How robust is unsupervised representation learning to distribution shift?
Authors: Yuge Shi
Imant Daunhawer
Julia E Vogt
Philip Torr
Amartya Sanyal
Venue: ICLR 2023 poster (2023)
Keywords: distribution shift
OOD generalisation
spurious correlation
simplicity bias
SSL
unsupervised learning
auto-encoder

Abstract: The robustness of machine learning algorithms to distributions shift is primarily discussed in the context of supervised learning (SL). As such, there is a lack of insight on the robustness of the representations learned from unsupervised methods, such as self-supervised learning (SSL) and auto-encoder based algorithms (AE), to distribution shift. We posit that the input-driven objectives of unsupervised algorithms lead to representations that are more robust to distribution shift than the target-driven objective of SL. We verify this by extensively evaluating the performance of SSL and AE on both synthetic and realistic distribution shift datasets. Following observations that the linear layer used for classification itself can be susceptible to spurious correlations, we evaluate the representations using a linear
head trained on a small amount of out-of-distribution (OOD) data, to isolate the robustness of the learned representations from that of the linear head. We also develop “controllable” versions of existing realistic domain generalisation datasets with adjustable degrees of distribution shifts. This allows us to study the robustness of different learning algorithms under versatile yet realistic distribution shift
conditions. Our experiments show that representations learned from unsupervised learning algorithms generalise better than SL under a wide variety of extreme as well as realistic distribution shifts.

Published as a conference paper at ICLR 2023
How ROBUST IS UNSUPERVISED REPRESENTATION LEARNING TO DISTRIBUTION SHIFT?
Yuge Shi*
Imant Daunhawer & Julia E. Vogt
Department of Engineering Science University of Oxford
Department of Computer Science
ETH Zurich
Philip H.S. Torr
Amartya Sanyal
Department of Engineering Science University of Oxford
Department of Computer Science & ETH Al Center
ETH Zurich
ABSTRACT
The robustness of machine learning algorithms to distributions shift is primarily discussed in the context of supervised learning (SL), As such, there is a lack of insight on the robustness of the representations learned from unsupervised methods, such as self-supervised learning (SSL) and auto-encodes based algorithms (AE), distribution shift. We posit that the input-driven objectives of unsupervised algorithms lead to representations that are more robust to distribution shift than the larget-driven objective of SL. We verify this by extensively evaluating the perfor- mance of SSL and AE both synthetic and realistic distribution shift datasets. Following observations that the linear layer used for classification itself can be susceptible spurious correlations, head trained on a small amount of out-of-distributioo (OOD) data, to isolate the robustness of the learned representations from that of the linear head. We also develop "controllable" versions of existing realistic domain generalisation datasets with adjustable degrees of distribution shifts. This allows to study the robust- ness of different learning algorithms under versatile yet realistic distribution shift conditions. Our experiments show that representations learned from unsupervised learning algorithms generalise better than SL under a wide variety of extreme well realistic distribution shifts.
evaluate the representations using a linear
INTRODUCTION
Machine Learning (ML) algorithms are classically designed under the statistical assumption that the training and test data are drawn from the same distribution. However, this assumption does not hold in most cases of real world deployment of MI. systems. For example, medical researchers might obtain their training data from hospitals in Europe, but deploy their trained models in Asia; the changes in conditions such imaging equipment and demography result in shift in the data distribution between train and test set (Dockès et al. 2021 Glocker et al. 2019 Henrich et al. 2010). To perform well such tasks requires the models generalise unseen distributions
important property that is not evaluated on standard machine learning datasets like ImageNet, where the train and test set sampled i.i.d. from the same distribution.
With increasing attention on this issue, researchers have been probing the generalisation performance of MI. models by creating datasets that feature distribution shift tasks (Koh et al., 2021 Gulrajani and Lopez-Pazz Paz 2020 Shah et al.) (2020) and proposing algorithms that aim to improve generalisation performance under distribution shift (Ganin al. 2016 Arjovsky al. 2019 Sun and Saenko 2016 Sagawa et al. 2020 Shi et al. 2022). In this work, we identify three specific problems with current approaches in distribution shift problems, in computer vision, and develop suite of experiments to address them.
"Corresponding author, yshi @robots.................o.....s. ax.a...... uk

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Published as a conference paper at ICLR 2023
CIAS
Cdsprites
Camelyan17
FMo
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Those sous los plii 1, Aqtarelime land, Ada, 2012
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Figure Synthetic vs. realistic distribution shift: The distribution shift in synthetic datasets (left, MNIST-CIFAR and CdSprites) usually extreme and controllable (adjusted via changing the correlation); for realistic datasets (right, WILDS MLDDS-Camllyon1 and FMoW) distribution shift can be subtle, hard identify and impossible to control.
1.1 EXISTING PROBLEMS AND CONTRIBUTIONS
Problem 1:
The outdated focus supervised regime for distribution shift In ML research, distribution shift has been studied in various contexts under different terminologies such as simplicity bias (Shah et al. 2020), dataset bias (Torralba and Efros 2011). shortcut learning (Geirhos et al.)
2020), and domain adaptation and generalisation (Koh et al. [2021] Gulrajani and Lopez- (020)
Most of these work are carried out under the scope of supervised leaning (SL), including vanous
works that either investigate spurious correlations (Shah et al. 2020) Hermann and Lampinen 2020
Kalimeris al., 2019) or those that propose specialised methods to improve generalisation and/or
avoid shortcut solutions (Arjovsky et al. [2119] Ganin et al. 2016 Sagawa et al. 22200 Teney et al.
2022). However, recent research (Shah et al. 2020 Geirhos al. (2020) highlighted the extreme
vulnerability of SL methods to spurious correlations: they are susceptible to learning only features that are irrelevant to the true labelling functions yet highly predictive of the labels. This behaviour not surprising given SL's target-driven objective: when presented with two features that are equally predictive of the target label, SL models have no incentive to learn both as learning only one of them suffices to predict the target label. This leads to poor generalisation when the learned feature is missing in the OOD test set.
On the other hand, in recent times, research in computer vision has seen surge of unsupervised representation learning algorithms. These include self-supervised learning (SSL) algorithms (e.g.. Chen et al. 2020a): Grill et al. (2020) Chen and He (202T)). which learn representations by enforcing invariance between the representations of two distinctly augmented views the same image, and auto-encoder based algorithms (AE) (Rumelhart et al. 1985 Kingma and Welling 2014 Higgins let al. 2017 Burda et al. 2016), which learn representations by reconstructing the input image. The balanced
immense popularity of these methods mostly owed their impressive performance in-distribution (ID) test datasets - how they perform on distribution shift tasks remains largely unknown. However, in distribution shift tasks, it is particularly meaningful to study unsupervised algorithms. This is because, in comparison to SL, their learning objectives are more input-driven i.e. they are incentivised to learn representations that most accurately represent the input data (Chen) al. [020aa] Alemi et al., (017). When presented with two features equally predictive of the labels, unsupervised learning algorithms encourage the model to go beyond learning what's enough to predict the label, and instead focus maximising the mutual information between the learned representations and the input. We hypothesise that this property of unsupervised representation learning algorithms helps them avoid the exploitation of spurious correlations, and thus fare better under distribution shift, compared to SL.
Contribution:
Systematically evaluate SSL and AE distribution shift tasks. We evaluate and compare the generalisation performance of unsupervised representation learning algorithms, including SSL and AE, with standard supervised learning. See Seelsintionn for more details on our experiments.
Disconnect between synthetic and realistic datasets Broadly speaking. there exists two types of datasets for studying distribution shift: synthetic datasets where the shift between train/test distribution is explicit and controlled (e.g. MNIST-CIFAM (Shah al., 2020), CdSprites (Shi et al.] ) and realistic datasets featuring implicit distribution shift in the real world (e.g.
Problem 2:
WILDS (Koh et al. 202T)). We provide visual examples in fig.
Synthetic datasets allow for explicit control of the distribution shift and are, thus, an effective diagnostic tool for generalisation performance. However, the simplistic nature of these datasets poses
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OOD Accuracy (higher is better)
79.9
06.1
83.11
26.92
25.73
89.8
35.6
80.91
29.64
51.5
44
16.26
86. 91
86. 06.04
SSL
SRL
AE:
SSL
SL
AE
SSL
AE
SSL
SL
SSL
5L.
