figure |] demonstrates how GIFT can improve iterative self- trainiiiing, in an example with Two-moon dataset (two interleaving half circles).
Our focus in this paper is not to provide a new state of the art on a specific benchmark, as we are limited by the availability of benchmarks that are specifically designed for gradual domain adaptation. Instead, we intend to provide a proof of concept for (1) how, why and when iteratively applying
self-training is helpful for gradual domain adaptation (Section 4. and 4.2) (2) There cases that not only iterative self-training does not help the model but also it hurts model performance on both source and target domains. In those cases, GIFT can mitigate the issue by using interpolations of features as intermediate examples (Section 4.1). We evaluate iterative self-training and GIFT for unsupervised domain adaptation on datasets with natural distribution shifts and show that they improve the performance of models on the target dataset compared to non-iterative self-training. On a synthetic benchmark, we show that in the absence of (i), GIFT performs better than iterative self-training. By tracking the accuracy and confidence of a model on different subsets of the target distribution, we show that with both GIFT and iterative self-training the order in which the models learn to correctly classify examples is aligned with their degree of perturbation. GIFT has two advantages over iterative self- trainina:::n: (1) It works better when the number of training iterations is limited, (2) it works better when the target distribution is not diverse enough to include mixture of easy and hard examples.
Accuracy ess
Accuracy 0.30
Besthe
Acouray 026
Aocuracy - 0.70
Figure 1: Demonstrating the power of self-training for shifting the model on the Two-moon dataset. On the left side, different colors determine the two ground truth classes. On the right, different colors depict predicted classes. Here the target data (bottom left) is the (909) rotated version of the source data (top right). In this example, it is not possible to achieve a good performance on both source and target at the same time, since they have conflicting labels for similar inputs. While the performance of the model trained only on source is around ~ 50% on the target data, if we have access to ground truth intermediate steps we can improve this number by 40% by gradual self-training (Kumar et al. 2010). In the absence of samples from intermediate distributions, our proposed method(GIFT) can increase the performance by 20% compared to no adaptation, while iterative self-training without access to intermediate examples leads to even worse accuracy. For this example, we use an MLP with one hidden layer and a Relu activation function. The code is provided at pitttps:: ////tttt....../. com/ anonymouse github/tthgte GIFT
2 SELF-TRAINING FOR UNSUPERVISED DOMAIN ADAPTATION
Being able to properly handle distribution shift is one of the primary concerns of machine learning algorithms. A common setting for this problem is unsupervised domain adaptation, where we have
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access to labeled data from multiple source domains, and unlabeled data from the target domain. Let (** denote the labeled data in the source domain, where X E RT,xd is the sample input matrix and Y E R", is the corresponding label matrix. Let X E R denote the unlabeled target domain data. Here ni and n, determine number of examples from source and target domains respectively, and & determines the number of classes. While, it not necessary for simplicity we assume number of classes and generally the task is the same in source and target. We assume some underlying or common features exist between source and target, while there is a substantial distribution shift between the two domains. The goal is to bridge the domain difference and learn a classifier minimizing the empirical risk on the target domain. The first assumption needed for domain adaptation to be successful (Ben-David et al., 2008). The latter emphasizes that model trained on the source domain presents noticeable performance gap on the target domain and hence needs to adapt to the target distribution. Self-training uses teacher model trained on source domain, P.. to produce pscudo labels, along with confidence scores, on unlabeled data from the target domain, Pt. and uses these predictions train a student model. In iterative self-training the teacher model is periodically updated and replaced by the student model. We examine how, in iterative trafnirain the confidence scores of the teacher model guide the student model to adapt to the target domain, and whether we can devise supplementary schemes that help the student adapt better.
3 GIFT: SELF-TRAINING WITH GRADUAL INTERPOLATIONS
If in addition to labeled data from the source domain and unlabeled data from the target domain, also have access to the intermediate distributions, i.c., unlabeled examples from data distributions between source and target, we can use them to boost the performance of the model domain, by applying self-training in a gradual manner. Kumar et al. (2020) show that this gradual adaptation leads to lower error bound the target domain. In order for this approach to be applicable, we need samples from intermediate steps that are annotated with the amount of shift from the source distribution. However, in many cases in practice, we either do not have access to samples of intermediate distributions or such examples do not exist. Even if they exist, it is less likely that they are annotated with the degree of shift.
the target
To circumvent the issue of lack of samples from intermediate distributions, we create the virtual samples from intermediate distributions by interpolating the input and hidden representations of the data from the source domain P. and target domain P,. Namely, let Mg be neural network model trained on source data and let z correspond to the representation of input x; E X from the source domain. We choose ærJ as a sample from the target domain (we explain the procedure to pick æf E X below). Let 2f correspond to the representation of input æ²) X that can be sampled from any of the layers of a neural network (including the input layer), and X E [0, 1]. We generate
Eg = (1 A)= Az), X E [0,
as sample representation of virtual intermediate distribution. Note that we do not seek to find corresponding input to the interpolated representation. Gradually increasing À from 0 to corresponds to feature representations that change from corresponding source distribution representations (A 0) to the target distribution representation (A = 1 ). lambda_ sccheduleceerrr in algorithm [ represent the scheduling function for gradually increasing X, which can be anything, in our experiments we use a linear function with fixed step size, ò, where the value of lambda increases by a constant value after every 8 training steps.
To choose which example from the source is interpolated with which example from the target, we either randomly align the samples or apply a cost-based alignment method based on the Ly distance of representations, and the similarity/equality of labels on the source and predicted target labels. To apply a cost-based alignment method, we use the Sinkhorn matching algorithm (Sinkhorn 1966 Peyré & Cuturi, 2019) to approximate the alignment with the lowest cost. Although iterative cost- alignment methods such as Sinkhorn come at a computational cost, compared to random alignment, we have observed that random alignment without taking (pseudo) labels into account leads to worse performance. To find a better trade-off' between alignment cost and performance, in our experiments, we also tried non-iterative heuristic (pseudo) label- based random alignment, where we randomly align examples that have the same (pseudo) labels. This is shown in Algorithm [ In our experiments, we report the result from cost- based alignment. We observed that pseudo-randon random alignment and cost-based alignment lead to more or less similar results and in practice, could simply use the
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Algorithm 1 GIFT: Gradual Interpolation
P.: source domain; Pt: target domain
M: Neural net (maps input to predictions).
