Do deep networks transfer invariances across classes?
Authors: Allan Zhou
Fahim Tajwar
Alexander Robey
Tom Knowles
George J. Pappas
Hamed Hassani
Chelsea Finn
Venue: ICLR 2022 Poster (2022)
Keywords: invariance
augmentation
nuisance transformation
imbalance
long tail

Abstract: In order to generalize well, classifiers must learn to be invariant to nuisance transformations that do not alter an input's class. Many problems have "class-agnostic" nuisance transformations that apply similarly to all classes, such as lighting and background changes for image classification. Neural networks can learn these invariances given sufficient data, but many real-world datasets are heavily class imbalanced and contain only a few examples for most of the classes. We therefore pose the question: how well do neural networks transfer class-agnostic invariances learned from the large classes to the small ones? Through careful experimentation, we observe that invariance to class-agnostic transformations is still heavily dependent on class size, with the networks being much less invariant on smaller classes. This result holds even when using data balancing techniques, and suggests poor invariance transfer across classes. Our results provide one explanation for why classifiers generalize poorly on unbalanced and long-tailed distributions. Based on this analysis, we show how a generative approach for learning the nuisance transformations can help transfer invariances across classes and improve performance on a set of imbalanced image classification benchmarks.

Published as a conference paper at ICLR 2022
Do DEEP NETWORKS TRANSFER INVARIANCES ACROSS CLASSES?
Allan Zhou" & Fahim Tajwar' Stanford University
Alexander Robey University of Pennsylvania
Tom Knowles
Stanford University
George J. Pappas& & Hamed Hassani University of Pennsylvania
Chelsea Finn
Stanford University
ABSTRACT
To generalize well, classifiers must learn to be invariant to nuisance transforma- tions that do not alter an input's class. Many problems have "class-agnostic" nuisance transformations that apply similarly to all classes, such as lighting and background changes for image classification. Neural networks can learn these invariances given sufficient data, but many real-world datasets are heavily class imbalanced and contain only few examples for most of the classes. We therefore pose the question: how well do neural networks transfer class-agnosti invariances learned from the large classes the small ones? Through careful experimentation. we observe that invariance to class-agnostic transformations is still heavily depen- dent on class size, with the networks being much less invariant on smaller classes. This result holds even when using data balancing techniques, and suggests poor invariance transfer across classes. Our results provide one explanation for why classifiers generalize poorly on unbalanced and long-tailed distributions. Based on this analysis, we show how a generative approach for learning the nuisance transformations help transfer invariances across classes and improve perfor- mance on a set of imbalanced image classification benchmarks. Source code for experiments is available at httts:://gtthuut ctwp AAl lanYangZhou/ wwweattiiiieiiiiiiiaae
transfer
INTRODUCTION
Good generalization in machine learning models requires ignoring irrelevant details: a classifier should respond whether the subject of image is a cat or a dog but not to the background or lighting conditions. Put another way, generalization involves invariance to nuisance transformations that should not affect the predicted output. Deep neural networks sufficiently many diverse examples. For example, we can expect our trained "cat vs dog" classifier be invariant changes in the background provided the training dataset contains images of cats and dogs with varied scenery. However, if all the training examples for the "dog" class are set in grassy fields, our classifier might be confused by an image of a dog in a house (Beery al., 2018).
and do learn invariances given
This situation is problematic for imbalanced datasets, in which the amount of training data varies from class to class. Class imbalance common in practice, as many real-world datasets follow a long-tailed distribution where a few head classes have many examples, and each of the remaining tail classes have few examples. Hence even the cumulative number of examples in a long-tailed dataset is large, classifiers may struggle to learn invariances for the smaller tail classes. And while augmentation can address this issue by increasing the amount and variety of data in the tail classes, this strategy is not feasible for every nuisance transformation (e.g., modifying ground scenery). On the other hand, many nuisance transformations such as lighting changes are "class agnostic:" they apply similarly examples from any class, and should generalize well across classes (Hariharan & Girshick 2016). Ideally a trained model should automatically transfer invari- ance to class agnostic transformations from larger classes to smaller ones. This observation raises the question: how well do deep neural network classifiers transfer learned invariances across classes?
image's back-
First two authors contributed equally.

---

Published as a conference paper at ICLR 2022
Expected KL divergence (eKLD) under transformation
K49-ROT-LT (Rotation)
K49-BG-LT (Background Intensity)
Method
ERM
2.0
CE+DRS
0.6
eKLD
1.5
0.2-
0.5
0.0
10
10 10
10 10F 10
10 10" 10
Class size
Figure 1: The expected KL divergence (eKLD, Eq. 2 measures how the classifier's ' estimated label probabil-
ities (=-(|ar) change under nuisance transformation, with lower eKI.D corresponding to more invariance. Each plot shows per-class eKLD of classifiers trained long-tailed Kuzushiji-49 (K49) dataset variant, ar- ranged by class size. Classifiers trained by either empirical risk minimization (ERM) delayed resampling (CE+DRS) show the same trend: invariance depends heavily on class size, and classifiers are more invariant on images from the larger classes. Shaded regions show 95% CIs over 30 trained classifiers.
In this work, we find empirical evidence that neural networks transfer learned invariances poorly across classes, even after applying balancing strategies like oversampling. For example, on a long- tailed dataset where every example is rotated uniformly at random, classifiers tend to be rotationally invariant for images from the head classes but not on images from the tail classes. To this end, we present a straightforward method for more effectively transferring invariances across classes. We first train an input conditioned but dlass-agnostic generative model which captures dataset's nuisance transformations, where withholding explicit class information encourages transfer between classes. We then we use this generative model to transform training inputs, akin to learned data augmentation training the classifier. We ultimately show that the resulting classifier is more invariant to the nuisance transformations due to better invariance on the tail classes, which in turn leads to better test accuracy on those classes.
Contributions. The primary contribution of this paper is an empirical study concerning whether deep neural networks learn invariances in long-tailed and class-imbalanced settings. We analyze the extent to which neural networks (fail to) transfer learned invariances across classes, and we argue that this lack of invariance transfer partially explains poor performance on real-world class- imbalanced datasets. Our analysis suggests that one path to improving imbalanced classification is to develop approaches that better transfer invariances across classes. We experiment with one such approach, which we call Generative Invariance Transfer (GIT), in which we train a generative model of task's 's nuisance transformations and then use this model to perform data augmentation of small classes. We find that combining GIT with existing methods such as resampling improves balanced accuracy on imbalanced image classification benchmarks such as GTSRB and CIFAR-LT.
RELATED WORK
Real-world datasets are often class imbalanced, and state-of-the-art classifiers often perform poorly under such conditions. One particular setting of interest is when the class distribution is long- tailed, where most of the classes have only few examples (Liu al., 2019] Guo al. 2016] Thomee et al.) 2016 Horn & Peronal 2017). Researchers have proposed many approaches for this setting, including correcting the imbalance when sampling data (Buda al. 2018 Huang et al.
2016 Chawla et al. 2002. He & Garcia 2009). using modified loss functions (Cao et al. 2019 Lin et al. Cui et al. 2019). and modifying the optimizer (Tang al., 2020). These methods generally do not study the question of invariance transfer and are complementary to Generative Invariance Transfer. (Yang & Xu (2020) study the mixed value of imbalanced labels and propose learning class-agnostic information using self-supervised training. while GIT learns class-agnostic transformations to use as data augmentation. Wang et al. (017)) propose implicit transfer learning from head to tail classes using meta-network that generates the weights of the classifier's 's model. Here we quantitatively measure per-class invariances to more precisely explain why transfer learning may help on imbalanced problems, and explicitly transfer across classes with generative model.
Toward understanding the failure modes of classifiers trained on real-world datasets, a rapidly grow- ing body of work has sought to study the robustness of commonly-used machine learning models.
2