AE
5SL
SL
Shift Sensitivity (lower is better)
47.6
5.6
37.7
47.5
10.72
12 26
6.35
8.77
29
1 63
4.09
13.7
17.3
4,99
9.15
3SL
SL
AE
SSL
AE
SSL
5L
SSL
SL
NE
SSL
(a) CIFAR
(b) CdSprites
(c)
Camelyom17.CS
(d) FMo CS
(c) Camelyon17
(l) FMoW
Figure Performance of auto-encoder (AB), self-supervised learning (SSL), supervised learning (SL)
models. Top row: the OOD test set accuracy (%) using linear heads trained on OOD data; Bottom row: Shift Sensitivity (see section 2 for definition), measures models' sensitivity to distribution shift.
Note here
for Camelyon17-CS, FMoW-CS, and CdSprites (see sections 3.1.2 and 3.2.2 2
concerns about the generality of the findings drawn from these experiments; a model's robustness to spurious correlation certain toy datasets is not very useful if it fails when tested similar real-world problems. On the other hand, realistic datasets often feature distribution shifts that are
subtle and hard to define (see fig. I right). As result, generalisation performances of different algorithms tend to fluctuate across datasets (Koh et al. 2021 Gulrajani and Lopez-Paz 2020) with the cause of said fluctuations remaining unknown.
Controllable but realistic distribution shift tasks. In addition to evaluating models on both synthetic and realistic datasets, we subsample realistic domain generalisation datasets in WILDS to artificially inject explicit spurious correlations between domains and labels. This allows us directly control the level of shift in these realistic distribution shift datasets. We refer them as Controllable-Shn (CS) datasets.
Contribution:
The linear classifier head strongly biases the evaluation protocol The most popular evaluation protocol for representation learning algorithms (both supervised and unsupervised) is linear probing. This involves freezing the weights of the representation learning model and training linear classifier head on top of that to predict the labels. For distribution shift problems, this linear classifier is typically trained on the same training set as the representation learning backbone. Kang ct al. (2020); Menon et al. (2020) observed the interesting phenomenon that this final layer linear classifier be extremely susceptible to spurious correlations, causing poor OOD performance. Under simple, synthetic set up. they showed that SL models' performance on OOD test set can be dramatically improved by simply retraining the linear classifier on data where the spurious correlation absent. This indicates that the linear classifier can be strong source of model bias distribution shift tasks, and disentangle the linear classifier bias from the generalisation performance of the learned representations, it is advisable to re-train the linear head on OOD data during evaluation. Note that although retraining linear classifier head already standard practice in transfer learning, its application is necessary as the pre-training task and target task are typically different; on the other hand, retraining linear head is neither necessary nor standard practice in distribution shift problems, despite the recognition of linear head bias in recent work (Kagg al. 2020; Menon et al. 2020
Problem 3:
Contribution: OOD linear head. When reporting OOD accuracy, we use a linear head trained on small amount of left-out OOD) data as opposed to ID data, is standard practice. This allows us to isolate the bias of the lincar head from the generalisability of learned representations. We also quantify the linear head bias to highlight the importance of this treatment. With these results, wish to establish OOD linear head evaluation as a standard protocol for evaluating robustness of representation learning algorithms to distribution shift.
While datasets like ImageNet-9 9 and SVSF also provides distribution shift controls for real images, our sub-sampling of realistic domain generalisation datasets allows us to gain such control cheaply on a large set of datascts, and in addition provide further analysis on models' performance on existing benchmarks (WILDS).
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In summary, we develop suite of experiments and datasets to evaluate the performance of various representation learning paradigms under distribution shift. FFguree provides a summary of our results, comparing range of methods from the following classes of algorithms: (i) SSL, (ii) AE, and (iii) SI.. Note that though the intuition that unsupervised objectives should be better at distribution shift tasks is well-established in theory (Chen et al.) 2020a Alemi et al., 2017). state-of-the-ar methods are predominantly developed under SL. To the best of our knowledge, we are the first to systematically evaluate and compare unsupervised representation learning methods to SL under distribution shift. The models are evaluated on both synthetic and realistic distribution shift datasets. Further. the models are also evaluated on CS datasets that contains controllable, explicit spurious correlations in realistic datasets. The main takeaways from this paper are:
SSL and AE are more robust than SL extreme distribution shift: Figures 2a to 2d shows results on distribution shift scenarios where the training set encodes extreme spurious correlations. In this setting. for both synthetic (figs. 2a and 2b) and real world (figs. 2cland 2d) datasets, SSL and AE consistently outperforms SL in terms of OOD accuracy (top row);
Compared to SL, SSL and AE's performance drop less under distribution shift: The bottom row of fg.. 2 compares the shift sensitivity (s) of different models (see ssction for definition). Smaller is desirable as it indicates lower sensitivity to distribution shift. Results show that SSL and AE algorithms are significantly more stable under distribution shift than SL,
Generalisation performance on distribution shift tasks can be significantly improved by re- training the linear head: We show a large performance boost for all models, when evaluated using linear head trained on a small amount of OOD data, in contrast to the baseline linear head trained on ID data. The surprising gain of this cheap procedure, even on realistic problems, highlights the importance of isolating the linear head bias when evaluating generalisation performance.
2 SETING UP
we identified three problems in the existing literature that we wish to address in this work. In this section, we will introduce the necessary experimental set-up in further details. In brief, we compare eight ML. algorithms on six datasets using three relevant metrics.
In|section
Algorithms: x3 SSL, x4 AE, x/ SL. We compare seven unsupervised representation learning algorithms against SL, including three SSL algorithms 1) SimCLR (Chen et al.) (2200)). 2) SimSiam
(Chen and He, 2021). and 3) BYOL (Grill et al. 2020y; and four AE algorithms 1) Autoencoder (Rumelhart et al. 1985). 2) Variational Autoencoder (VAE) (Kingma and Welling 2014), 3) VAE
(Higgins et al. (017) and 4) Importance Weighted Autoencoder (IWAE) (Burda et 20.6)) These popular methods in SSL and latent generative models have not yet been systematically evaluated under distribution shift tasks prior to our work. We compare the performance of these models against a standard supervised learning (SL) algorithm used as a representation learning model.
Datasets: x2 synthetic. x2 realistic, x2 controllable shift. We evaluate our models on two synthetic datasets, namely MNIST-CIFAR (Shah et al. (2020); seefsection 3.1. and CdSprites (Shi et al. (2022) :
see Section 3.2. well as realistic datasets from WILDS (Koh et al. 2021): Camelyon
and FMoW (see section 3.2.T. However, as mentioned in (section 1.1 both the synthetic and the realistic datasets have their own drawbacks. To further understand the models' performance and draw conclusions that are generalisable, we also provide framework for creating controllable shift datasets from realistic datasets like those in WILDS, by subsampling the data introduce spurious correlations between the domain and label information in the training set. Changing this correlation varies the degree of distribution shift between the (ID) train and (OOD) test split, which allows us to analyse the models' performance more effectively under realistic, yet controllable, distribution shift. We refer to this controllable shift versions of the two datasets Camelyon17-CC and FMoW-CS, and provide further details the datasets in scccionn 3.2.2
Evaluation: 3 metrics. Before discussing our proposed metrics, we first define some necessary notations. We separate model trained to perform a classification task into two parts, namely, 1) backbone f. denoting the part of the model that generates representations from the data, and 2) final linear head c, which takes the representations from f and outputs the final prediction. Further, refer to the final linear head trained on representations from the ID train set as c, and that trained on representations from the OOD test set co Since the backbone f is always trained the II)
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train set, do not make any notation distinction its training distribution. We also denote the accuracy of f and c on the ID test data as ac,, c), and on the OOD test data as acco c).
As noted in section 1.1 report the OOD accuracy of the algorithms using linear heads trained on OOD data (instead of those trained on ID data as per standard practice), i.c. afc,(f.cc) This is necessary to disentangle the bias of the linear head from that of the representations. To highlight the importance of this treatment in isolating the generalisability of the representation learning algorithm from the that of the linear head, we also define the linear head bias. It the difference between the OOD test accuracy evaluated by OOD linear head and that evaluated by the ID linear head, i.e.
af co) (f...f.c.).
(1)
In related work, TTori et al. (020) proposed to evaluate the effective robustness of OOD generalisa- tion defined (C, aCc. ci), which quantifies the drop in performance (e.g. accuracy)
when evaluating the model on OOD test set vs. ID test set. A small p desirable, as it indicates that the performance of the model is relatively insensitive to distribution shiff However, note that simple decomposition of effective robustness (p) shows a hidden linear head bias (b) term acc; ()) -cco cz) = acc;(J, .4) (c,,(J,es) - accolJ, (a) + accolS,co)
effective robusiness
p
acco co) acc, (f. c.) acc, c.) (f,
(2)
lincar head bins
shift sensitivity
Thus, we remove the effect of the linear head bias by subtracting b from p and reporting the last term in inleq. (2) We refer to this as shift sensitivity:
b. Alternatively, it is the difference between the OOD accuracy using linear head trained on OOD data, and accuracy using linear head trained on ID data. Larger marks higher sensitivity of f to distribution shift, which is, possibly, dangerous for the deployment of such models. In summary, for each experiment we report the following three metrics: OOD linear head accuracy acc, co), linear head bias b and shift sensitivity s.