M partial neural net (maps input to features of layer L)
M M partial neural net (maps features of layer L to predictions)
d: student neural net parameters; 0: teacher neural net parameters
6: step size for interpolation coefficient X.
N: number of training iterations for each teacher update. number of examples in batch.
a: confidence threshold
Notation: [m] (1,...m)
1: Ma t Ma. + 0
2: while A <= do
3:
for step E [N] do
4:
(mfm) V
P.
5:
mx] Pt.
6:
m]
+ (a
7:
mi (a
8:
Fmm) - Ma(afm) (m))
9:
index.,, index; (lign(y(m) s(m)) (Algorithm 2
10:
m/ + (1 x iudex x index.
11:
Fmm] + (M)
12:
conf ranks + rankkmaar (21m)) - min min( (T((..)))
13:
conf indices + conf ranks|: : a:
14:
mi Miml [[con[_indicens "ecoon_innnies
15:
Fit Mss to (3mm) mmm))
16:
end for
17:
X A- lambda scheduler(2,
18:
Mg MM
end while
Algorithm Align: Label-based Random Alignment
1: Input: Vim.j lfm)
2: Output: index,, index;
3: index, + 2,., len(y(
4: index; + [
5: for E index, do
6: indices + [1, .... .en..._ ((f()
7: ihufiee__indiess permale(indices))
for [m]] = yili
8: matching_scorcssmg
00 for [m[m]] * y
9: index + argmax (wwatciingsscorss(slllll.. inddccss
10: apfeddaepeed indices/index)
11: end for
pscudo-random alignments. It is important to note that both for cost-based and pscudo-random alignment the pseudo labels predicted by the teacher model since we do not have access to ground truth labels for data points from the target domain.
In standard iterative self-training (Habrard et al.) 2013), the data used in each self-training iteration is a subset of the target distribution, whereas in GIFT we apply the iterative self-trane teff-raining procedure on virtual intermediate distribution representations to gradually adapt the model to the target domain. We
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start by using teacher model trained on the source distribution and move to train the student model in the representation space. The self- training procedure at each step proceeds by assigning pseudo labels to virtual intermediate representations that generated by equation [ Next, the student model is updated using pseudo-labeled representations. Then the student becomes the teacher for the next iteration and the procedure continues. We start with À O, which generates representations from the source domain. At each iteration of self-training, we increase the value of À to generate virtual representations that are closer to the target distribution and hence gradually move the model toward the target distribution (A 1). The details are shown in Algorithm| |I Similar to standard iterative self self-training, we assign a confidence score to each pseudo-labeled data point and only update the student model with pseudo-labeled data which their confidence score is in the top g-percentile. In Alorithm | y is specified by Confidence Thershold. As a confidence score, we use the gap between the highest and lowest logit for each sample, as proposed in Kumar et al. (2020).
4 EXPERIMENTS
In our experiments, first, we examine the power of iterative self-training and GIFT for unsupervised domain adaptation on a dataset with synthetic shifts, where we can track the amount of shift and control the gap between the source and targets distribution. We demonstrate the implicit curriculum followed by iterative self- training and GIFT and show that when condition (i) does not hold, GIFT performs better than iterative self-training. Next, we showcase the performance of these methods in more realistic settings, on datasets with natural distribution shifts.
The training setup that we propose has three main phases: (i) Pre- Pre-training: Pre- traininiin the model on a large scale dataset (ImageNet-Il 1k in our experiments) (ii) on a labeled source domain with or without leveraging samples from an unlabeled target domain. (iii) Adaptation: Applying self-training based approach to shift the model towards the unlabeled target domain. In the fine-tuning stage, step (ii), we compare (A) simple fine-tuning on the source domain with standard augmentation techniques, i.e., random flip and random crop, (B) fine-tuning on the source domain with variants of Mixup (Zhang et al. 2018a) as an augmentation technique, and (c) Domain Adversarial training that uses unlabeled examples from the target domain to learn domain invariant representations (Ganin et al.) 2016). In step (iii), the adaptation phase, we compare three self-training based strategies: (I) one-step self-training, (2) iterative self-training and (3) GIFT, which is similar to iterative self-training except that during the intermediate iterations the model is trained with samples from virtual intermediate states instead of actual samples from the target distribution.
Training the pre-trained model
4.1 BENCHMARKS WITH SYNTHETIC PERTURBATIONS
To investigate the effect of the type and degree of shift, on the success of iterative self-training and GIFT we compare their performance, on a synthetic benchmark. In this benchmark, the target domain is created by applying synthetic perturbations examples from the source domain, such as applying noise, rotating, scaling or translating images.
To create these benchmarks, we split the training set of CIFAR1O (Krizhevsky al. 2009) into equal-sized splits, where each split contains examples with different degrees of perturbation. We use four types of perturbation: rotation, scale, translate and blur. For rotation, we split the training data into three parts. In the first split, images have a rotation angle of 0 to 5 degrees. In the second split, images have rotation angle of 5 to 55 degrees, and in the last split, images have rotation angle of 55 to 60. We use the first split, 0_5, as the source domain and the third split 55 60 as the target domain. For scale, translate and blur, we split the training data into two splits. where we use the first part with no perturbation as the source domain, and we apply the perturbation on the second part to get the out-of- diitr---iitiiittioon target domain. For both scale and translate, we have no variation in the source and some variation in the target. For the blur, we only have one degree of blurring perturbation in the target and none in the source domain.
The results on 10 with different perturbations are shown in Tables I and 2 They indicate the superiority of GIFT to iterative self self-training. The advantage of GIFT over iterative self-training is more apparent when the target distribution does not include diverse set of samples (Translated vs Blur) or when the two distributions are not overlapping (0% 100%) vs Translated(504s 50%% 100%)). Additionally, compared to GIFT, the performance of iterative self-training drops more
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Table Results of different adaptation techniques on perturbations of CIFARIO in terms of accuracy
on the test set, with 8 The total number of training steps is 1000, with batch size of 512. The number of self-trainin self-training iterations is and 20 for iterative self-training, and GIFT respectively. None refers to the zero-shot performance of the pretrained model. In all cases, GIFT outperforms the baselines.