---

Published as a conference paper at ICLR 2022
Notably, researchers have shown that the performance sfate-of-the-eee art models is susceptible to wide range of adversarial attacks (Biggio & Roli 2018 Goodfellow et al. [014 Madry et al. 2017] Wong & Kolter 2018 Robey et al. 200 and distributional shifts (Taori et al. [222 Hendrycks et al.)
2020 Koh et al. 2.21). ). Ultimately, the fragility of these models is a significant barrier to deploy- ment in safety-critical applications such medical imaging (Bashyam al. (020) and autonomous driving (Chernikova et al. (011)). In response to these fragilities, recent methods have learned the distributional shifts present in the data using generative models and then use these learned transfor- mations for robust training (Robey et al., |020] 2021b] Wong & Kolter 2020). These works assume pairs or groupings of transformed and untransformed examples, so that generative model can learn the distribution shift. In our imbalanced setting, generative invariance transfer aims to learn transfor- mations from the head classes that apply to the tail classes of the same dataset, and does not assume
the data is paired or grouped.
There is general interest in obtaining invariances for machine learning models (Benton et al, 2020 Zhou et al. 2021). Data augmentation (Beymer & Poggio 1995 Niyogi et al. 1998) can be used to train classifiers to be invariant to certain hand-picked transtormations, but requires the practitioner to know and implement those transformations in advance. In search of greater generality, Antoniou et al. (2017) use a trained GAN as data augmentations for training a downstream classifier. Similarly, Mariani al. (2018) use GAN to generate more examples for the minority classes in imbalanced classification. Learned augmentation can also be done in feature space, to avoid learning a generative model of the high dimensional input space (Yin al. 2018 Chu et al., 2020). In the low-shot Hariharan & Girshick (2016) study the notion of transferring generalizable (or class- agnostic) variation to new classes, and Wang al. (2018) learn to produce examples for new classes using meta-learning. Work in neural style transfer (Gatys et al. 2015b a Johnson et al. 2016)
has long studied how to leverage trained neural networks to transfer variation between images or domains. In particular, GIT leverages advances in image-to-image translation (Isola et al. 2016 Zhu jet al. 2017: Huang et al. 2018) as a convenient way to learn nuisance transformations and transfer them between classes. Our work carefully quantifies invariance learning under class imbalance, which can explain why leveraging generative models of transformations can improve performance. affected by noise and
There is prior work analyzing how learned representations and invariances regularization (Achille & Soatto 2018), task diversity (Yang et al.) 2019), and data diversity (Madan et al. 2021). The latter is most relevant to our own analysis, which studies how invariance is affected by the amount of data per class.
3 MEASURING INVARIANCE TRANSFER IN CLASS-MMBALANCED DATASETS
In this section we empirically analyze the invariance of trained classifiers to nuisance transforma- tions, and the extent to which these classifiers transfer invariances across classes In particular, we first introduce concepts related to invariance in the imbalanced setting, then define a metric for measuring invariance before describing our experimental setup. Finally, we present and analyze the observed relationship between invariance and class size.
3.1 SETUP: CLASSIFICATION, IMBALANCE, AND INVARIANCES
In the classification setting, we have input-label pairs (I, y). with y taking values in {1.-.., C} where C' is the number of classes. We will consider neural network model parameterized by weights w that is trained to estimate the conditional probabilities Pw jlzz). The classifier selects the class j with the highest estimated probability. Given training dataset (x((), (1))) ())) ~ Pinins empirical risk minimization (ERM) minimizes average loss over training examples. But in the class- imbalanced setting, the distribution of (2) in our training dataset is not uniform, and ERM tends to perform poorly on the minority classes. In real world scenarios typically want to perform well on all classes, e.g. in order to classify rare diseases properly (Bajwa et al.) 2020) or to ensure fairness in decision making (Hinnefeld et al., 2018). Hence we evaluate classifiers using class-balanced metrics, which is equivalent to evaluating on a test distribution Piest that is uniform over y-
To analyze invariance, we assume there is a distribution T(-[x:) over nuisance transformations of x. Given that nuisance transformations do not impact the labels, we expect a good classifier to be invariant to such transformations, i.e.,
P. = (-1(',)), L' d'~ <'-(((-)))
(1)
That is, the estimated conditional class probabilities should be unchanged by these transformations.
3

---

Published as a conference paper at ICLR 2022
3.2 MEASURING LEARNED INVARIANCES
To quantify the extent to which classifiers learn invariances, we measure the expected KL divergence (cKLD) between its estimated class probabilities for original and transformed inputs:
eKLD(Pw) Eg af TT-la) DKL (Pl((
(2)
This is a non-negative number, with lower eKLD corresponding to more invariance; classifier totally invariant to T would have an eKLD of O. We can estimate this metric in practice given a trained classifier if we have a way to sample x' ~ T(-lz). To study how invariance depends on class size, we can also naturally compute the class-conditional eKLD by restricting the expectation over examples from a given class j.
Calculating eKID and studying invariance requires access to a dataset's underlying nuisance trans- formation distribution T, but for most real world datasets we do not know T a-priori. Instead, we create synthetic datasets using a chosen nuisance distribution. Like RoMMNIST (Larochelle et al. 2007 common benchmark for rotation invariance, we create these datasets by transforming each example from a natural dataset. This is different from data augmentation, where multiple randomly sampled transformations would be applied to the same image throughout training. We want to test how classifiers learn invariances from limited amount of data diversity; providing the transforma- tion as data augmentation artificially boosts the observed data diversity and we use as an Oracle comparison in later experiments.
We modify Kuzushiji-49 (Clanuwat et al. 2018) to create three synthetic datasets using three differ- ent nuisance transformations: image rotation (K49-RA -OT-RO,,L,,, varying background intensity (K49- BG-LT), and image dilation or erosion (449-DIL-LTT Appendix Figure 7 shows representative im- age samples from each of these datasets. To make the training datasets long-tailed (LT), we choose an arbitrary ordering of classes from largest to smallest. Then we selectively remove examples from classes until the frequency of classes in the training dataset follows Zipf's law with parameter 2.0, while enforcing a minimum class size of 5. We repeat this process with 30 randomly sampled order- ings of the classes from largest to smallest, construct 30 different long-tailed training datasets for each variant. Each long-tailed training set has 7864 training examples, with the largest class having 4828 and the smallest having 5. Since we are interested in either per-class or class-balanced test metrics, we do not modify the test set class distribution.
Good classifiers for K49-ROT-LT, K49-BG-LT, and K49-DIL-LT should clearly be rotation, back- ground, and dilation/erosion invariant, respectively, for inputs from any class. We can train clas- sifiers and measure their invariance for inputs of each class by estimating per-class eKID. That is, we first sample more transformations and then measure how predictions change on held-out test inputs. For training we use both standard ERM and CE+DRS (Cao et al. 2019), which stands for delayed (class-balanced) resampling with standard cross-entropy loss. DRS samples training examples naively just as in ERM for the initial epochs of training, then switches to Mlass-balanee sampling for the later epochs of training. We train separate classifier using each method on each training dataset, then calculate each classifier's per-class eKLD on held out test examples.
Figure 1 shows how the resulting per-class eKID varies with class size. The eKLD curves for both methods show a clear pattern on all three transformation families: invariance decreases as classes get smaller. This result, while intuitive, shows quantitatively that deep neural networks learn invari- ances non-uniformly on imbalanced datasets. It suggests that they fail to transfer learned invariances across classes despite the nuisance transformation families being fairly class-agnostic. Although these results use a ResNet architecture, Appendix C.2 shows similar results for non-ResNe CNNs. Note that by construction, smaller classes contain both fewer original K49 examples and less trans- formation diversity. Yet Appendix shows the same trend for datasets where the number of original K49 examples the same across all classes, with larger classes only containing more sampled trans- formations of the same images. This shows that the trend is largely due to observed transformation diversity, rather than the number of original K49 examples.
Figure also shows that training classifiers with resampling (CE+DRS) results in generally lower eKLD (more invariance) for the same class size. This effect may partly explain why resampling can improve class balanced metrics such as balanced test accuracy. However, the eKLD curves show that there is clearly still room for improvement and even DRS does not achieve close to uniform invariance learning across classes. One explanation for this is that DRS can show the classifier the
4