3 EXPERIMENTAL RESULTS
We perform a hyperparameter search on learning rate, scheduler, optimiser, representation size, etc. for each model. We use the standard SSL augmentations proposed in He et al. (2020); Chen al. (2020b for all models to ensure fair comparison. See appendix B for details.
3.1 SYNTHETIC DISTRIBUTION SHIFT
In this section, we evaluate the performance of SL, SSL and AE algorithms on synthetic distribution shift tasks, utilising the MNIST-CIFAR dataset (Shah et al.) (020) and the CdSprites dataset (Shi cet al. 2022). All results are averaged over 5 random seeds.
3.1.1 MNIST-CIFAR
Finding:
Under this extreme distribution shift setting, SSL and AE significantly outperform SL. The OOD accuracy of SSL and AE can be notably improved by retraining the linear head on OOD data, however the OOD accuracy of SL. remains low even with the OOD-trained linear head.
The MNIST-CIFAR dataset consists of concatenations of images from two classes of MNIST and CIFAR-I0. In each concatenated image, the classes of the two datasets are either correlated or uncorrelated depending on the split as discussed below (See fig.. MNIST-CIFAR for an example):
Correlation between MNIST and CIFAR-10 labels is one. Each image belongs to one of the two classes: 1) MNIST "0" and CIFAR-10 10 "aut le", and 2) MNIST "1 and CIFAR-10 10 "plane" (Figure top row);
ID train, test:
OOD train, test: Zero correlation between MNIST and CIFAR-10 labels, images from the two classes are randomly paired (Figure bottom row).
Since the MNIST features are much simpler than the CIFAR features, a model trained on the ID train set can use MNIST only predict the label, even though the CIFAR images are just as predictive
We negate the original definition of effective robustness from Taori al. 2020) for ease of understanding.
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Table I: Evaluations on the MNIST-CIFAR dataset. We report accuracy on MNIST and CIFAR trained using OOD linear head (f, co)), linear head bias (b) and shift sensitivity (s).
MNIST (%)
CIFAR (%)
Regime Method
(cc.(f, c.)
8
b
aoc, co) f
8 4
AE
99.9 (+
0.0 (#1e2)
0.0 (=2--)
81.1 (#1:00)
18.8 (=1e-0)
30.2 (=/exo)
VAE
99.8 (#/+-))
-0.1 (#+-3)
(=te4)
79.7 (t4we))
20.2 (=3--0)
29.2 (=66-0)
AE
TWAE
99.8 (#:9e-))
0.0 (#444)
0.1 (=5-a)
80.8 (+:2=0)
19.0 (=:+-))
30,0 (#:4--)
B-VAE
99.8 (+:2-2)
0.0 (#44-2)
-0.1 (=3e2)
78.0 (#:3+w0)
21.8 (=44-0)
28.0 (=:4--0)
AE average
99.8 (+.ee)
0.0 (#2-2)
0.7 (=
79.9 (#:rw0)
20.0 (=---))
29.3 (1:4-0)
SimCLR
99.7 (1:r-22
0.2 (atee)
-0.2 (2:61)
85.8 (#ir=))
14.1 (=:2-0)
35.5 (=/e-0)
SSL
SimSiam
99.8 (122-1)
0.1 (aie-1)
(199-2)
87.8 (1i2ee))
12.1 (a2e-0)
35.6 (1ife-0)
BYOL
99.8 (1)4e2)
0.0 (aze2)
(=
84.8 (=9e-1)
15.0 (=ze-0)
33.2 (=1e-00
SSL average
99.8 (1:8-2)
0.7 (35e3)
0.2 (23e-))
86./ (=3ew0)
13.7 (13e=a)
34.8 (2:4--)
SL
Supervised
97.7 (19e-1
1.4 (=7e-0)
-0.3 (1tee0)
51.5 (1it+))
47.6 (s.c-0)
0.8 (1.%
Shah et al. 2020). This results in poor performance when predicting the CIFAR label on the OOD test set, where there is no correlation between the MNIST and CIFAR labels.
We train a CNN backbone on the ID train set using the eight SL, SSL and AE algorithms listed in section 2. At test time, we freeze the backbone and train two linear heads on ID train and OOD train set respectively, and evaluate their performance on the ID and OOD test set to compute 1) OOD linear head accuracy acc, (f, Co), 2) shift sensitivity s and, 3) linear head bias b. See results table
We observe that all models achieve near perfect performance when predicting the MNIST label on OOD test set, all with low shift sensitivity and small linear head bias. However, when predicting the labels of the more complex CIFAR images, unsupervised algorithms have a clear advantage over the supervised one: SSL achieves the highest OOD accuracy at 86.1%, followed by AE at 79.9% and SL at 51.5% (near random). The shift sensitivity s of the three objectives follow similar trend, with SSL and AE scoring significantly lower than SL. This indicates that unsupervised representations are significantly less sensitive to distribution shift compared to those from SL, with the latter suffering a drop as large 47.6%. Interestingly, the classifier head bias b for SSL and AE are relatively high (around 30%), and is very low for SL (0.8%), indicating that the representations learned from SL is intrinsically un-robust distribution shift. That is, while there exist (linearly separable) CIFAR features in the representations of SSL and AE that can be extracted using a linear head trained on un-biased (OOD) data, these features are absent from the representations of SL.
3.1.2 CDSPRITES
Finding: Similar to MNIST-CIFAR, under extreme distribution shift, SSL and AE are better than SL: when the shift is less extreme, SSL and SL achieve comparably strong OOD generalisation performance while AE's performance is much weaker.
CdSprites is colored variant of the popular dSprites dataset (Matheyy al. 2017). which consists of images of 2D sprites that are procedurally generated from multiple latent factors. The CdSprites dataset induces spurious correlation between the color and shape of the sprites, by coloring the sprites conditioned on the shape following a controllable correlation coefficient ria. Seeffig. 1 for an example: when rid 1 color is completely dependent on shape (top row, oval-purple, heart-cyan, square-white), and when rid 0, color and shape are randomly matched (bottom row).
Shi et al. 22022) observes that when rid is high, SL model tend to use color only predict the label while ignoring shape features due to the texture bias of CNN (Geirhos et al. 2019: Brendel and Bethge 2019) First, we consider the setting of extreme distribution shift similar to MNIST-CIFAR by setting Fiu in the ID train and test splits. In the OOD train and test splits, the correlation coefficient set to zero to investigate how well the model learns both the shape and the color features. Table 2 reports the three metrics of interest using the same evaluation protocol as before.
Similar to MNIST-CIFAR, we observe that all models achieve near perfect performance when pre- dicting the simpler feature, i.e. color on the OOD test set. However, when predicting shape, the more complex feature on the OOD test set, SSL (and also AES to a lesser extent) is far superior to SL. Ad- ditionally, the shift sensitivity of SSL (and AE to a lesser extent) are much smaller than SL, indicating that SSL/AE models are more robust to extreme distribution shift. The linear head bias also follows showing that representations learned using SL methods are
similar trend as for MNIST-CIFAL inherently not robust to spurious correlations. This is not the case for SSL and AE algorithms where a large linear head bias shows that is the IDD linear heads and not the representations that injects the bias.
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Table 2: Evaluations on the CdSprites dataset with ri = 1.0. We report accuracy for color and shape classifiers trained using OOD linear head (acc, Co)), linear head bias (b) and shift sensitivity (s).