TARGET DOMAIN
NONE
SELF-TRAINING
ITERATIVE SEL.-TRAIINNG
GIFT
ROTATED CIFARIO
0.38
0.406
0,396
0.436
0.559
0.558
0.615
TRANSLATED(O%
100%--0000 (00%) CIFARIO
0.551
0.676
0.808
0,859
(500LLA CIFARIO
0.262
0.421
0.658
0.729
BLURRED CI
0.351
0.355
0.311
0.545
Table 2: Performance of GIFT and iterative self-training for WideResnet18- trained perturbations of CIFAR 10 in terms of accuracy on the target. The total number of training steps is 500, with batch size of 512. The number of teacher updates is and 20 for iterative self-training and GIFT, respectively. Comparing these results to Table [ with the total number of training steps of 1000 indicates noticeable drop the performance iterative self-training while GIFT's performance is more robust.
TARGET DOMAIN
ITERATIVE SELF-TRAINING
GIFT
SCALED CIFAR 1O
0.573
0.6767
TRANSI -OE 100%) CIFAR
0.629
0,83499
T CIFARIO
0.477
0.8319
BLURRED CIFARIO
0.3551
0,5213
GIFT Translated 09%-1008)
Ieeaative self-training Translated (0%- 100%)
GIFT Translated (50%-100%%
Iterative self-training Translated (50%- 100%))
0.75
Fveeations
200
400)
0.50
600
800
0.25
1000
0.00
10-70
70-80000100
30-40 50-50 20-3090-166 % translation
10:30 50-601 70-80 90-100
30-40 70-80 100
56 translation
% translation
translation
Accuracy
GIFT Translated (0% 100%))
Iterative self-truining Translated (0%- 100%)
GIFT Translated (50%)-1000 100%)
Iterative self-training
Translated (50% (000))
Toetations
200)
0:75
400
0.50
000
800
0.25
1000
0.00
10-20
10-40 51-00 10-80-9-1000 10-20 Sn-ll 50/-00 20-3090-106 10-30 M0-8 50-60 90-T00 10-20 30-40 SoaeD 70-8019-110
S translation
% translation
&. translation
translation
(b) Confidence
Figure 2: Accuracy and Confidence of GIFT and iterative self-training, function of the number of training iterations on different bins of the translated CIFARIO. We evaluate the accuracy for the test data with translations between and 100% (where zero means shift, and 100% means the maximum possible amount of shift, i.e., IMAGE WIDTH/2). The iterative self-training model has teacher updates over 1000 training iterations (i.e. updates happen after 0, 200, 400, 600, 800 iterations). GIFT has 20 teacher updates over 1000 iterations (i.e. updates happen after 0, 50, 100, 950 iterations). The left panels in each row correspond models trained for the target dataset Translated (0%-1109% CIFAR1O. The right two panels in each row correspond to models trained for the target dataset Translated (50%-100%) CIFAR1O.
significantly when decreasing the total number of training steps. We can see this by contrasting the results in Table and
Investigating the Curricula: To empirically confirm the hypothesis that both iterative self-training and GIFT gradually guide the model to fit the distribbbti target distribution, we track the accuracy and confidence of the models different subsets of the target data throughout the training.

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Translated(OS... 100%)
Blurred *
Translated 100%)
0.8
0.8
Accuracy
Accuracy
0.6
0.6
0.4
0.4
0.2
0.2
10
20
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40
Number of teacher updates
Number of teacher updates
(a) Iterative self-training (1000 steps)
(b) GIFT (1000 steps)
0.8
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Accuracy
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0.2
0.2
10
5
10
20
Number of teacher updates
Number of teacher updates
(c) Iterative self-training (500 steps)
(d) GIFT (500 steps)
Figure 3: Accuracy of iterative self-training and GIFT on perturbations of CIFARIO as function of the number of teacher updates when the total number of training steps is 1000 and 500. Accuracies of both models improve by increasing the number self-training iterations up to a threshold. Beyond this threshold, while iterative eeff-training performance deteriorates, GIFT saturates and hence shows more robustness.
This shown in Figures We see that, for both methods, the accuracy and confidence measures are increasing incrementally from easier examples, i.e., examples with smaller amounts of perturbation, to harder examples, i.e., examples with larger amounts of perturbation.
For GIFT, the number of iterations is tied to the steps in which we increment the interpolation coefficient, X, and it interesting to see that there a correlation between À and the accuracy and confidence of the model on actual intermediate steps, shown in Figure 2 For iterative self-training, the model selects training examples for which to compute the loss based on its confidence. Hence, function of translation percentage during training allows to whether
tracking the confidence the model is indeed selecting less perturbed examples earlier and more perturbed examples later, in Figure 2 for both iterative self-training and GIFT the
thus creates its own curriculum. As confidence of the models decreases gradually for data with an increased level of perturbation. Note also that the confidence scores show very similar patterns the accuracies. This confirms that the reason behind the success of iterative self-training is the implicit curriculum strategy, and that the gradual interpolation strategy that we employ in GIFT can be good proxy for gradual self-training when we do not have access to the gradually shifted data.
Effect of number of intermediate steps: We examine the effect of the number of intermediate steps when the total number of training steps is fixed. As illustrated in Figure 3 increasing the number of intermediate steps (teacher updates), which means taking smaller steps in the gradual adaptation procedure, leads better performance up to a threshold for GIFT and iterative self- Soff-training. If we keep increasing the number of intermediate steps, the performance of the models decreases rapidly for iterative self-training. Whereas GIFT is more robust to the number of intermediate steps. This decrease in the performance is potentially due to accumulations of the errors of the self-training process or because with a fixed number training steps, increasing the number intermediate steps leads to decrease in the number of iterations in each self-training step, which could mean the model can not adapt well to each intermediate step. The robustness of the GIFT, in this case, could mean that
that this method needs fewer iterations in each intermediate step. Comparing Figure for both iterative self-training and GIFT, decreasing the number of total training steps (500 vs 1000), reduces the effective number of teacher updates. This confirms the hypothesis that the model can
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Table 3: Accuracy on target domain on benchmarks with natural distribution shift, For the experiments in this table we use ResNet- 101 pretrained on ImageNet- 1k.