---

Published as a conference paper at ICLR 2022
K49-DIL-LT Original
Generated samples
K49-BG-LT Original
Generated samples
Largest class
Largest class
Smallest class
Smallast
class
Figure 2: Samples from MITNNs trained to learn the nuisance transformations of K49-BG-LT (hackground intensity variation) and K49-DII.-I.T (dilation/erosiin).. Each row shows multiple transformations of the same original image. We see diversity of learned nuisances, even for inputs from the smallest class (bottom row).
same minority class images more often, but cannot increase the transformation diversity those im- ages (e.g., DRS cannot by itself create more examples of rotated images from the minority classes). This suggests that learning the transformation distribution, combined with resampling schemes, can help classifiers achieve uniform invariance across classes.
4 TRANSFERRING INVARIANCES WITH GENERATIVE MODELS
We' ve seen that classifiers do a poor job learning invariance to nuisance transformations on the tail classes of long-tailed datasets. Here we explain how generative invariance transfer (GIT) can transfer invariance across classes by explicitly learning the underlying nuisance distribution (-)
4.1 LEARNING NUISANCE TRANSFORMATIONS FROM DATA
If we have the relevant nuisance transformations, we can use them as data augmentation to enforce invariance across all classes. Since this is rarely the case in practice, GIT approximates the nuisance distribution T(-[z) by training inpuat-coniitoone generative model T(- An input-conditioned generative model of the transformation is advantageous for class-agnostic nuisances. Since the class- specific features are already present in the input, the model focus on learning the class-agnostic transformations, which by assumption should transfer well between classes.
To train the generative model in the image classification setting, we borrow architectures and train- ing procedures from the literature concerning multimodal image-to-image translation networks (MI- ITNs). MIITNs can transform a given input image x according to different nuisances learned from the data to generate varied output samples. The multimodality is ideal for capturing the full diversity of nuisance transformations present in the training data. Our experiments build off of particular MIITN framework called MUNIT (Huang al. 2018), which we modify to learn transformations between examples
single dataset rather than between two different domains (see Appendix A for details). As we are not aware of any work that successfully trains MUNIT-like models to learn rotation, we focus on training MUNIT models to learn background intensity variation (K49-BG-LT) and dilatiion/erosion (K49-DIL-LIT) Figure shows the diversity of transformations these models produce from a given input. We see qualitatively that these models properly transform even inputs from the smallest class, evidencing successful transfer between classes. While these and later re- sults show MUNIT successfully learns certain natural and synthetic transformations in imbalanced datasets, note that GIT does not make MUNIT-specific assumptions, and other approaches for learning transformations can be considered depending on the setting.
Once we have the trained generative model, GIT uses the generative model as a proxy for the true nuisance transformations to perform data augmentation for the classifier, with the goal of improv- ing invariance to these nuisance transformations for the small classes. Given a training minibatch {(x(() , ( we sample transformed input 50(() +- ((- while keeping the label fixed. This augments the batch and boosts the diversity of examples that the classifier sees during training, particularly for the smaller classes. The pre-augmentation batches can be produced by an arbitrary sampling routine BATCHSAMPLER such as class-balances sampler. We can also augment more selectively to mitigate the possibility of defects in the generative model hurting performance, espe- cially on the large classes where we already observe good invariance and where the augmentation may be unnecessary. First, we introduce cutoff K such that GIT only augments examples from classes with fewer than K examples. Second, we use GIT to augment only a proportion p E [o. 1] of each batch, so that the classifier our experiments, and K can range between 20 500 depending on the dataset. Algorithm [ details the GIT augmentation procedure explicitly.
mix of augmented and "clean" data. Typically p 0.5 in
5

---

Published as a conference paper at ICLR 2022
Algorithm Generative Invariance Transfer: Classifier Training
Input: D, the imbalanced training dataset
Input: BATCUSAMPLER, a minibatch sampling subroutine
Input: T. generative model of transformations trained on D
Input: UPDATEMODEL, a procedure that updates a classifier model given a minibatch
while not done do
B <- ((x(1) ()) | BATCHSAMPLERR
P Sample raw batch
for i = 1. (pund(p [B]) do
b Augment proportion p of batch > Optionally only augment the smaller classes
if CLASSSIZE(())
S K then
Remove (2:(1) ()( from B Sample z(1)
(())=(())
Transform input with generative model
Add (i(+) (0) to B
end if end for UPDATEMODEL(B)
D Update model on batch
end while
4.2 GIT IMPROVES INVARIANCE ON SMALLER CLASSES
As we saw in Figure 2 MIITNs can be trained to learn the relevant nuisance transformations for K49-BG-LT and K49-DIL-LT. Thus, given trained MIITN, we aim evaluate whether GIT can actually improve invariance on the smaller classes by transfering invariances from large to small classes. To do so, we measure the per-class eKLD metric on GIT-trained clas- sifiers, with lower eKLD suggesting greater in- variance. In particular, we train the classifiers using Algorithm [ where BATCHSAMPLER is the delayed resampler and where UPDATE- CLASSIFIER uses gradient updates with respect to the cross-entropy (CE) loss function; we re- fer to this combined method CE+DRS+GIT (all classes). "All classes" refers to the fact that, for the K49 experiments only, we disable the class size cutoff K, to observe GIT's effect at all class sizes. As an "Oracle" comparison we also replace GIT augmentation by the true nuisance trans- formation we used to construct the dataset, providing an unlimited amount of true transformation diversity (the training scheme is otherwise identical to CE+DRS).
eKLD after Generative Invariance Transfer (GIT)
K49-BC-LT (Background Intensity)
K49-DIL-LT (DiletionvErosion))
cca
84-
8:0
80
Class
ERM
CE4DRS
GE+DRS+GIT dalse))
Graale
Figure 3:
We observe that the expected KL divergence (eKLD) is lower for smaller classes when using genera- tive invariance transfer (GIT). That is, GIT makes clas- sifiers more uniformly invariant to the nuisance trans- form regardless class size.
Figure shows the average per-class eKLD of classifiers trained by CE+DRS+GIT, compared with ERM, CE+DRS, and the Oracle. We clearly observe that GIT achieves more uniform invariance across class sizes than CE+DRS or ERM, with the biggest improvements for the smallest classes. We also observe that GIT can hurt invariance ground truth data such that imperfections in the generative model end up degrading performance. This will justify using the class-size cutoff K for GIT augmentations in our later experiments.
the largest classes, where there is already sufficient
5 EXPERIMENTS
We have seen in Section 3 that classifiers transfer invariances poorly and can struggle to learn in- variances on the smallest classes, and in Sec Generative Invariance Transfer (GIT) can lead to more uniform invariances across all class sizes. In this section, we verify that more invariant classi- fiers do indeed perform better, as measured by metrics such balanced test accuracy. We also aim to understand whether GIT can be combined with other techniques for addressing class imbalance, and determine whether empirically important to only augment smaller classes.
5.1 EXPERIMENTAL SETUP
Comparisons. In our main comparisons, we will evaluate the performance of Generative Invari- ance Transfer (GIT) and study how it interacts with other techniques for addressing class imbalance,