Color classification (%)
Shape classification (%)
Regime
Method
aco, f
+
b
acc,(/.c)) f
+
AE
100.0 (20-=0)
0.0 (=tes))
0.3 (1see))
46.1 (2de-1)
53.9 (1oe-1)
12.7 (2see1)
AE
VAB
99.7 (+:+-1)
0.3 (=3ed)
-0.3 (#tw))
52.4 (=2m-0
47.6 (#2440)
18.9 (#344))
IWAE
100.0 (20+-0)
0.0 (=2m3)
0.4 (25-1)
58.9 (:2m-0)
41.1 (130s))
25.6 (12700))
AE average
99.9 (19--r)
0.7 (ase-a)
0,7 (1:9-1)
52.5 (122-0)
47.5 (120s0)
19.7 (2:2e0))
SimCLR
100.0 (2)eeo)
0.0 (á:ceo)
0.0 (+
87.8 (#35-))
12.2 (3:5e
54.5 (1:5-1)
SSL
SimSiam
100.0 (=)++0)
0.0 (#0ceo)
0.1 (+te-)
69.2 (=2x-0)
30.8 (#2e10)
35.6 (#2+10)
BYOL
100.0 (10=+0)
0.0 (10ev0)
0.0 (20010)
91.1 (1:4e-0)
8,9 (1:4-0)
57.9 (1:4010
SSL average
100.0 (#0ev0)
0.0 (10cv0)
(133-2)
82.7 (12:10)
17.3 (=2c10)
49.3 (=dee00
SL
Supervised 100.0 (#0+0)
0.0 (#0+e0)
(+:+-2)
44.0 (+7-1)
56.0 (+7-1)
10.7 (#7e.1
Controllable distribution shift We extend this experiment to probe the performance of these algorithms under varying degrees of distribution shifts. We generate three versions of the CdSprites dataset with three different correlation coefficients ria E {0, 0.5, 1} of the ID train set. As before, the correlation coefficient of the OOD split is set zeroThe rest of the experimental protocol stays the same. The OOD test accuracy and the shift sensitivity for varying Iw is plotted in fig. and a detailed breakdown of results is available in inlapendix A]
shows that despite increasing distribution shift between the ID and OOD splits (with increasing r'a) the OOD performance of SSL and AE does not suffer. However, the OOD accuracy of SL. plummets and its shift sensitivity explodes at ria = 1. Interestingly, SSL maintains a high OOD test accuracy regardless of the level of distribution shift: when rid < its performance is on par with SL, and when the distribution shift becomes extreme with rid = 1 it significantly outperforms SL both in terms of accuracy and shift sensitivity. In comparison, AE models' accuracy lingers around 50% with increasingly higher shift sensitivity as ria increases. However, under extreme distribution shift with Tid = 1 still performs better than SL, with slightly higher OOD accuracy and lower shift sensitivity.
Figure 3
3.2 REAL-WORLD DISTRIBUTION SHIFT
In this section we investigate the performance of different objectives on real-world distribution shift tasks. We use two datasets from WILDS (Koh et al. 202T): 1) Camelyon17, 17, which contains tissue scans acquired from different hospitals, and the task to determine a given patch contains breast cancer tissue; and 2) FMoW, which features satellite images of landscapes on five different continents, with the classification target as the type of infrastructure. See examples in Figuur 1] Following the guidelines from WILDS benchmark, we perform 10 random seed runs for all Camelyon17 17 experiment and 3 random seed runs for FMoW. The error margin in Figure 3 represent standard deviation.
3.2.1 ORIGINAL WILDS DATASETS
Findings:
SLis is significantly more sensitive distribution shift than SSL and AE; representations from SSL obtain higher OOD accuracy than SL on Camelyon17 17 but lower on FMoW. AE is consistently the least sensitive to distribution shift though it has the lowest accuracy. The performance of all models significantly improves by retraining the linear head on a small amount of OOD data.
The original Camelyon17 and FMoW dataset from WILDS benchmark both contains the following three splits: ID train, OOD validation and OOD test. We further create five splits specified as follows:
ID train, test:
Contains 90% and 10% of the original ID train split, respectively; OOD train, test: Contains 10% and 90% of the original OOD test split, respectively; OOD validation: Same as the original OOD validation split.
Following WILDS, we use OOD validation set to perform early stopping and choose hyperparameters:
we also use DenseNet- 121 (Huang et al., (017) as the backbone for all models. We follow similar evaluation protocol as previous experiments, and in addition adopt 10-fold cross-validatio for the OOD train and test set. See results in Tables 3 ]and]]] where following WILDS, we report performance on Camelyon17 using standard average accuracy and on FMoW using worst-group accuracy.
One immediate observation is that in contrast to our previous experiments on synthetic datasets, SL's OOD accuracy is much higher in comparison performing model on FMoW with 35.6% worst-group accuracy on OOD test set; its OOD accuracy the lowest Camelyon17, 17, however it is only 3% worse than the highest accuracy achieved by SSL
realistic distribution shift tasks: it is the best
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Table 3: Evaluations on test set of Camelyon17, all metrics computed using average accuracy.
Table 4: Evaluations on test set of FMoW, all
metrics computed using worst-group accuracy.
Metries (%)
Metrics (%)
Regime
Method
Rogime
Method
acc,[/.co] 1
6
b
84.4 (1
-0.6 (1
(1
AE
26.9 (Lw-9
(1
5.8 (L
VAE TWAE
88.1 (=2v10)
0.5 (#22e9)
39.0 (=2++0)
VAE
21,7 (=6-2)
4,7 (stte)
(=0-)))))
AE
88.1 (L)mw))
-0.9 (1
39.1 (1ime))
AB
IWAE
20.9 (L.wa)
(1200)
7.8 (11+3)
3 VAE
87.1 (24m00)
0.2 (14400)
36.0 (1o==0)
3- B-VEE
21.7 (szed)
3.4 (1s-3)
(1
AE average
86.9 (17mw))
.0.2 (130w0)
31.7 (1 frwa)
average
(L.
(12m))
(136))))
SimCLR
92.7 (=2v10)
0.4 (+11119)
8.3 (+1+10)
SinCLR
29.9 (=
10.7 (=te-)
(+7--)
SSL
SimSlam
86.7 (=teve)
3.1 (#:te09)
7.9 (+F++0)
SSL
SimSiam
27.8 (=2-2)
4.6 (.1-1)
6.3 (=2+3)
BYOL
89.9 (=te10)
1.4 (#11119)
10.3 (=2r10)
BYOL
31.3 (el+3)
12.1 (+7e-)
7.9 (+162)
SSL average
89.8 (=3ee0)
7.6 (37740)
(27-v0)
SSL. average
(22-0)
(34-3)
(.3
SL
Supervised
86.8 (=2xx0)
3.5 (#:2449
7.4 (#3++0)
SL
Supervised
35.6 (c7ea))
37.7 (34033 (=9v-)
(89.8%). This highlights the need to study realistic datasets along with synthetic ones. Nonetheless, we find that SSL is still the best performing method on Camelyon17 17 and achieves competitive performance on FMoW with accuracy 29.6% - despite learning without labels! AE has much lower OOD accuracy on FMoW compared to the other two methods:
believe this is due to its reconstruction-basel objective wasting modelling capacity on high frequency details, phenomenon frequently observed in prior work (Bao al. 2021 Ramesh al.. 2021). Note that the standard deviation for all three methods are quite high for Camelyon172 7: this is a known property of the dataset and similar pattern observed across most methods on WILDS benchmark (Koh et al. 2021).
In terms of shift sensitivity, unsupervised objectives including SSL and AE consistently outperforms SL- this stands out the most on FMoW, where the shift sensitivity of SSL and AE are 9.1% and 5.0% respectively, while SL is as high as 37.7%. This observation further validates our previous finding on synthetic datasets, that SSL and AE's ID accuracy is a relatively reliable indication of their generalisation performance, while SL can undergo huge performance drop under distribution shift, which can be dangerous for the deployment of such models. We highlight that, in sensitive application domains, low shift sensitivity is important criterion as it implies that the model's s performance will remain consistent when the distribution shifts. Another interesting observation here is that for all objectives on both datasets, the classifier bias b is consistently high. This indicates the bias of the linear classification head plays a significant role even for real world distribution shifts, and that it is possible to mitigate this effect by training the linear head using small amount of OOD data (in this case 10% of the original OOD test set).
3.2.2 WILDS DATASETS WITH CONTROLLABLE SHIFT
Findings: SL's OOD accuracy drops as more the distribution shift becomes more challenging, with SSL being the best performing model when the distribution shift is the most extreme. The shift sensitivity of SSL and AE are consistently lower than SL regardless of the level of shift.
To examine models' generalisation performance under different levels of distribution shift, we create versions of these realistic datasets with controllable shifts, which we name Camelyon17-cC 17-CS and FMoW-CS. Specifically, we subsample the ID train set of these datasets to artificially create spurious correlation between the domain and label. For instance, given dataset with domain A, B and label 0, 1, to create a version of the dataset where the spurious correlation is 1 we would sample only examples with label 0 from domain A and label 1 from domain B. See Appendix C for further details.