Method
FMoW
Camelyon17
Fine-tuned on Source (A)
0,502
0.807
Mixup-Convex (B)
0.525
0.591
Mixup- Wasserstein (C)
0.499
0.896
DANN (D)
0,505
0,934
Best (A, B, C. D) Self-training
0.530
0.962
Best (A, B, C. D) + Iterative Self-training
0.539
0,966
Best (A, B, C. D) GIFT
0.539
0.973
benefit from more teacher updates it has enough time to properly adapt to each intermediate step. We provide more analysis for this in Appendix
4.2 BENCHMARKS WITH NATURAL DISTRIBUTION SHIFT
We report results on two datasets with natural distribution shifts: FMoW (Christie et al. 2018)) and Camelyon 17 (Bandi et al. 2018) from the WILDS benchmark (Koh al. 2021). Here we briefly introduce each of these datasets:
FMoW is a variant of the Functional Map of the World dataset that contains satellite imagery of the earth. The images belong 62 building or land use categories, and the domain represents both the year the image was taken as well as its geographical region. Here we only address the domain shift problem over time. For the adaptation phase, we use unlabeled samples from the nut-of-distribution test split of the dataset.
Camelyon17 is the patch-based variant of Camelyon17 (Bandi al. 2018 with hospitals (0, 1,, 2,3, 4) as domains. The task is to predict if a given region tissue contains a tumor. We 0, 1, source during fine-tuning, but for adaptation we only labeled data from domain 0. We use 3 as the target domain. This is an example of a dataset, for which annotated intermediate distributions between different domains do exist naturally.
As shown in Table 3 on datasets with natural shift, all three self-training based approaches, self- training, iterative self-training and GIFT improve the accuracy the best fine-tuned models. While on FMoW performance of GIFT is on par with iterative self-training, it achieves higher accuracy on Camelyon17. An advantage for GIFT over iterative self-training in these scenarios is that, the performance of GIFT does not rely on the assumption (i) ,that the target distribution should include samples from intermediate steps since in the intermediate steps of training merely learns from the interpolated samples.
5 RELATED WORK
Unsupervised domain adaptation: In unsupervised domain adaptation, have access to labeled examples from the source domain(s) and unlabeled examples from the target domain(s) and the goal to get a good performance on the target domain. Unsupervised domain adaptation techniques fall within three main categories (Sun et al.) (020):: (1) Methods based on matching the feature distributions of source and target domains. Algorithms in this group rely on the assumption that the models can learn domain invariant representations, and they employ different self-supervised based losses to enforce this invariance by exposing the model the unlabeled data from the target distribution (Ganin et al.) 2016) Ben-David et al. 2006). (2) Methods based on transforming source and target distributions. They analyze the input space and project source and target data to a lower dimensional manifold and try find transformation between the two (Fernando
al. 2013 Gopalan et al.) 2011 Harel & Mannor 2010). Another approach in this line of work is to transform the source data to be close the target data as possible. For example, /Sun al. (2017) matches
the second order statistics of the input spaces. (3) Self-training based methods.
Self-training: Recent works have shown significant progress using self-trand self-training in computer vision (Xie et al.) 22200] Yalniz et al.) 2019 Zoph al., 2020). Self-training has also been used for domain adaptation by generating pseudo labels in the target domain and directly training a model for the
target domain (Xie et al. 2018, Saito et al. 2017 Chang et al. 2019 Manders al. 2018 Zou et al.
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2019; 2018 Xie et al. (2018) align labeled source centroids and pseudo-labeled target centroids. (Chang et al. 2019) uses different normalization parameters for source examples and pseudo labeled examples in the target domain. Zou et al. (2019) introduced label-regularized self-training which generates soft pseudo-labels for self-training. Different from these works, we use a curriculum learning approach where we generate pseudo labels for intermediate virtual examples and gradually adapt the model to the target domain. Curriculum learning: Curriculum learning (Elman 1993
Sanger 1994: [Bngii et al.] 2009) has led to better performance in terms of generalization and/or
convergence speed in many domains such as computer vision (Pentina et al. 20155 Sarafianos et al.
2017: Guo et al. 2018: Wang et al. 2019), natural language processing (Cirik et al. 2016 Platanios
ct al. 2019) and neural evolutionary computing (Zaremba & Sutskever] (2044). On the other hand. there have been some negative results neural machine translation (Kocmi & Bojar 2017] Zhang et al. 2018b 2019). In this work, we investigate it in the unsupervised domain adaptation scenario. Different notions of "difficulty" of examples are used in the literature, such as using the loss value of pre-trained model (Bengio et al. 2009). or the first iteration in which an example is learned and
remains learned after that (Toneva et al. 2019). Jiang et al. (2020) have proposed using a consistency score calculated based on the consistency of model in correctly predicting particular example's label trained on i.i.d. draws from the training set. [w et al. (202I) show that all these difficulty scores consistent. Here, we use the coefficient of linear interpolation between source and target representation as a measure of the difficulty of a (virtual) sample.
Leveraging synthetic data for domain adaptation: We build top of the existing work that incorporate synthetic data to bridge between source and target domain Gopalan et al. (2014); Gong et al. (2019); Cui et al. (2020) Na et al. (2021). Similar Na et al. (2021)
mixup create intermediate samples, but instead of using fixed mixup rates, we incorporate an annealing strategy so the created instances, gradually move away from the source domain and get closer to the samples from the target domain. Additionally, we apply mixup both in the input layer and representations obtained from various layers of the models. Gong et al.] (2019) proposes create intermediate domains using CycleGAN (Hoffman et al. (0018). wheras in GIFT, we create the intermediate domains in the representational space of the model and abstract away from actual images corresponding those representations.