---

Published as a conference paper at ICLR 2022
which include resampling schemes and modified loss functions. We use ERM to denote the standard training procedure with cross entropy loss, where examples for training minibatches are sampled uniformly from the dataset. As in Section we can alternatively train with delayed resampling, which we will refer to as CE+DRS. In addition to the typical cross entropy loss, we will compare to two recent loss functions that representative of state-of-the-art techniques for learning from long-tailed data: the LDAM (Cao et al.) 2019) and Focal (Lin et al., 2017) losses, which are de- signed to mitigate the imbalanced learning problem. Throughout the experiments, we will combine these loss functions with different sampling strategies (e.g. CE+DRS) and (optionally) GIT, e.g. "LDAMMDDS++II." For the K49 experiments in particular, we also compare against an Oracle that does data augmentation with the same transformation we used to construct the dataset. We evaluate all methods by balanced test set accuracy.
Datasets. We evaluate combinations of these methods on several long-tailed image classification benchmarks. Following the standard in long-tailed literature, we construct long-tailed training datasets by removing examples from certain classes until the class frequencies follow a long-tailed distribution. Appendix Figure 7 shows random samples from each the head and tail classes of each dataset. Aside from the long-tailed Kuzushiji-49 (K49-LT) variants of Section
we use:
GTSRB-LE LT is a long-tailed variant of GTSRB (Stalkkamp et al. 2012; 201T) which contains images from 43 classes of German traffic signs in large variety of lighting conditions and backgrounds, a natural source of nuisance transformations. We resize every image to have dimensions 32x32, randomly sample 25% of our training tailed training dataset. We make the training dataset long-tailed by selectively removing examples so that the class frequencies follow Zipf"s 's law with parameter 1.8. We fix the minimum number of training samples for a particular class to be 5 - resulting in training dataset where the most fre- quent class has 1907 examples, and the least frequent class has 5 examples. Since we are calculating class-bale balss-blanned test metrics, we leave the test set unchanged.
the validation set and use the rest to construct the long-
CIFAR-IO-LT and CIFAR-1O0-LT are long-tailed CIFAR (Krizhevsky vious long-tailed classification literature (Cao et al. 2019: Tang et al. 2020) It has with 32 x 32 images in 10 or 100 class, respectively. Our setup is identical to Cao et al. (2019), with class fre- quency in the training set following an exponential distribution with the imbalance ratio (ratio of number of training examples between most frequent and least frequent class) set to 100. Similar to GTSRB-LT, we keep the test sets unchanged as we calculating bansncbllanced test metrics.
2009
variants used in pre-
TinylmageNet-Lz LT is constructed from TinyImageNet (Le & Yang 2015) similarly to CIFAR-LT. TinylmageNet has 200 classes, with 500 training and 50 test example per class. We remove training examples to achieve an imbalance ratio of 100 and keep the test sets unchanged.
iNaturalist is a large scale species detection dataset (Horn al. 2018). with 8142 classes, 437,513 training and 24,426 validation images. The training set is naturally ly long-tailed and the validation set is balanced.
Training. For GTSRB-LT and CIFAR-LT we train ResNet32 (He et al. 2015) models for 200 epochs with batch size 128, optimized by SGD with momentum 0.9, weight decay 2 x 10-1, and initial learning rate 0.1. The learning rate decays by factor of 10 at epochs 160 and 180. For K49-LT we use a ResNet20 backbone trained for 50 epochs, with learning rate decays 30 and 40 epochs. For Tiny Iiny-mageNet-LT we use an EfficientNet-b4 (Tan & Le 2019) backbone and a cosine annealing learning rate scheduler (Loshchilov & Hutter 2017). For iNaturalist-201s we train a ResNet50 backbone for 90 epochs with a learning rate 0.1. with the learning rate annealed by 0.01 and 0.001 at epochs 30 and 60. See appendices B and C. for further classifier training details. We implement the GIT MIITNS using MUNIT (Huang et al. 2018)) trained for 140, 000 steps (GTSRB- IT and CIFAR-LT), 200, 000 steps (TinylmageNett-IT) 100, 000 steps (iNaturalist) or 10, 000 steps
(K49-LT). We use Adam (Kingma & Ba 2014) with learning rate 0.0001 and batch size 1.
5.2 RESULTS
K49-LT. In Section 4.2 we saw that using GIT to augment training led to more uniform invari- ance against each dataset's nuisance transform K49-BG-LT and K49-DIL-LT, with the largest improvements on the smallest class sizes. Table sshows that GIT also improves balanced accuracy over DRS, for both the CE and LDAM losses. For K49-BG-LTT, we find that GIT actually outper-
7