Similar to CdSprites, we create three versions of both of these datasets with the spurious correlation coefficient rid {0, 0.5, 1} in ID (train and test) sets. The OOD train, test and validation set remains unchanged Using identical experimental setup as in (section 3.2.1 we report the results for Camelyon17-CS and FMoW-CS in Figure 3 with detailed numerical results in Appendix A.2
For both datasets, the OOD test accuracy of all models drop as the spurious correlation ria increases (top row in Figure 3). However, this drop is the far more obvious in SL than in SSL and AE: when Tia = 1, SL's accuracy is 10% lower than SSL on Camelyon17 and 2% lower on FMoW - a significant drop from its original 3% lag on Camelyon17 and 5% lead on FMoW. This demonstrates that SL. is less capable of dealing with more challenging distribution shift settings compared to SSL and AE, In terms of shift sensitivity (bottom row, fig. 3). SL's remains the highest regardless of ria: curiously, we see a decrease in SL's shift sensitivity as ria increases in FMoW-CS, however this has more to do with the ID test set accuracy decreasing due to the subsampling of the dataset.
Note that even when rsa 0, distribution shift hetween the ID and OOD splits exists, as the spurious correlation is not the only source of the distribution shift.
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Test accuracy (1)
Test accurany
80
Test accuracy
30
80
SL
70
20
0.0
0.5
1.0
0.5
1.0
60
10
Fi
Shift Sunskivity (1)
20
Shift Sensliviy
SNR Sanstvitty
-0
SSL AE
5t
10
20
20
0.0
0.0
0.5
1.0
1.0
Fiz
(a) Camelyon17-CS 17-CS
(b) FMoW-CS
(c) CdSprites
Evaluations on Camelyon Mamellyon1--CS 7-CS, FMoW-CS, and CdSprites with ria E 00,0.5 1.0.. We report OOD test accuracy using OOD-trained linear head (acc, (f,, co)) and shift sensitivity (s). Blue lines are results averaged over AE models, green lines are SSL models and grey is SL.
Figure 3:
4 RELATED WORK
While we are the first to systematically evaluate the OOD generalisation performance of unsupervised learning algorithms, there other insightful work that considers the robustness to distribution shift of other existing, non-specialised methods/techniques For instance, Liu et al. (2022) studies the impact of different pre-training set-ups distribution shift robustness, including dataset, objective and data augmentation. Ghosal et al. (2022) focuses on architecture, and found that Vision Transformers are more robust to spurious correlations than ConvNets when using larger models and are given more train- ing data; further, Liu et al. (202T) found that SSL is more robust to data imbalance. AAziz et al. (2022) also performed extensive studies on the generalisation performance of SSL algorithms on medical data. Interestingly, [Robinson [Robinnsonn et al. (2021) also investigates the robustness of contrastive-SSL. methods against extreme spurious correlation (i.e.simplicity bias). However, their work did not consider the linear head bias found in (Kirichenko et al. 2022 Kang et al. (220)) and led to opposing conclusions. In contrast, our work investigates the distribution shift performance of unsupervised algorithms, with experiments on both synthetic and realistic settings that go beyond the data imbalance regime. By iso- lating the linear head bias in our experiments, we find that unsupervised, especially SSL-llerned repre- sentations, achieves similar if not better generalisation performance than SL under a wide range of dis- tribution shift settings. See Appendix Difor a more detailed discussion on distribution shift problems.
5 CONCLUSION AND FUTURE WORK
In this paper, we investigate the robustness of both unsupervised (AE, SSL) and supervised (SL) objectives for distribution shift. Through extensive and principled experiments on both synthetic and realistic distribution shift tasks, we find unsupervised representation learning algorithms to consistently outperform SL when the distribution shift is extreme. In addition, we see that SSL's OOD accuracy is comparable, if not better to SL in all experiments. This is particularly crucial, as most work studying distribution shift for images are developed in the SL regime. We hope that these results inspire more future work on unsupervised/semissuppe superviisd representation learning methods for OOD generalisation. Another important finding is that unsupervised models' performance remains relatively stable under distribution shift. This is especially crucial for the real-world application of these machine learning systems, as this indicates that the ID performance of SSL/AE algorithms are a more reliable indicator of how they would perform different environments at deployment, while that of SL is not. It is also worth noting that while models trained with AE objectives are consistently the least sensitive to distribution shift on realistic datasets, their OOD performance can be low especially when presented with complex data (such as FMoW). This is consistent to the observation in prior work that these models can waste modelling capacity on high frequency details, and suggests that one should be careful about employing AE algorithms on large scale, complex tasks. Finally, key contribution of this work is establishing the existence of linear head bias even for realistic distribution shift problems. We believe that using an OOD-traines linear head is necessary be able to make comparisons between various algorithms irrespective of the final downstream task, and on the other hand, more efforts in the field of distribution shift could be devoted into balanncing the linear layer.
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ACKNOWLEDGEMENTS
YS and PHST were supported by the UKRI grant: Turing AI Fellowship EP/W002981/1 and EPSRC/MURI grant: EP/N019474/1. We would also like thank the Royal Academy of Engineering and FiveAI. YS was additionally supported by Remarkdip through their PhD Scholarship Programme. ID was supported by the SNSF grant #200021 1 188466, AS was partially supported by the ETH Al Center postdoctoral fellowship. Special thanks to Alain Ryser for suggesting the design of controllable versions of the WILDS dataset, and Josh Dillon for helpful suggestions in the early stage of this project.
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Test accuracy (1)
Shift Sunsitivity $141
Linsar head blas
AE
AE
IWAE SIMCLRR
IAAE SIMCLR BYOL SimSiam
BVOOL
SimStam
SL
AE
SmmLk
SL
WAE
BYOL
random
5imSiom
(a) acco co) (%)
(b) Shift sensitivity 8 ((%).
(c) Linear head bias b (%).
Figure 4: Evaluations on the CdSprites dataset with ria E {0.25, 0.5, 0.75, 1.03. We report shape classification accuracy using OOD-trained linear head (acc. C. shift sensitivity 8, and linear head bias b. Results are shown for individual models from the class of AE (blue), SSL (green), and SL (grey) algorithms. The black horizontal line denotes the random baseline (33.3% for three classes).
A ADDITIONAL EXPERIMENTAL RESULTS
A.1 CDSPRITES
In addition results in table 2 where
dataset with perfectly correlated features (ria = 1) to train the backbones, in fig. 4 we vary rid to analyse the effect of imperfectly correlated features. Notably, with imperfect correlation (Ni 1), the OOD linear heads trained on top of the SL and SSL backbones perform perfectly. For the AE, we observe that the performance of the OOD linear head does not depend on the correlation ria in the data used train the backbones. Our results suggest that with imperfect correlation between features, SL and SSL models learn a linearly separable representation of the features, whereas AE does not.
In lig. 5] we provide an ablation where we also vary Food. the correlation in the data used to train and evaluate the linear head. Figures 5bd corroborate our results that SSL performs on par with SL for 1 and strictly better when ria = I. For the AE (Figure 5a we observe an interesting pattern where the performance of the OOD linear head depends on the OOD correlation Foods but not on the correlation in the data used to train the backbones. Hence, the ablation corroborates our result that SL and SSL models learn a linearly separable representation of the shape and color features when there is an imperfect correlation between the features, whereas AE does not.
102
100
104
104
10C
1142
102
100
10c
110
102
100
11:0
33.6
033
03.7
13
200
203
383
55
283
-28
-3
64.
-53
3
53.2
523
535
539
31.3
20.3
50.4
369
075
(a) AB
(b) SSL
(c) SL
Figure 5: Correlation coefficient ablation for CdSprites. Shape classification accuracy for the CdSprites experiment with varying correlation of the ID training data (ria. x-axis) and OOD) training and test data (Fond, y-axis). Backbones were trained on data with correlation ria and linear classifiers trained and evaluated on top of the frozen backbones with correlation Tood.
A.2 CAMELYON17- 17-C AND FMOW-C
In this section we report the numerical results for Camelyon17-CC and FMoW-C with Fia = 0.5 (see tables and and ria 1 tseels and
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Table Evaluations on test set of Camelyon C with rid 0.5, all metrics computed using average accuracy.
Table Evaluations on test set of FMo with = 0.5, all metrics computed using worst- group accuracy.
Metrics (9)
Metrics (%)
Regime
Method
Regime Method
acc,[f.ca] f
4
b
802,(f.c.)