6 DISCUSSION AND CONCLUSION
We establish the importance of having proper curriculum for the success of self-training algorithms for domain adaptation. We demonstrate that iterative self-training can successfully adapt the model to the new target distribution if the target distribution contains the intermediate examples. We show that iterative self-training is less effective if the source and target distributions are not overlapping. Our proposed method, GIFT, is specifically designed to deal with cases where there is a gap between source and target distributions. In such scenarios, applying self-traimin examples based on the confidence of the model would not result in a proper curriculum since the intermediate examples are missing. We propose and perform controlled experiments on distribution shift on a synthetic benchmark created from CIFAR10. More specifically, we control the amount of shift, the type of shift, and whether there is gap between the data distributions in the source and target domain. Our experiments confirm the importance of the presence of samples from intermediate distributions for the success of iterative self-training and show that in the absence of intermediate samples, GIFT improves the results over iterative self- eeff-training. We observe similar results on datasets with natural distribution shifts.
iteratively, and filtering
GIFT is inspired by existing works that rely on interpolating representations in the input or feature space (Gion et al. 2012, Verma al. 2019a by Neyshabur et al. 2020). An interesting direction for future work is to investigate other ways of interpolating in the feature space and explore the use of more sophisticated interpolation schemes, such as schemes based on optimal transport. Moreover, the experiments in this paper are limited to image classification. Extending our approach beyond classification and to other data modalities such as textual data is an interesting next step. Lastly, we emphasise the importance of designing benchmarks specifically for the purpose of evaluating gradual domain adaptation techniques under different conditions, as one of the most important steps in this line of research.

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REPRODUCIBILITY STATEMENT
We have shared the details of the proposed algorithms and experimental setup in sections 3 and Additionally, we provide simple implementation of the main algorithms proposed at ht ntsps:
/ gi wow.tctooocccccccc.ooooooocctctt g
We ran experiments on dataset with synthetic shifts, for which we thoroughly explain how is created in section 4.1 as well as two datasets with natural distribution shifts which are already available as part of the WILDS benchmark (Koh et al. 2027).
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A EXPERIMENTAL SETUP
Optimizer and learning rate schedule. In all our experiments on datasets with natural distribution shift, we use Adam optimizer. When training on the labeled source domain we use learning rate schedule with cosine decay and initial learning rate of le-4 and when adapting to the target domain we use a learning rate of le-5 with an exponential decay rate of 0.9. For pretraining the models on ImageNet-Ile 1k, epochs) + cosine decay with the base learning rate of 0.1.
batch size of 1024 and the learning rate schedule is linear warmup (for 5
For Perturbed Cifar 10 experiments, the source domain, the learning rate schedule is cosine decay with an initial learning rate of 0.1. In all experiments, we use L.2 loss with the weight of le-5, During the adaptation phase, size of 256 and the learning rate is constant and set to le-3, For experiments on Perturbed Cifarl0 with a higher number of training steps (20000 steps), we use a lower learning rate of le-4 in the adaptation phase.
SGD with momentum. During the pretraining stage on
a batch
Neural network architectures. For experiments on datasets with natural shifts, use ResNet101. For the experiments on Perturbed Cifar10, we use a Weee 10 with a dropout rate of 0.3. For the virtual interpolations in GIFT: use the first three layers (input, initial convolution layer, and the layer above it).
Training on source during the adaptation phase. We do not train the model on the source data during the adaptation phase. While in some cases this could result in a better performance on both the source and target domain, our assumption here is that there is no reason for the source and target data to be compatible, i.e. it is possible for the model to not be able to fit both distributions simultaneously.
Regularization During adaptation, we use the weight decay of 0.01. In addition to weight decay, we use another regularization term that encourages the model to stay close to its initial state. This regularization term is simply computed as the L2 distance of the parameters of the model and their value at its initial state. We set the weight for this factor to 0.001 in all adaptation experiments.
Backpropagating gradients through interpolations. We train the model with the representations of virtual examples that we create by interpolating the representations from real examples. During pretraining the source domain, we manifold mixup regularization, where between representations of labeled source examples. During the adaptation stage that is part of GIFT, interpolate between labeled source representations and unlabeled target representations. One the
interpolate
important nyper-parameter related to this is whether in the backward pass we gradients all the way down to the input layer or stop the gradients at the layer in which the interpolated representations are computed. In our experiments, similar to Verma et al. (2019)) we allow the gradients to pass through the interpolated activations.
B TRAINING ON LABELED SOURCE DOMAIN
We compare four different approaches for training the model on labeled source data.
Standard fine-tuning: Given labeled examples from a source domain, we employ a model that is pretrained on some large scale dataset, Imagenet-1k k in our case, replace its head (projection layer) with a new head for the task at hand, and update all its parameters to fit the source domain data. Mixup with convex combination interpolations: During fine-tuning on labeled source data, we apply mixup/manifold (Zhang et al. 2018a; Verma et al., 2019a) on the input and activation from the first simply compute the convex combination of features for two randomly aligned examples. Mixup with wasserstein interpolations: During fine- tuning on labeled source data, apply variant of mixup/manifold mixup where interpolations computed using the closed-form Monge Map for Gaussian Wasserstein distances. In our experiments, we observed that in some cases, interpolating examples in this alternative way leads to better results compared to the convex interpolations used in Verma et al. (2019)). Domain adversarial neural networks (DANN): Given labeled samples from a source domain and unlabeled samples from the target domain, DANN (Ganin et al. 2016) learns domain invariant representations, while minimizing its error labels source data. In our experiments, the output of the prelogits layer is fed to the domain classifier, and the scheduling of the weight of the domain classification loss is the same as what is suggested in Ganin et al. (0016).