---

Published as a conference paper at ICLR 2022
Dataset
Baseline
Stralegy
K49-BG-LT
K49-DIL-LT
GTSRB-LT
CIFAR-IOLT
CIFAR-100
TiayImageNes
ERM
39.49
1.47
39.49 4: 1.47
68.88 4: 1.75
70.74 0.74:0.11 0.13
38.69 0.32
16.33 + 0.10
CE + DRS
42.21
1.36
30.48 + 1.47
64.45 1.15
74.28 0.56
40.97 = 0.40
16.98 + 0.18
+GIT
49.90 + 1.25
49.18 1.23
0..59
77.25 0.18
42. 12.73-2 0.27
17.43 0.18
-Oaake
44.22 = 1.36
33.55 +: 1.21
Focal + DRS
65.68 2.09
73.51 = 0.50
10.17 0.21
16.87 = 0.17
+GIT
71.29 0.73
76.87 0.14
41.25 1 0.26
17.70 = 0.18
LDAM + DRS
54.08 = 1.21
50.44 1.21
77.25 11:25::1120 1.29
76.13=201
13.21 = 0,31
20.54
+GIT
38.86
1.11
56.76 1.11
0.19
44.35 0.21
21.99 =
-Oaace
14.49=112
60.37 + 1.07
Table I: Average balanced test accuracy with or without GIT on diffcrent benchmarks. Adding GIT improves all resampling methods, with LDAM+DRS+GIT performing best overall. Uncertainty corresponds to 95% CT's across 30 instances for K49 variants, and the standard error over training runs for the rest.
GTSRB-LT
Original
Generated samples
CIFAR-100-LT Original
Generated samples
Largest
50
50
50
50
50
Largest class
Smallest class
20
Smallest class
Figure 4: Samples from MIITNs trained to learn the nuisances of GTSRB-LT and CIFAR-I00-LT, for use in GIT training. Each row shows sampled transormations of single input image. We see the diversity of learned transformations, including changing lighting, object color/texture, and background.
forms the Oracle. This suggests that GIT may be learning natural nuisances from the original K49 dataset, in addition to the synthetic background intensity transformation.
GTSRB-LT, CIFAR-LT, Tint and iNaturalist. Table shows that adding GIT improves upon all three baseline methods on the GTSRB-LT, CIFAR-ET and LinylmageNet-L1 benchmarks. Improvements are especially large on GTSRB-LT where street signs can appear under varying lighting conditions, weather, and backgrounds; here GIT improves LDAM+DRS by 4%. Figure S shows samples from the trained MIITNs: we see that it learns to vary lighting conditions, object color, and background, even for inputs from the smallest classes. Tables and combinations of GIT with different imbalanced training methods, where we see that GIT gives the largest improvements when combined with resampling based methods. Intuitively, GIT helps by augmenting examples from smaller classes, which appear more often when resampling.
and 4 show further
In contrast the previous benchmarks, adding GIT shows no improvements on iNaturalist (Ap- pendix Table 5). Because iNaturalist is by far the largest of the datasets and contains the most classes, powerful MIITN may be needed preserve class information while fully modeling the diverse nuisance transformations of this dataset.
6 ABLATION STUDIES
The samples generated by the trained MI- and 4 capture a diverse of nuisances, but have poorer image quality than the original images. When introducing GIT in Algorithm M we hypothesized that poor generated sample quality could hurt performance for classes that already have lot of examples, so we introduced class size cutoff K to only augment classes with fewer than K examples. By disabling this cutoff and applying GIT to all classes, we can inspect how GIT affects test accuracy for each individual class to validate this hypothesis.
GIT class size cutoff:
100
0.55
ITNs (Figures and
0.50-
0.80
0.15
0.65
LOON D9S LO4N Intlerte
0.00
100
167
Train Class size
Figure 5: Test accuracy vs train class size for CIFAR-I0 LT. Ap- plied naively (in red), GIT per- forms better on smaller classes and worse on larger ones.
Figure 5 reports per-class performance for each the ten classes in CIFAR-IO-LT, arranged by class size. We see that using GIT without the cutoff boosts accuracy for the smaller classes, but can lower accuracy for the larger classes. In contrast, using the cutoff (K = 500) reduces the accuracy drop on the largest classes, while maintaining strong improvements small classes. Table 2 directly compares GIT against the version with disabled cutoff, i.e. GIT
8

---

Published as a conference paper at ICLR 2022
(all classes). We that using class-size cutoff improves performance across the board. The differences are most pronounced for GTSRB followed by CIFAR-100 and CIFAR-IO. We expect that this might be the case because CIFAR-10 has more coarse class definitions, such that the MIIIN is less likely to corrupt the label.
Automated data augmentation: Since can interpret GIT as form of learned data augmentation, we also compare it to RandAugment (Cubuk et al.] 2019), an automated data augmentation scheme carefully designed have small search space over augmentation parameters. As Randmnggent has published tuned hyperparameters for CIFAR 10/100, we use those and compare in CIFAR-LT. GIT outperforms RandAugment when using the LDAM loss, but RandAugment performs compa- rably to or better than GIT with CE or FOCAL loss. This indicates that RandAugment's 's set of transformations and search space work well in the CIFAR setting.
Dataset
Baseline
Strategy
GTSRB
CIFAR
CIFAR
CE + DRS
RugnAngment GIT (all classes)
78.78 0.99
45.53 + 0.20
66.22 + 1.12
76.29 + 0.20
39.77 + 0.16
GIT
75.19 1: 0.50
77.25 = 0.18
42.73 + 0.27
FOCAL DRS
RandAugment GIT (all classes) GIT
78.02
45.15 0.46
68.92 + 1.15
76.44 0.34
39.90 + 0.19
71.29 +: 0.73
76.87 0.14
41.25 + 0.26
LDAM + DRS
RandAngment GIT (all classes)
77.67 0.07
43.36 + 0.70
78.51 +
78.00
43.21 0.22
GIT
81.39 +: 0.98
78.76 + 0.19
44.35 + 0.21
Table 2: Ablations for the effects of the GIT class size cutoff,, and RandAugment instead of GIT augmentation. We report the average balanced test accuracy and the standard error of the mean for 3 runs. GIT uses cutoff K 25, 500, and 100 for GTSRB-LT, CIFAR-IO LT and CIFAR-100 LT, respectively. This outperforms GIT (all classes) on all three datasets.
7 CONCLUSION
We study how deep neural network classifiers learn invariances to nuisance transformations in the class imbalanced setting. Even for simple simple class agnostic transforms such as rotation, we find that learned invariance depends heavily on class size, with the trained classifier being much less in- variant for inputs from the smaller classes. This suggests that classifiers do not inherently do good job of transferring invariances learned from the larger classes to the smaller classes, and is one way of explaining why they tend perform poorly on heavily imbalanced or long-tailed classification problems. Motivated by the transfer problem, we explore Generative Invariance Transfer (GIT) as a method for directly learning a generative model of dataset's nuisance transformations. We use this generative model during classifier training a form of data augmentation to enforce invariance and observe both more uniform invariance learning across class sizes and improved balanced test accuracy long-tailed benchmarks. Despite the observed improvements, GIT relies being able to train a generative model of the dataset's nuisance transformations. The generative model may struggle to preserve class relevant information on large datasets with many classes. We speculate that future improvements in generative modeling could mitigate or resolve this issue. Since this work is about transferring invariances between classes, the focus is largely on class-agnostic trans- formations. Class-specifis transformations would not be amenable to transfer, and handling them will likely require a different approach.
Our analysis also raises the question: why do deep classifiers struggle to transfer class-agnostic in- variances across classes? We believe that an explanation for this effect an interesting problem to be resolved by future work in the theory of deep learning. Additionally, although our analysis focused on the interaction between class size and invariance, these techniques used here could be extended to measure invariance in other contexts. Finally, a dataset can be class-balanced but im- balanced along other semantic dimensions not captured by the label, such groupings often studied in distributionally robust optimization (Sagawa et al. 2019). Further research on transferring invari- ances despite imbalance along more general dimensions could lead to more broadly generalizable and robust deep learning methods.