#4
AE
80.4 (L
6.0 (12-0)))
19.0 (14re))
AE
23.4 (L))ee)
8.6 (1A-1)
4.2 (L
AE
(:2vs0)
(ttveo)
17.8 (2need)
AE
(16--)
IWAT
87.8 (L))w))
-0.2 (Live))
26.4 (inre))
TWAE
18.5 (1
7.3 (1tre))
2.2 (Liree)
V-V
88.5 (:Svv0)
(ase-z)
19.7 (aneed)
B-VAB
21.4 (22ea)
(1se2)
(bred)
AE average
86.3 (=2010)
1.4 (#tee of
20.7 [+Se10)
AE iveerage
20.5 (+2
6.9 (#S--)
3.0 (+9-J)
SimCLR
84.5 (=2-10)
8.0 (tiee d)
6.6 (#2+10) 0)
SimCLR
29.5 (=9-1)
9.2 (#ie-1)
(+7-1)
SSL
SimSiam
86.1 (=2vx0)
5.7 ((3e-0)
8.3 (#4--0)
SSL
SimSiam
27.9 (12re0)
7,5 (sfeee)
4.6 (t.eee)
BYOL
86.4 (13rw0)
4.5 (12--0)
(14ew0)
BYOL
(L
(12+a0)
SSL average
85.7 (=7mx0)
6.7 (33--0)
7.9 (s3e-))
SSL average
(2.00))))))
8.2 (sfeww)
6.7 (57(e)))))
SL
Supervised
81.5 (=5+10)
13.2 (#3200)
3.4 (#w--0)
SL
Supervised
32.3 (#2.10)
25.1 (#3+e0)
6.0 (#2v.0)
Table 7: Evaluations on test set of Camelyon1 C with ria 1, all metrics computed using aver- age accuracy.
Table 8: Evaluations on test set of FMoW-C with Fid = all metrics computed using worst-group accuracy.
Metries (%)
Metrics (%)
Regime
Metbod
Regime Method
(o.) 1
+
b
ao., 1
8
75.7 (=:es0)
7.3 (22e-o)
(2seed)
AE
10.0 (25--)
(+/v-)
VAE
86.0 (=2v10)
2.7 (tie d)
12.4 (=4e10)
VAE
16.6 (#9-1)
8.6 (=ler0)
2.8 (+a-J)
AE
AE
IWAE
86.1 (=tes0)
(#
(2:6-0)
IWAE
17.2 (a5ed)
(1se-1)
(t5ed)
V-VAE
84.7 (=2v10)
3.8 (tie d)
15.5 (+4e10)
B-VAE
16.7 (=3-1)
7,9 (#4+-1)
3.2 (+4.J)
AE average
83.7 (=te10)
4.7 (3ie-o)
18:0 (SRee0)
AE average
18.3(83))))
8.8 (1707))
3.4 (16-1)
SimCLR
85.8 (=
2.8 (1:4-1)
6.2 (12--))
SimCI R
26.3 (L)to))
7.2 (Eteeo)
SimSiam
82.1 (Livwe)
(1.--))
(14e-))
SimSiam BYOL
(Laee)
(12-1)
(Li-))
BYOL
74.8 (=5vv0)
10.3 (#:2400)
-2.2 (#4440)
27.4 (#2v40)
11.1 (tiee))
6.5 (#240)
SSL average
(L
(10--)
(13sw))
average
(6.9(1
(
(1)e0)
SL
Supervised
73.4 (=5e10)
10.7 (#3te00)
(sSe-0)
SL
Supervised
25.7 (25eo)
12.3 (+2r19)
5,3 (+lero)
B ARCHITECTURE AND HYPERPARAMETERS
In this appendix we list the architecture and hyperparameters used in our experiments. Our code is developed the amazing solo-learn code base (da Costa al. (0022), which is originally developed as a library for SSL algorithms. For all experiments we tollow the standard set of augmentations established in He al. 2020): Chen et al. (020b), including random resize crop, random color jittering, random grayscale, random Gaussian blur, random solorisation and random horizontal flip. An exception is the CdSprites experiment where we remove color jittering, as color classification is one of the tasks we are interested in and color jittering would add noise to the labels. For MNIST-CIFAR, we independently apply random augmentation to MNIST and CIFAR respectively (drawn from the same set of augmentations as detailed above) and then concatenate them to construct training examples.
Please see implementation details for each dataset in the respective subsection.
B.1 MNIST-CIFAR
We use the same hyperparameter search range for models in each category of AE, SSL and SI., as outlined in table 9 The chosen hyperparameters for each model are specified in table 10
In Shah et al. (2020) where MNIST-CIFAR was originally proposed, authors utilised more complex backbone architecture such as DenseNet and MobileNet. However in our experiments, we find that lightweight 4-layer CNN can already achieve very high accuracy on both MNIST and CIFAR. The architecture of the CNN we use can be found in ttble II] Note that for SL and SSL we only use the encoder and for AE we use the decoder as well. The size of base channel and latent dimension L found through hyperparameter search.
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Table 9: Hyperparameter search range for MNIST-CIFAR, including base channel size of CNN (C), learning rate (I:), weight decay (wd.), optimiser (optim.), learning rate scheduler (Ir. scheduler).
wd.
Optim.
Ir. scheduler
AE
[16, 32, 64, 128)
11e-4, Se-4, 1e-3, 3e:3, 1e-2)
[0. le-4]
[Adam, SGD)
[warmup cosine, step, none]
SSL
[16, 64, 128]
uniformly sampled from [0.1, 1]
[0, le-4)
[Aaam, SGD)
[warmup cosine, step, none] [warmup cosine, step, none)
SL
(16, 32, 64, 128]
(le-4, So-4, 1e-3, le-2. 1e-1,
10. le-4)
(Adam, SGD)
Table 10: Chosen hyperparameters for MNIST-CIFAR including latent dimension (T.), base feature size of CNN (C), batch size (B), learning rate (Ir), weight decay (wd.),, optimiser (optim.), learning rate scheduler (Irscheduler).
L
wd.
Optim.
Ir. schoduler
AE
128
16
128
1e-3
0
Adam
warmup cosine
VAE
128
32
128
lc-4
Adam
warmup cosine
IWAE
128
32
128
le-4
0
Adam
step
V-VAR
128
16
128
1e-4
0
Adam
step
SimCLR
128
32
128
6e-1
le-4
SGD
warmup cosine
BYOL
128
64
128
Te-1
0
SGD
warmup cosine
SimSiam
128
128
128
le-5
SGD
warmup cosine
Supervised
128
16
128
le-4
SGD
warmup cosine
Encoder
Input R2X644332
4x4 cony. C stride 2x2 pad 1xl & ReI.U
conv. 20 stride 2x2 pad 1xl ReLU
4x4 conv. 4C strid 2x2 pad 1xl & ReLU
4x1 4C stride 2xl pad Lx0 & ReLU
4x4 conv. L striee pad 0, 4x4 conv. L Stride 1xl pad 0x0
Decoder
Input C RC
pad OxO 4x1 upconv. 4C' stride 2xl pad Ix0 & ReI.U
4x4 upconv. 4C
4x4 upconv. 2C
pad 1xl
4x4 upconv. C. stride 2x2 pad 1x1 & ReLU
upconv. stride 2x2 pud
Sigmoid
Table 11: CNN architecture, MNIST-CIFAR dataset.
B.2 CDSPRITES
We found all models be relatively robust to hyperparameters, as most configurations result in close to perfect shape and color classification accuracy on the ID validation set. The chosen hyperparameters for each model are specified in table 12] We omit 3-VAE from the comparison, as we empirically found that 3 leads to the best performance on the ID validation set and therefore the results for the VAE would be similar to the VAE. We use the same augmentations (random crops and horizontal flips) for all models and use color augmentations in order keep the invariance of the learned representations with respect to color. The encoder and decoder architectures are described in table 13
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Table 14: Hyperparameter search range for Camelyon17, including decoder type, latent dimension
(L), learning rate (Ix), weight decay (wd.), optimiser (optim.), learning rate scheduler (Ir. scheduler).
Devoder type
wd.
Opti..
scheduler
AE SSL
(CNN, MLR ReaNes]
[256, 512, 1024]
[1o4 So.4, le-s, Seid, 1e-2]
[a. To-1
[Adamn, SGI)
(warmap cosine, steg, none]
[256. 512, [024]
[le-4, Se-4, le-3, Se-3, le-2, le-l, Se-1, 11
[0, le-3, le-4, le-S)
[Adam, SCD;
wwarmpp cosine. step, none
SL
1256, 312, 1024]
[1e-4, Se-4, 1o3, 56-3, les, Se-1)
[0. le-41
[Adam, SGD)
warrmap cosine, step, none)
Table 12: Chosen hyperparameters for CdSprites including latent dimension (L), base feature size of CNN (C), batch size (B), learning rate (Ir), weight decay (wcl), optimiser (optim.), learning rate scheduler (Irscheduler).
C
B
Ir.
wd.