layer of the model, and to compute the interpolations
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B.1 MANIFOLD MIXUP WITH WASSERSTEIN INTERPOLATION
During training on the labeled source dataset, we use a variant of manifold mixup \Verma et al. 2019a) with adapted strategy for interpolation. In manifold mixup (Verma al. 20T9a), representations
of virtual examples are created by linearly interpolating representations of two randomly aligned examples (xy, xTy) in randomly selected layer of the neural network Ma. The labels for the interpolated examples, Pig. are computed by interpolating the labels of the aligned examples, (yt. My). using the same interpolation coefficient, X. This is summarized in equation
2
X)Ma (24) (2)())
0i = (1 A)ys + Ayy
Here My denotes the part of the neural network that outputs the activations of layer The interpolated representations are then fed into the rest of the neural network at layer, L, and together with the interpolated labels, they serve as additional 'data' to which the model is
In our experiments, we take different approach to interpolation. Inspired by the style transfer method discussed in Mrouch (2020b), we use interpolations based on the Wasserstein distance between two Gaussian distributions that are fit to representations of two input images. i.e., the spatial features in the representations of two images are the data points for two datasets. We estimate the empirical mean and diagonal covariance matrices for these data points and use the closed-fome optimal transport map between two Gaussian distributions to interpolate the spatial features between two representations. More precisely, given two images 3; and zj. we compute representations 2 (a:) and 2j (a;;), where 2; and 2j are three-dimensional tensors with width WL, height H and channel size C*., Each spatial feature vector of size C³ within 2; and 2, is considered one data point. We compute the average feature vectors within 2; and Zj. denoted by μ4 and μj respectively, as well as the variances of and oz. Note that we are approximating the empirical covariance matrices with diagonal matrices with the variances of and of on the diagonals. Given these quantities, we can compute the closed-form Monge map between two Gaussian distributions with diagonal covariance matrices as
Te, (2) Mi + diag
(z
pz)-
Here 2 is understood to be a feature map of the same size as 2; and 2j. Interpolated representations then computed with
E.g = (1 A)2; + (z))
Similar to its use in style transfer (Mroueh, 2020b), we assume this transformation does not change the content of the representation, and we therefore do not apply an interpolation scheme to the labels y and yy of datapoints and zy. Instead, we use the label dis- = for the virtual representation &g.
In Verma et al. (2019a) the interpolation coefficient À sampled from a Beta distribution Beta(a, B). where and |3 are hyperparameters. In our experiments we set both and /3 to 1, so that we are effectively sampling uniformly from the interval [0, 1).
C EFFECT OF NUMBER OF TEACHER UPDATES
To better distinguish the effect of the number of teacher updates from the number of training steps between each two consecutive teacher updates, in Figure 4 we plot the accuracy as a function of the number of teacher updates with a fixed number of training steps. That means, in this setup, the total number of training steps increases as we increase the number of teacher updates. For GIFT, we observe an increasing trend in the accuracy as the number of teacher update increases on all the benchmarks. However, for iterative self seff-training, we only see benefit in increasing the number of teacher updates for datasets with range of perturbations in the target domain, such the Translated CIFARIO datasets, as opposed to Blurred CIFARIO.
Additionally, Figure 5 shows the effect of the number of teacher updates when the total number of training steps is 1000 for non-gradual version of GIFT, where all the interpolations are presented to the model simultaneously. We observe that, in this case, compared to GIFT, where the value of the interpolation coefficient À gradually increases, having more teacher updates is less beneficial.
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Translated (0%-1000)
Transhatel(305-1000
Blurred
0.8
0.8
Accuracy
0.6
Accuracy
0.6
0.4
0.4
0.2
0.2
2
20
5
20
Number of teacher updates
Number of teacher updates
(a) iterative self-training
(b) GIFT
Figure 4: Effect the number of teacher updates on the accuracy when the number of training steps before each teacher update is fixed and set to 100, for different perturbations of CIFARIO. For Translated (0%- 100%) CIFAR1O and Translated (50%- 100%% CIFARIO, we see an increasing trend in accuracy we increase the number of teacher updates for both iterative self-training and GIFT. Whereas for Blurred CIFARIO. 10, the accuracy decreases for iterative self-training.
0.8
Scaled
Accuracy
0.6
Translated (0S-100%)
Blurred
Translated(50S-
0.4
0.2
5
10
20
Number of teacher updates
Figure 5: Effect of the number of self-training iterations on accuracy when all interpolations are represented to the model the same time with the total number of training steps of 1000 for different perturbations of CIFAR1O. 10. Similar to iterative self-training, the performance improves by increasing the number of self-training iterations up threshold. Beyond the threshold, the performance deteriorates.
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Reviews:
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This work seems to have certain novelty. I haven't seen papers that anneal the mixup weights. However, it's unclear to me how much this strategy helps DA. I didn't find an ablation study that use a fixed mixup weight.\n2. The technical novelty is a bit limited, as it's a simple extension of manifold mixup. To convince readers of its practical value, the authors should do more extensive experiments as well as ablation studies. In natural images, the two used datasets FMoW and Camelyon17 are not typically used to evaluate DA. The authors also should compare with many more existing methods. One important related method is Tent [1].\n\n[1] Tent: Fully Test-time Adaptation by Entropy Minimization, ICLR 2021.\n", "summary_of_the_paper": "This work adddresses domain adaptation (DA) by a GIFT method. GIFT consists of a manifold mixup technique, which generates virtual samples by mixing up the features of source and target domains samples. The mixup coefficient is annealed over time to bias towards the target domain. Another ingredient of GIFT is a co-teaching strategy that lets two networks teach each other. On a few small synthetic as well as natural image datasets, GIFT outperforms a few baseline methods.", "summary_of_the_review": "The technical novelty of GIFT is limited. Hence, the authors should focus on showing the empirical benefits of GIFT. However, the experiments are highly insufficient, with missing ablations and baselines. Moreover, the evaluation datasets are not so popularly used. Therefore, it's hard to judge how much empirical value this work brings. ", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "pDxsuhBoNui", "reviewer": "Reviewer_peK3", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "main_review": "Strengths:\n1. This paper is well-motivated since the gradual domain adaptation is still an under-explored problem.\n2. The motivation and the overall idea of the paper is easy to follow.\n\nWeaknesses:\n1. novelty concerns:\n\n(a) The main concern for this paper is the novelty. The main idea to address Gradual Domain Adaptation in this paper is to create synthetic data from source and target domains. There are already several previous papers working on this idea, such as DLOW [1], GVB [2], FixBi [3]. Although the above methods are not proposed to directly solve the gradual domain adaptation problem, they can be adapted to this problem. To prove that the proposed GIFT is better, the above methods should be compared after applying to the same problem.