---

Published as a conference paper at ICLR 2022
8 ACKNOWLEDGEMENTS
We would like to thank Archit Sharma and Eric Mitchell for insightful discussion during early phases of this work. We also gratefully acknowledge the support of Apple and Google.
REPRODUCIBILITY STATEMENT
For our baseline experiments, we use publicly available implementations and their existing hyperpa- rameter values, linked or cited in Appendix B For Generative Invariance Transfer we use publicly available MUNIT implementation, with our modifications described Appendix [A] Classifier train- ing with GIT is described in Algorithm [ Since GIT effectively acts as a learned data augmentation and doesn't it require modifying the classifier itself, for ease of comparison and reproducibility we kept details such classifier architecture and optimization hyperparameters unchanged relative to the baselines. Appendix C.2 describes how to construct the K49-LT datasets, while Section [.T describe the GTSRB-LT and CIFAR-LE -T datasets. All code and pre-trained MIITN and classifier weights will be released upon publication.
REFERENCES
Alessandro Achille and Stefano Soatto. Emergence of invariance and disentanglement in deep rep- resentations. The Journal of Machine Learning Research, 19(1):1947-198) 2018.
Antreas Antoniou, Amos Storkey, and Harrison Edwards. Data augmentation generative adversarial networks. arXiv preprint
2017.
Muhammad Naseer Bajwa, Kaoru Muta, Muhammad Imran Malik, Shoaib Ahmed Siddiqui, Stephan Alexander Braun, Bernhard Homey, Andreas Dengel, and Sheraz Ahmed. Computer- aided diagnosis of skin diseases using deep neural networks. Applied Sciences, 10(7):2488, 2020.
Vishnu M Bashyam, Jimit Doshi, Guray Erus, Dhivya Srinivasan, Ahmed Abdulkadir, Mohamad Habes, Yong Fan, Colin L Masters, Paul Maruff, Chuanjun Zhuo, et al. Medical image harmo- nization using deep learning based canonical mapping: Toward robust and generalizable learning in imaging. arXiv preprint arXiv:2010.05355, 2020.
Sara Beery, Grant Van Horn, and Pietro Perona. Recognition in terra incognita. In Proceedings of the European conference on computer vision (ECCV), pp. 456-473, 2018.
Gregory Benton, Mare Finzi, Pavel Izmailov, and Andrew Gordon Wilson. Learning invariances in neural networks. arXiv preprint arXiv:2010.1 /882, 2020.
David Beymer and Tomaso Poggio. Face recognition from one example view. Proceedings of IEEE International Conference Computer Vision pp. 500-507. IEEE, 1995.
Battista Biggio and Fabio Roli. Wild patterns: Ten years after the rise adversarial machine learning. Pattern Recognition, 84:317-331, 2018.
Mateusz Buda, Atsuto Maki, and Maciej A. Mazurowski. A systematic study of the class im- balance problem in convolutional neural networks. Neural Networks, 106:249- 2018. ISSN 0893-6080. doi: occ.oe/c........c.c.cc.a.eoooooa sciencedirects www.eet.ccoscccccee
200. URL https://wwwer //www.
Kaidi Cao, Colin Wei, Adrien Gaidon, Nikos Arechiga, and Tengyu Ma. Learning imbalanced
datasets with bhbelldisribbtion-awwwe aware margin loss. In Advances in Neural Information Processing Systems, 2019.
Nitesh Chawla, Kevin Bowyer, Lawrence Hall, and W. Kegelmeyer. Smote: Synthetic minority over- sampling technique. Journal of Artificial Intelligence Research (JAIR), 16:321-357, 06 2002. doi: 10.1613/jair.953.
Alesia Chernikova, Alina Oprea, Cristina Nita-Rotan Rotaru, and BackGyu Kim. Are self-driving cars secure? evasion attacks against deep neural networks for steering angle prediction. In 2019 JEEE Security and Privacy Workshops (SPW), pp. 132-137. IEEF, 2019.
10

---

Published as a conference paper at ICLR 2022
Peng Chu, Xiao Bian, Shaopeng Liu, and Haibin Ling. Feature space augmentation for long-tailed data. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXIX 16, pp. 694-710. Springer, 2020.
Tarin Clanuwat, Mikel Bober-Irizar, Asanobu Kitamoto, Alex Lamb, Kazuaki Yamamoto, and David Ha. Deep learning for classical japanese literature. CoRR, abs/1812.01718, 2018. URL hthtttp
7/arxiv. owg.v.org/aoo. abs aww.aass11. 1812.8111.. 01718
Ekin D Cubuk, Barret Zoph, Jonathon Shlens, and Quoe V Le. Randaugment: Practical au- tomated data augmentation with a reduced search space. arxiv e-prints, page. arXiv preprint arXiv: 13719, 2019.
Yin Cui, Menglin Jia, Tsung-Y Yi Lin, Yang Song. and Serge Belongie. Claas-balanced loss based on effective number of samples. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2019.
Leon Gatys, Alexander $ Ecker, and Matthias Bethge. Texture synthesis using convolutional neural networks. Advances in neural information processing systems, 28:262-270, 2015a.
Leon A Gatys, Alexander S Ecker, and Matthias Bethge. A neural algorithm of artistic style. arXiv preprint arXiv: 06576 2015b.
Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial examples. arXiv preprint arXiv: 2014.
Yandong Guo, Lei Zhang, Yuxiao Hu, Xiaodong He, and Jianfeng Gao. Ms-celeb- Im:: A dataset and benchmark for large-scale face recognition. In Bastian Leibe, Jiri Matas, Nicu Sebe, and Max Welling (eds.), Computer Vision ECCV 2016, pp. 87-102, Cham, 2016. Springer International Publishing, ISBN 978-3-319-46487-9,
Bharath Hariharan and Ross Girshick. Low-shot visual recognition by shrinking and hallucinating features. corr. arXiv preprint arXiv: 0288,, 2016
Haibo He and Edwardo A. Garcia. Learning from imbalanced data. IEEE Transactions on Knowl- edge and Data Engineering, 2199)12633111 2009. doi: 10. 20900K0DE..0008.02002
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recog- nition. corr ab2.155 (2015), 2015.
Dan Hendrycks, Steven Basart, Norman Mu, Saurav Kadavath, Frank Wang. Evan Dorundo, Rahul Desai, Tyler Zhu, Samyak Parajuli, Mike Guo, et al. The many faces of robustness: A critical analysis of ofits---dittibutioo generalization. arXiv preprint arXiv:2006. 16241, 2020.
J Henry Hinnefeld, Peter Cooman, Nat Mammo, and Rupert Deese. Evaluating fairness metrics in the presence of dataset bias. arXiv preprint arXiv: /ottiv:/800. /00.//00990000 2018.
Grant Van Hom and Pietro Perona. The devil is in the tails: Fine-grained classification in the wild. CORR, abs/1 709.01450, 2017. htttlhttt://arrtt wttp://wwrr/bb/////o3/ 01450
Grant Van Horn, Oisin Mac Aodha, Yang Song, Yin Cui, Chen Sun, Alexander Shepard, Hartwig Adam, Pietro Perona, and Serge J. Belongie. The inaturalist species classifi- cation and detection dataset. In 2018 IEEE Conference on Computer Vision and Pat- tern Recognition, CVPR 2018, Salt Lake City, UT. USA, June 18-22, 2018, pp. 8769- 8778. Computer Vision Foundation / IEEE Computer Society, 2018. doi: 10.1 10.1/09. 2018.00914. htt./htttp://opeacccess
thecvf. com/ _eanttet__evpr____ (mpr__218/html] Van Horn The INaturalist Species CVPR_ paper. html
Chen Huang, Yining Li, Chen Change Loy, and Xiaoou Tang- Learning deep representation for im- balanced classification. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2016.
Xun Huang, Ming- Yu Liu, Serge Belongie, and Jan Kautz. Multimodal unsupervised image-to- image translation. In Proceedings of the European conference on computer vision (ECCV), pp. 172-189, 2018.
11