Optim.
none
AE
512
64
128
5e-5
le-4
Adam
none
VAE
512
128
5e-5
lc-4
Adam
none
IWAE
512
64
128
5o-5
1c-1
Adam
SimCLR
64
32
64
5e-3
le-5
SGD
warmup cosine
BYOL
64
32
64
5e-1
le-5
SGD
warmuup cusine
SimSiam
64
32
64
8c-2
lc-5
SGD
warmup cosine
Supervised
512
64
128
5e-5
le-4
Adam
nune
Encoder
Input R0064X61
4x4 conv, C stride 2x2 pad Ixl & ReLU
4x4 conv. 2C stride 2x2 pad 1x1 ReLU
4x4 conv, 4C stride 2x2 pad Ixl & ReLU pad
4x4 80
4x4 cOIN. strido pad 0
Decoder
Input R--
4x4 upconv. 8C stride 1xl pad 0x0 ReLU
4x4 upconv. 4C stride 2x2 pad 1xl ReLU
4x4 upconv. 2C' stride 2x2 pad 1x1 ReLU
4x4 upconv. C stridc 2x2 pad Ixl & ReLU
4x4 upconv. stride 2x2 pad
Table 13: CNN architecture, CdSprites dataset.
B.3 CAMELYON17 AND FMoW
For hyperparameters including batch size, epoch and model selection criteria, we follow the same protocol as in WILDS (Koh et al.) (02T): for Camelyon17 we use a batch size of 32, train all models for 10 epochs and select the model that results the highest accuracy on the validation set, and for FMoW the batch size is 32, max epoch is 60 and model selection criteria is worst group accuracy on OOD validation set. For the rest, we use the same hyperparameter search range for models in each category of AE, SSL and SL, as outlined in table 14] The chosen hyperparameters for Camelyon17 17 are specified in Italle 15] and for FMoW in table 16 For Camelyon17-6 and FMoW-C we use these same hyperparameters.
Table 15: Chosen hyperparameters for Camelyon17 7 including latent dimension (I.,, learning rate (Ir.), weight decay (wd.), optimiser (optim.), learning rate scheduler (Ir. scheduler).
Decoder
Ir.
Optim.
Ir. scheduler
AE
ResNet
5c-4
le-5
SGD
warmup cosine none
VAE
MLP
lc-4
Adam
IWAE
MLP
le-4
Adam
none
8-VAE
MLP
lc-4
Adam
none
SimCLR
lc-1
SGD
none
BYOL.
le-1
le-5
SGD
warmup cosine
SimSiam
le-1
le-5
SGD
warmup cusine
Supervised
lc-3
SGD
none
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Table 16:
Chosen hyperparameters for FMoW including latent dimension (L), learning rate (Ir.)
weight decay (wd.), optimiser (optim.), learning rate scheduler (Ir. scheduler).
Decoder
wd.
Optim.
Ir. scheduler
AE
CNN
le-1
le-4
SGD
none
VAE
MLP
le-4
step
IWAE
MLP
lc-6
le44
Adam
step
3-VAE
MLP
lc-6
le-4
Adam
step
SimCLR
5c-4
1c-3
SGD
BYOL
le-2
lc-4
SGD
step
SimSiam
5c-4
SGD
step
Supervised
le-4
Adam
step
We follow Koh et al. (2021) and use DenseNet121 (Huang et al. 2017) as backbone architecture. For the decoder of the AE models, we perform hyperparameter search between three architectures:
a CNN (see table 17), simple 3-layer MLP (see table 18) and a ResNet-like decoder with skip connections (see table 19).
CNN, Decoder
Inpul
R
4x4 8C stride 2x2 pad 1xl ReL.U
4x4 upconv. SC' stride 2x2 pad 0x0 ReLU
4x4 upceav. 4C stride 2x2 pad 1xl ReLU pad
4x4 upconv. 2C stride
ReLU
4x4 upceav. stride 2x2 pad 1xl & ReLU Sigmoid
4x4 upconv. stride 2x2 pad
Table 17: CNN architecture, Camelyon17 dataset.
MLP,, Decuder
Inpat E Rd fo. 27 ReLU fc. 4T & ReLU 3-96*96
Table 18: MLP architecture, Camelyon17 dataset.
ResNet, Decoder
Input E R
3x3 conv. 16C stride 1xl pud 1xl
16C stride pad Ixl
x2 upsample
SC stride pad 1x1
3x3 conv. 8C stride Ixl pad lxl upsample
3x3 conv. 8C' stride Ixl pad lxl
3x3 SC stride Ixll pad Ixl
3x3 conv. 3 stride 1xl pad Ixl
Table 19: ResNet decoder architecture, Camelyon 17 dataset.
C CONSTRUCTING CAMELYON17-CS AND FMOW-CS
We subsample Camelyon17 and FMoW dataset to create varying degree of spurious correlation between the domain and label information. We refer to these datasets as Camelyon and FMoW-CS, To construct such datasets, we first find some domain-label pairing in each dataset, such that if we sample the dataset according to this pairing, the population of each class with respect to the total number of examples in the dataset remains relatively stable. The Tı = versions of both Camelyon 17-CS and FMoW-CS can be acquired by simply subsampling the dataset following the domain label pairing; to ensure fairness in comparison, when constructing the ria E {0, 0.53 versions of these datasets, first mix in anti-bias samples (i.e. samples that not in the domain-label
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Linea head bias
10.0
Linear head blas b
SSL
Af
bios
7.5
AE
SSL
20
5.0
2.5
AE
%
0.0
0.5
1.0
fd
Figure 6: Linear head bias controllable shift datasets
pairing) to change the spurious correlation, and then subsample the dataset such that the size of the dataset is the same as the Tid = 1 version.
The domain-label pairing of Camelyon can be found in table 20 and FMoW-CS in table 21
Linear head bias We also plot the linear head bias for the experiments conducted on Camelyon CS, FMoW-CS, and CdSprites in Figure 6 The experimental protocol follows that from Figure
Table 20: Domain- label pairing for Camelyon 7-CS.
Domain (hospital)
Label
Hospital 1,
Benign
Hospital 3
Malignant
Table 21: Domain-label pairing for FMoW-CS.
Domain (region)
Label
Military facility, multi-unit residential, tunnel opening, wind farm, toll booth, road bridge, oil or facility, helipad, nuclear powerplant, police station, port
Asia
Smokestack, har, waste disposal, hospital, water treatment facility, amusement park, fire station, fountain, construction site, shipyard, solar farm, space facility
Europe
Place of worship, crop field, dam, tower, runway, airport, electric substation, flooded road, border checkpoint, prison, urchueolugical sile, factory or powerplant, impoverished settlement, lake or pond
Africa
Recreational facility, swimming pool, educational institution. stadium, golf course, office building. interchange. car dealership. railway bridge. storage tank, surface mine. 2oo
Americas
Single-unit residential, parking lot or garage, track, park, ground transportation station, shopping mall. airport terminal, airport hangar. lighthouse, gas station, aquaculture. burial site. debris rubble
Oceania
D OTHER RELATED WORK
Explicit, extreme distribution shift Refers when the features that caused distribution shift is explicit, known, controllable, and in some cases, extreme (c.g. MNIST-CIFAR CdSprites). This type of settings are popular works that investigate simplicity bias (Shah al. 2020). dataset bias (Torralba and Efros 2011) and shortcut learning (Geirhos et al. allows for users to easily adjust the level distribution shift between train and test set. Various specialised methods that either mitigate address these problems under the supervised learning regime have been proposed, including Teney et al. (2022) that proposes to find shortcut solutions by ensembles, Luo al. (2021) that avoids shortcut learning by extracting foreground objects for representation learning only, as well as Torralba and Efros (201T); (0mm):[Kim Kim et al. (2019); Le Bras et al. (2020) that re-sample the dataset reduce the spurious correlation.
et al. 2019), as
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Importantly Kirichenko et al. (2022) Kang et al. (2020) shows that this extreme simplicity bias be mitigated in some cases by retraining the final linear layer. This a game changer, as it for the first time decouples the bias of the linear head from that of the main representation learning model. Interestingly, |Robinson et al. (021) also investigates the robustness of contrastive-SSI. methods against simplicity bias. However, without training the linear head OOI) data, their finding is opposite to ours that SSL methods are not able to avoid shortcut solutions.
Implicit, subtle distribution shift This type of problem is commonly seen in realistic distribution shift datasets (such as WILDS) and are often studied in Domain generalisation (DG). In this regime, the training data are sampled from multiple domains, while data from new, unseen target domain is used as test set. Note that here omitted the discussion domain adaptation (DA), in DA models typically have access to unlabelled data from the target domain, which different from the settings we consider in this work.