\n\nReferences:\n\n[1] Rui Gong, et al. \"DLOW: Domain Flow for Adaptation and Generalization\", CVPR, 2019.\n\n[2] Shuhao Cui, et al. \"Gradually Vanishing Bridge for Adversarial Domain Adaptation\", CVPR, 2020.\n\n[3] Jaemin Na, et al. \"FixBi: Bridging Domain Spaces for Unsupervised Domain Adaptation\", CVPR, 2021.\n\n2. technical detail concerns:\n\n(a) lambda scheduler: It should be critical to find the best way to transfer the intermediate data smoothly from source to target. However, the proposed lambda scheduler is a linear function with a fixed step size. The step size could be different when facing different datasets, making the current scheduler heuristic and not generalized.\n\n(b) alignment method: it is still unclear which method is adopted for the final model according to the context. Pseudo-random alignment or cost-based alignment? This part is confusing.\n\n3. experiment concerns:\n\n(a) Table 1: The number of self-training iterations is different for iterative self-training and GIFT (5 and 20). This would make the comparison unfair. Why not keep the same training setup?\n\n(b) Separating Tables 1 and 2 is confusing: It is unclear what the difference is between these two Tables. Is the main difference in the total number of training steps (1000 vs. 500)? Moreover, it is not clear why we can claim GIFT is more “robust” than iterative self-training. For Translated (50%-100%) CIFAR-10, iterative self-training raises the accuracy from 0.477 to 0.658 when increasing the training step number from 500 to 1000. However, GIFT drops the accuracy from 0.832 to 0.729. In this case, it is weird to claim GIFT is more robust.\n\n(c) Figure 3: It is weird to compare with different numbers of teacher updates. It would be great to provide an explanation about this.\n\n(d) Table 3: With the same baseline (i.e., Best (A, B, C, D)), GIFT does not have a clear improvement over iterative self-training.\n\n4. other concerns:\n\n(a) The publications in the Reference Section should be updated:\n\n(1) Dan Hendrycks, Steven Basart, Norman Mu, Saurav Kadavath, Frank Wang, Evan Dorundo, Rahul Desai, Tyler Zhu, Samyak Parajuli, Mike Guo, Dawn Song, Jacob Steinhardt, and Justin Gilmer. “The many faces of robustness: A critical analysis of out-of-distribution generalization”. ICCV, 2021.\n\n(2) Ananya Kumar, Tengyu Ma, and Percy Liang. “Understanding self-training for gradual domain adaptation”. ICML, 2020.\n\n(3) Behnam Neyshabur, Hanie Sedghi, and Chiyuan Zhang. “What is being transferred in transfer learning?”. NeurIPS, 2020.\n\n(4) Pang Wei Koh, Shiori Sagawa, Henrik Marklund, Sang Michael Xie, Marvin Zhang, Akshay Balsubramani, Weihua Hu, Michihiro Yasunaga, Richard Lanas Phillips, Irena Gao, Tony Lee, Etienne David, Ian Stavness, Wei Guo, Berton A. Earnshaw, Imran S. Haque, Sara Beery, Jure Leskovec, Anshul Kundaje, Emma Pierson, Sergey Levine, Chelsea Finn, and Percy Liang. “WILDS: A Benchmark of in-the-Wild Distribution Shifts”. ICML, 2021.\n\n(5) Qizhe Xie, Eduard Hovy, Minh-Thang Luong, and Quoc V Le. “Self-training with Noisy Student improves ImageNet classification”. CVPR, 2020.\n\n(6) Barret Zoph, Golnaz Ghiasi, Tsung-Yi Lin, Yin Cui, Hanxiao Liu, Ekin D. Cubuk, and Quoc V. Le. “Rethinking Pre-training and Self-training”, NeurIPS, 2020.\n\n", "summary_of_the_paper": "The paper proposes to address the gradual domain adaptation problem by creating virtual samples from intermediate distributions by interpolating representations of examples from source and target domains.", "summary_of_the_review": "The proposed method in this paper is not novel although creating virtual examples is a reasonable direction for addressing gradual domain adaptation. I suggest the authors can still work on this direction but propose a more novel way to create virtual examples that contain better intermediate information. The experimental results do not support what the paper claims and do not show significant improvement over previous methods. Therefore, I recommend rejecting this paper.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "1: The contributions are neither significant nor novel."}, "extra_text": {}}, {"review_id": "RqkoDjjAQBt", "reviewer": "Reviewer_v3Ep", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "main_review": "+ The problem is well motivated and illustrated through different experiments and toy examples.\n+ paper is well written and easy to follow\n\nClarification need:\n- In Algorithm 2: matching scores are 1 for the same class, so if there are false positives(which happens a lot in real datasets), then the alignment will be biased towards them leading to poorer student network training?\n- the choice of target examples to be mixed may create difficult examples early on, it is not clear how random assignments can overcome this situation? Also, the Align function along with the \\lambda value will together decide, the hardness of the intermediate examples created.\n- lambda_scheduler tuning is not discussed properly, will it depend on the gap between the two domains? if yes, then how should be handled?\n- mismatch in lambda_scheduler step size notation \\delta in Algorithm 1 and \\sigma on page 3\n- figure 1 has \"gradual self-training\" as a caption in one of the subplots but this method is not mentioned or cited.\n", "summary_of_the_paper": "This work builds on the previous work[1] and extends it for a more general scenario, where per sample intermediate distribution shift is hard to quantify. They propose gradual feature interpolation for the case where samples from intermediate distribution are missing. Iterative self-training fails in such cases. The work presents results on synthetic and natural distributions to evaluate their claim.\n\n[1] Ananya Kumar, Tengyu Ma, and Percy Liang. Understanding self-training for gradual domain adaptation. arXiv preprint arXiv:2002.11361, 2020.", "summary_of_the_review": "The work puts forwards an interesting work to gradually align two domains. Though different experiments are shown to support their claim, there are few clarifications needed as mentioned in the main review.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "KtEdpfB5wN", "reviewer": "Reviewer_KPWG", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "main_review": "Strength:\n\nThis paper is well written and easy to understand. The proposed method is simple but effective. The analyses of how, why, and when iterative self-training is helpful can benefit the community, which is important.\n\nWeakness:\n1.\tGenerating intermediate data in domain adaptation is not a new thing, it is recommended to discuss with related works, such as [1,2].\n2.\tAs shown in Table 3, the proposed method does not bring significant improvement over iterative self-training. It is recommended to perform evaluations on more datasets with natural distribution shifts.\n\n[1] DLOW: Domain Flow for Adaptation and Generalization\n\n[2] Unsupervised Adaptation Across Domain Shifts by Generating Intermediate Data Representations\n", "summary_of_the_paper": "This paper introduces how to deal with the situation when intermediate distributions are unavailable. The basic idea is to create virtual samples by interpolating source and target representations. The effectiveness of the proposed method is evaluated and results in several interesting conclusions.", "summary_of_the_review": "My major concern is the effectiveness of the proposed method on datasets with natural distribution shifts. Although this method works well on synthetic data, its applicability to real datasets should be further justified and evaluated.