---

Published as a conference paper at ICLR 2022
Yerlan Idelbayev. Proper ResNet implementation for CIFARIO/CIFAR 100 in PyTorch. https: //tithub.comm///// cotp.///..aaaaatttts//occcccccca respeeterccrrreeeeeeeeeeeeeeeeee cifarl0 2018.
Phillip Isola, Jun-Yan Zhu, Tinghui Zhou, and Alexei A Efros. Image-to-image translation with
conditional adversarial networks. arxiv (2016). arXiv preprint arXiv: 1,07004, 2016.
Justin Johnson, Alexandre Alahi, and Li Fei-Fei. Perceptual losses for real-time style transfer and super-resolution. In European conference computer vision, pp. 694-711. Springer, 2016.
Bingyi Kang, Saining Xie, Marcus Rohrbach, Zhicheng Yan, Albert Gordo, Jiashi Feng, and Yannis Kalantidis. Decoupling representation and classifier for long-tailed recognition. In International Conference on Learning Reprexentations, 2020. B
id=r1gRicvEv3
Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint 11Xiv:1412.6980, 2014.
Pang Wei Koh, Shiori Sagawa, Henrik Marklund, Sang Michael Xie, Marvin Zhang, Akshay Balsub- ramani, 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. In International Conference on Machine Learning (ICML), 2021.
Alex Krizhevsky. Learning multiple layers of features from tiny images. MSc thesis, Department of Computer Science, University of Toronto, 2009, URL BRLhtttss:// https:///www.ooo www. www.:ccs.trootoccom Krriiiiieee
Hugo Larochelle, Dumitru Erhan, Aaron Courville, James Bergstra, and Yoshua Bengio. An empir- ical evaluation of deep architectures on problems with many factors of variation. In Proceedings of the 24th international conference on Machine learning, pp. 473 480, 2007.
Ya Le and Xuan Yang. Tiny imagenet visual recognition challenge. CS 231N, 7(7):3, 2015.
Tsung-Y Yi Lin, Priya Goyal, Ross B. Girshick, Kaiming He, and Piotr Dollár. Focal loss for dense object detection. 2017 IEEE International Conference on Computer Vision (ICCV), pp. 2999- 3007,2017,
Ziwei Liu, Zhongqi Miao, Xiaohang Zhan, Jiayun Wang. Boqing Gong, and Stella X. Yu. Large- scale long-tailed recognition in an open world. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019.
Ilya Loshchilov and Frank Hutter. SGDR: stochastic gradient descent with warm restarts. In 5th International Conference Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings. OpenReview.net, 2017. URL htttttts:///peereeeee
Spandan Madan, Timothy Henry, Jamell Dozier, Helen Ho, Nishchal Bhandari, Tomotake Sasaki, Frédo Durand, Hanspeter Pfister, and Xavier Boix. When and how do cnns generalize to out-of- distribution category-viewpoint combinations. arXiv preprint arXiv:2007.0800 000020 2021.
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu. Towards deep learning models resistant to adversarial attacks, arXiv preprint arXiv: 06083, 2017.
Giovanni Mariani, Florian Scheidegger, Roxana Istrate, Costas Bekas, and Cristiano Malossi. Bagan: Data augmentation with balancing gan. arXiv preprint arXiv: 1803.09655, 2018
Partha Niyogi, Federico Girosi, and Tomaso Poggio. Incorporating prior information in machine learning by creating virtual examples. Proceedings of the IEEE, 86(1 (8111)::296220000 1998.
Alexander Robey, Hamed Hassani, and George J Pappas. Model-based robust deep learning: Gen- eralizing to natural, dutti---ist data. arXiv preprint arXiv:2005. 10247, 2020.
12

---

Published as a conference paper at ICLR 2022
Alexander Robey, Luiz Chamon, George Pappas, Hamed Hassani, and Alejandro Ribeiro. Adversar- ial robustness with semi-in semi-infinite constrained learning. Advances in Neural Information Processing Systems, 34, 2021a.
Alexander Robey, George Pappas, and Hamed Hassani. Model-based domain generalization. Ad- vances in Neural Information Processing Systems, 34, 2021
Shiori Sagawa, Pang Wei Koh, Tatsunori B Hashimoto, and Percy Liang. Distributionally robust neural networks for group shifts: On the importance of regularization for worst-case generaliza- tion. arXiv preprint arxiv: /9/ 1.08731, 2019.
Stallkamp. M. Schlipsing, J. Salmen, and C. Igel. Man vs. computer: Benchmarking ma- chine learning algorithms for traffic sign recognition. Neural Networks, 32:323-332, 2012. ISSN 0893-6080. doi: http:://iiion///000000...eeeeeet
URL http:::/t////t Selected Pa-
sciencedirect www./o///ca...oe ort.o///c...c..aarrce//////0000.
pers from IJCN 2011.
Johannes Stallkamp, Mare Schlipsing, Jan Salmen, and Christian Igel. The german traffic sign recognition benchmark: multi-class classification competition. In The 2011 International Joint Conference on Neural Networks, pp. 1453-1460, 2011.
doi: 10.1 200.:UCCCCN.211..03333333
Mingxing Tan and Quoc Le. EfficientNet: Rethinking model scaling for convolutional neural net- works. In Kamalika Chaudhuri and Ruslan Salakhutdinov (eds.). Proceedings of the 36th In- ternational Conference on Machine Learning, volume 97 of Proceedings of Machine Learning Research, pp. 6105-611 6135-6112 14. PMLR, 09-15 Jun 2019. URL htttp:://ppppeeeeeeeeeeeeee .mg.mmmeinnsmm .mlr.
Sress/v97/c0 19. ht.ml
Kaihua Tang, Jianqiang Huang, and Hanwang Zhang. Long tailed classification by keeping the good and removing the bad momentum causal effect. arXiv preprint arXiv:2009. 12991, 2020.
Rohan Taori, Achal Dave, Vaishaal Shankar, Nicholas Carlini, Benjamin Recht, and Ludwig Schmidt. Measuring robustness to natural distribution shifts in image classification. arXiv preprint arXiv:2007.00644 2020.
Bart Thomee, David A. Shamma, Gerald Friedland, Benjamin Elizalde, Karl Ni, Douglas Poland, Damian Borth, and Li-Jia Li. YFCC100M: The new data in multimedia research. Communica- tions of the ACM, 6442),64-73, 2016. URL http:////e/ htap:://aamm..o acm. org otggmmaaazins/20115 2/19 wtlooyffcc1110ffm11111m
Yu-X Yu-Xiong Wang, Deva Ramanan, and Martial Hebert. Learning to model the tail. In Proceedings of the 31st International Conference on Neural Information Processing Systems, pp. 7032-7042, 2017.
Xu-Xiong Wang, Ross Girshick, Martial Hebert, and Bharath Hariharan. Low-shot learning from imaginary data. In Proceedings of the IEEE conference on computer vision and pattern recogni- tion, pp. 7278-7286, 2018.
Eric Wong and J Zico Kolter. Learning perturbation sets for robust machine learning. arXiv preprint arXiv.2007.08450. 2020.
Eric Wong and Zico Kolter. Provable defenses against adversarial examples via the convex outer adversarial polytope. In International Conference on Machine Learning, pp. 2285-5295. PMLR, 2018.
Guangyu Robert Yang, Madhura R Joglekar, Francis Song, William T Newsome, and Xiao-Jing Wang. Task representations in neural networks trained to perform many cognitive tasks. Nature neuroscience, 22(2):297-306, 2019.
Yuzhe Yang and Zhi Xu. Rethinking the value of labels for improving class-im insalannbd learning. arXiv preprint ar Xivv:2006.0752 2020.
Xi Yin, Xiang Yu, Kihyuk Sohn, Xiaoming Liu, and Manmohan Chandraker. Feature transfer leamn ing for deep face recognition with redre-tepresented data. arXiv preprint 1rX3v 090014 2018.
13