There are mainly two lines of work in DG, namely 1) Distributional Robustness approaches (DRO), which minimises the worst group accuracy to address covariate shift (Gretton et al. 2009 b) and subpopulation shift (Sagawa et al. 2020 Hu et al. 2018); 2) Domain invariance, which consists of methods that directly learn representations that invariant across domains (Ben-David et al. 2010)
Ganin et al., 20166; Wang et al. 2019), encourage the alignment of gradients from different domains (Koyama and Yamaguchi| 2021 Lopez-Paz and Ranzato 2017, [hi et al. 2022), or optimise for representations that result in the same optimal classifter for different domains (Arjovsky et al.) 2019). Apart from these supervised learning methods, the recent advancement of SSL has also inspired works in unsupervised domain generalisation (Zhang et al. 2022 Harary et al. (002)). While all these methods achieved impressive performance, we note that they are all specially designed for DG with the majority of the methods relying on domain information and label information. In contrast, our work studies how existing standard representation learning methods such as SSL and AE performs on DG tasks, with none of the methods relying on human annotations.
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Reviews:
[{"review_id": "oyIWxTZxM6Y", "reviewer": "Reviewer_ekJ8", "summary": "", "questions": "", "limitations": "", "rating": 5, "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": "", "summary_of_the_paper": "Studying the robustness of learned representations in unsupervised learning such as self-supervised learning or auto encoders as opposed to the traditional supervised learning settings when there exists distribution shifts in data.\n\n", "summary_of_the_review": "Please refer to the strengths and weaknesses. IMO, the weaknesses out-weight the strengths in this paper.", "strength_and_weaknesses": "# Pros:\n\n- The paper is well-written, easy to understand and follow along.\n\n- The explorations to identify the significance of representations with unsupervised learning in a distribution shift are interesting.\n\n- Literature is covered adequately.\n\n# Cons:\n\n\n- Significance of the following contributions highlighted is questionable:\n  - Systematically evaluate SSL and AE on distribution shift tasks.\n  - The proposed solution in the paper is what everyone uses and is a standard practice, how is it different from what already exists or known to the community\n  - Controllable-Shift (CS) datasets, are they used only during evaluation or they used in training also?\n  - OOD linear head. Again, fine-tuning the pre-trained model on a small set of left out data is also a known practice then what is your contribution here to highlight this as a stand out contribution?\n\n- Figure 2 is referenced first and Figure 2 later, better move Figure 1 to the end of page 3 or page 4.\n\n- Figure 1 also warrants focussed attention of the reader to understand forcing the reader to spend a few extra minutes. Not an ideal presentation style.\n\n- The subsampling used to prepare the CS datasets is not entirely clear. How can you guarantee that the samples picked result in spurious correlations? Are the real world sets by default contains spurious correlations in the entire dataset so that you can pick any subsample of images randomly to mimic this behavior? A small algorithm on CS dataset prep in appendix also could be of value.\n\n- How did you train CNN back bone? No details on hyper params used, network architecture, number of epochs. As per the loss functions used, those eight SL, AE and SSL have the standard ones so that is fine. Also, how long did you fine-tune the pre-trained backbone (f) on the held-out OOD data?\n\n- Another question, why a simple CNN why not the state-of-the-art SSL methods such as contrastive learning or the more recent CNNs architectures such as ResNets, etc.? Will the results hold true with more advanced networks? This question remains more true given the performance of the unsupervised methods on real world datasets, the results in 3.2.1\n\n\n ### Minor comments: \n - “This is becaues, …” should be “This is because,...”\n - “under distribution shif, …” should be “under distribution shift, …”\n\n  - Too many forward references, this is not a thesis introduction chapter, but a research paper, please minimize the number of forward references.\n", "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": "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": "NRfKSzIPvJq", "reviewer": "Reviewer_JB4R", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "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": "", "summary_of_the_paper": "This paper benchmarks self-supervised learning (SSL) techniques and auto-encoder (AE) techniques under synthetic and realistic distribution shifts. The main conclusion is that the SSL and AE methods are less sensitive to distribution shifts. Also, the linear classification head is the main source of the spurious bias. Finally, the paper also develops ways to create different levels of shifts in real-world shifts datasets.", "summary_of_the_review": "It will be nice if the scale of the research is a bit larger than the current one. By scale, I mean the coverage of different SSL methods and AE methods, the scale of the dataset, and the architecture. Because what is still unknown to the community is the limit of scaling up in using SSL or AE in domain adaptation/generalization/distribution shifts. ", "strength_and_weaknesses": "Strength:\n\nThe empirical contribution should be appreciated by the community, as it is something people have been discussing for a long time. It is good to see a concrete evaluation paper.\n\nThis paper is very clearly written. \n\nWeakness:\n\nThe fact that this paper only discusses image data may limit its impact. To be honest, I think the conclusion is sort of known to the community already. Pretraining in the source domain and fine-tuning the linear layers in the target domain has been shown to be an effective transfer learning method. So I feel what is more interesting in the direction is the large language models or vision-transformers. \n\nOn the other hand, I think the elephant in the room is still unknown: To what extent can we really rely on the pretrained representations to do the transfer and adaptation? What is the limit?\n\nThe way we set up the problem may also have some impact on the results. For example, the way we \"control\" the shift in the images may not be generalizable to real-world shifts in, for example, fairness problems/subpopulation shifts, where we cannot easily create shifts in a meaningful way. So, I also suggest adding discussions on the limitations of the work. \n\nIn table 4, why the SL accuracy is much higher?\n\n", "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": "6S3h8zQuP7", "reviewer": "Reviewer_xV8K", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "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": "", "summary_of_the_paper": "The submission provides an extensive empirical study on supervised (SL), unsupervised (autoencoder, AE), and self-supervised (SSL) representation learning algorithms in a distribution shift scenario. The key contribution is comparing these algorithms when the representation is learned on the source task while the classifier is learned on the target task. The findings are that (1) SL is more sensitive to distribution shift than SSL and AE, and (2) there is a remarkable difference between the performance of classifier heads trained on source and target distributions.", "summary_of_the_review": "I'm voting for accept as the claims in the paper are clearly stated and well motivated and supported. I elaborated on these points in the Strengths/Weaknesses section and provide a few suggestions.", "strength_and_weaknesses": "The consideration of training the classifier head on the target distribution is reasonable and important in my opinion. In domain shift tasks the source domain is generally of a much larger scale than the target task. It is then reasonable to assume that the representation is trained on the source domain and the classifier (which needs less data if it is given a high quality representation) is trained on the smaller target domain dataset.\n\nThe set of algorithms and tasks are sufficiently diverse. There is ample evidence for all the claims in the paper. The only exception is the \"Findings\" paragraph in Section 3.2.2. Figure 3 is supposed to back this claim but the plots show high levels of noise and mixed patterns. For example, in fig 3 (a, top) the error bars mostly overlap and in Fig 3 (b, bottom) SL shows a drop in sensitivity. I suggest adding more runs, more levels of r_id, and clarifying the number of runs and what error bars represent.\n\nI would also like to see a detailed discussion on the augmentation methods used for SSL as this is critical to the performance of the representation learning method. What augmentation methods are used? For each pair of images concatenated together, is the same augmentation method used for both images? Are the two images modified exactly the same way (e.g. if both are rotated, are both images rotated in the same direction and by the same angle)?\n\nMinor comment: The first sentences of the first two bullet points at the end of the introduction are worded too close to each other. I understand that the first point refers to accuracy and the second point refers to shift sensitivity but this is not what those two sentences convey.", "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": "2ETSppH_4w", "reviewer": "Reviewer_Bhk8", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "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": "", "summary_of_the_paper": "This paper provides a comprehensive empirical study of the OOD generalization performance of SSL, AE and SL. In addition to testing standard algorithms on standard distribution shift datasets, the paper proposes a new controllable realistic distribution shift task, and also consider a setting where the linear head is retrained on the OOD data. Results suggest that SSL and AE are more robust to distribution shift than SL.", "summary_of_the_review": "I think this paper provides a reasonably good empirical comparison between SSL/AE and SL in various settings with different datasets. Although the result doesn't sound surprising, it's good to have this as an addition to the community, hence I would love to recommend for its acceptance.", "strength_and_weaknesses": "Strength:\n- The experiments are very comprehensive and implementation details are provided.\n- The construction of the controllable distribution shift dataset is novel.\n- As far as I know, this is the first work that explicitly takes retraining the linear head into consideration, and compare its performance side by side with using the ID linear head. This could be an important point that is worth highlighting to the community.\n\nWeakness\n- There's limited explanation about why SSL/AE works better than SL on shifted distribution beyond what people already know in the literature.\n- To some extent, I feel there's nothing surprising about the findings in this paper. Although it's always nice to have more comprehensive experiments, it's unclear what's the conceptual insight that a reader can gain from this paper. ", "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": {}}]

Author rebuttal:

Decision: Accept: poster