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "54ddxKpqJa", "reviewer": "Reviewer_Les7", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "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": "", "main_review": "This work considers the problem of gradual domain adaptation, where a model should be gradually adapted from the source to the target domain. I found the idea of generating data (at a lower-dimensional space) from intermediate distributions interesting and appealing from a practical perspective. In the following, I present my major concerns, questions, and suggestions. \n\n\n- It is not clear from the manuscript why gradual domain adaptation is a setting that should be considered in cases where no samples from intermediate distributions are available. As far as I understand, gradual domain adaptation is a setting to be considered when the distribution yielding the data is evolving over time (Kumar et al. 2020) and the goal is to incorporate this knowledge about the problem structure in the model adaptation process. Given that, it is not clear to me why considering this setting in a case where the data distribution is not gradually shifting would make sense. If this is the case, why not directly use any other domain adaptation approach?\n\n\n - A major claim of this contribution is that by mixing-up representations of both source and target domains, examples from “intermediate” distribution would be generated. Although I can get a rough intuition of what an intermediate distribution could be (e.g. a mixture of source and target domains), there is no definition or discussion regarding this in the manuscript. I suggest the authors include in the manuscript a clear definition of what such distributions are, as well as include evidence that manifold mix-up is capable of generating samples from them. \n\n\n- Experiments\n  - The authors mentioned that the decrease in confidence/accuracy observed on examples with higher levels of perturbation observed in \nFigure 2 confirms that the reason behind the success of iterative self-training is the implicit curriculum strategy. Although I understand that this observation indicates the existence of an implicit curriculum, it is not clear to me why it indicates it is the reason behind the success of iterative self-training.\n  - It is not clear to me whether the results presented in Tables 1 and 2 are good. Even though I understand that the goal of this work isn’t to achieve state-of-the-art results in benchmarks, it is hard to assess the merit of the improvements reported in these tables without knowing how established baselines would perform in such test cases. I strongly encourage the authors to include for comparison at least DANN and CDAN.\n  - In Table 3, the authors presented results obtained on two datasets. They mentioned that in the case of Camelyon17, hospitals 0, 1, and 2 were considered as source domains while hospital 3 was the target. However, in Table 3, it seems that only results with domain 0 as the source were reported. Why is it the case? Please clarify this and modify the text accordingly.\n   - It is hard to tell whether the results presented in Table 3 indicate a relevant improvement of self-training approaches and the proposed GIFT in comparison to the considered baselines. The authors did not report if more than one run was performed. In case only one run was performed, I don’t think it is possible to draw conclusions from these experiments since models adapted via DANN, for example, are known to be quite sensitive to the initialization. \n\n\n- In addition to the aforementioned concerns, this manuscript presents several presentation and clarity issues that make it difficult to understand. In the following, I outline the major issues:\n  - In Section 2, the authors introduced the considered setting but there are several missing points regarding the introduced notation. Please properly define $n_s$, $d$, $k$, and $n_t$. Moreover, the authors did not specify the underlying assumptions of the proposed approach, i.e., is the covariate assumption required? Is label shift allowed? \n  - Furthermore, in Section 2, the authors mentioned that “The goal is to bridge the domain difference and learn a good classifier for the target domain.” What exactly does “a good classifier” mean in this sentence? I believe the authors are considering the risk minimization setting from Ben-David et al. 2010, but please let this clear in the text.\n  - It is quite difficult to parse the information contained in Algorithms 1 and 2. Several variables were not introduced, and there is no comment to explain what each line is doing. Summing this up with the fact that there is barely any explanation about GIFT training procedure and the Label-based Random Alignment throughout the text, it is hard to properly understand what the main contributions of this work are really doing. Moreover, the clarity of the Algorithms and the aforementioned contributions should be improved to facilitate the reproduction of the reported results. \n\n\n- Minor\n  - It is hard to compare the results reported in Tables 1 and 2 because they are placed too far apart in the manuscript. I think it is possible to merge both into a single table.\n  - The symbols $P_s$ and $P_t$ are used to denote different objects in the text. In Section 2, they are referred to as the source and target domains, respectively, while in Algorithm 1 they denote source and target datasets, respectively. \n", "summary_of_the_paper": "This work proposes an iterative self-training approach for unsupervised domain adaptation. In particular, the authors aim at gradually adapting a model trained on a source domain to the target domain. Based on the claim that previous work on this setting assumed that samples from distributions that represent gradual changes from the source to the target domain are available when adapting the model, the authors proposed a strategy to generate such intermediate samples for cases where they are not available. The introduced approach, named GIFT, consists in performing manifold mix-up between representations of examples from the source and target domains considering an increasing value of the hyperparameter that accounts for the weight of the representation of the target domain example. By doing so, the authors claim an automatic curriculum is introduced in the training. Moreover, since labels from the target domain examples are not available, the authors also introduced a heuristic to pair the examples that are mixed. GIFT was empirically validated on experiments with synthetic domain shifts on the CIFAR-10 dataset and was shown to outperform iterative self-training in terms of target accuracy. Experiments on two datasets presenting natural domain shifts were also performed.  ", "summary_of_the_review": "This work proposes an iterative self-training approach for unsupervised domain adaptation. In particular, the authors aim at gradually adapting a model trained on a source domain to the target domain. The main contribution is a strategy to generate examples from the so-called intermediate distribution between the source and target domains. Despite the reported empirical improvement over the considered baselines, I found the motivation of the proposed approach unclear, and I found that the main claim is not well-supported (i.e. is GIFT indeed capable of generating examples from intermediate distributions? Also, what are such intermediate distributions?). Moreover, the manuscript lacks clarity in several aspects and I have concerns regarding the significance of the reported results since it seems only a single run was considered in each test case. All in all, my initial assessment is that this manuscript is not ready for publication yet.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Meta-review: Most reviewers agree that the paper addresses a relevant problem. However, they also  believe that
the paper lacks in several points : not-well supported claim, sometimes clarity, incremental in term of novelty.
Decision: Reject