---

Published as a conference paper at ICLR 2022
Allan Zhou, Tom Knowles, and Chelsea Finn. Meta-learing symmetries by reparamettrizzatoon. In International Conference on Learning Representations, 2021. URL http:::///ppeeeeeiie... net/ 1tte/Errrumn1.d=0044m4
Jun- Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. In Proceedings of the IEEE international conference on computer vision, pp. 2223-2232, 2017.
14

---

Published as a conference paper at ICLR 2022
A MUNIT TRAINING DETAILS
We implement our generative models using the MUNIT architecture and training algorithm (Huang et al. 2018), using the official source code at httts:://githit though the architectures, optimizers, and most other training details are unchanged, MUNIT is de- signed to train on two datasets A and B and learns two generative models GA- and G-++A to map between them. As we are only interested in learning transformations between images in the same (imbalanced) dataset, we set both A and B to be our one dataset and, after training, arbitrarily take GA-B as the learned generative model T. Sampling ī ~ T(-2z) corresponds to sampling different latent "style" vectors that are used as input to the MUNIT decoder. We observe in Figure and Figure S that MUNIT produces a diverse set of transformed samples.
com /VVaabs / /MUNIT Al-
For all MUNIT training we use identical optimization hyperparameters as in the official source code (Adam (Kingma & Ba| 2014) with learning rate 0.0001 and batch size 1). We sample training exam- ples with class balanced sampling, and as per the original implementation we rescale the pixel values between [-1,1] and apply random horizontal flips data augmentation (images from iNaturalist- 2018 is resized so that their shorter sides are of size 256, and then a random crop of 224 x 224 is taken from them without any padding). The image reconstruction loss has weight 10, while the adversarial loss, style reconstruction loss, and content reconstruction loss all have weight 1. We dis- able the domain-invariant perceptual loss. The generator architecture hyperparameters to the "edges - handbags" experiment from Huang et al.] (2018), and the discriminator is also the same except that we use a single scale discriminator instead of 3 scales. For K49-LT we train the MUNIT architectures on the 28 x 28 image inputs for 10, 000 steps. For GTSRB-LE - and CIFAR-LT we train on 32 x 32 imputs for 140, 000 steps. For TinylmageNet-LT we train on 64 x 64 inputs for 200, 000 steps, and for iNaturalist-201 we train on 224 x 224 inputs for 100, 000 steps.
identical
B CLASSIFIER TRAINING DETAILS
Optimization. For fair comparison, nearly all of our classifier training hyperparameters are identical to those used the CIFAR experiments of Cao et al. (2019): 200 training epochs with a batch size of 128, optimized by SGD with momentum 0.9 and with weight decay 2 x 10 10-4, The initial learning rate is 0.1 and decayed by a factor of 10 160 epochs and further decayed by the same factor at 180 epochs. Only the K49-LT experiments use slightly modified training schedule of 50 epochs with learning rate decays at 30 and 40 epochs. For Delayed Resampling (DRS) the resampling stage starts 160 epochs for GTSRB LT and CIFAR-LT and at 30 epochs for K49-LT. For iNaturalist, following Cao et al. (2019) we train for 90 epochs with batch size 256 and learning rate 0.1, with further decaying the learning rate by 0.01 and 0.001 epochs 30 and 60 respectively. The other hyper-parameters related to LDAM baseline are identical to (Cao et al., 2019).
Data augmentation. For the CIFAR-LT experiments used random crop (with padding 4) and random horizontal flip (with probability 0.5) on all non-GIT methods. For methods that use GIT, random horizontal flip is first applied to the entire batch. Then we apply the GIT augmentation to half the batch, and the random crop augmentation to the other half. For TinyImageNet-Ba random crop to size 64 64 with padding For iNaturalist, we first resize each training image to have the shorter side to have size 256. Next, we take a random crop of size 224 x 224 without any padding from this image or its random horizontal flip with equal probability. For all datasets, we normalize the images to the pixel mean and standard deviation of the respective training dataset.
we use
Since MUNIT training uses random horizontal flip augmentation. we tried adding random horizontal flip augmentation for classifier training in K49-LT and GTSRB-LT experiments but found that it worsened performance on those datasets. This may be because handwritten characters and text on street signs are not actually flip invariant. Classifier training for K49-LT and GTSRB-LT does not use any additional data augmentation, except for the learned augmentations for the GIT methods.
Architecture. Like Cao et al. (2019), we use family of ResNet (He et al. 2015) architecture implementations designed for CIFAR (Idelbayev 2018) for all experiments. We use the ResNet20 architecture for the K49-LT experiments and the ResNet32 architecture for the GTSRB-LT and CIFAR-LT experiments. Finally, we use EfficientNet-be (Tan & Le. 2019) for TinylmageNet-LT and ResNet50 for Naturralis..
15

---

Published as a conference paper at ICLR 2022
C FULL EXPERIMENTAL DETAILS AND RESULTS
C.I METHODS
We use three loss functions for experiments the standard cross entropy loss (CE), Focal loss (Lin et al., 2017) and LDAM (Cao et al. 2019). The last two are specialized loss functions designed for imbalanced dataset learning. Following Cao et al. (2019), we choose
1 as the hyper- parameer for Focal loss, and for LDAM loss, the largest enforced margin is chosen to be 0.5.
We couple these loss functions with variety of training schedules, described below:
Class balanced reweighting (CB RW) (Cui et al. 2019): Instead of reweighting the loss for particular training example proportional to the inverse of corresponding class size, we reweight according to the inverse of the effective number of training samples in the corresponding class:
1 3N Nof = 1 1
(3)
where No f is the effective number of training examples in class i, N is true number of training samples for class i, and (3 is a parameter, which we typically set to 0.9999 for all our experiments.
Class balanced resampling (CB RS) Cui 2019): We resample the training examples in particular class with probability proportional the inverse of effective number of training samples (see Equation 3) in that class.
Resampling (RS): This is the regular resampling strategy, where we resample the training examples in a particular class with probability proportional to the inverse of (true) number of training samples in that class.
Delayed reweighting (DRW) (Cao et al. 2019): part of the training, and reweight the loss according to the inverse of the effective number of samples (Equation] 3 in training class only at the last phase of the training. For GTSRB- LT and CIFAR-LT, we typically train for 200 epochs, and reweight the loss function starting at 160 epochs.
We train in a regular way for the initial
Delayed resampling (DRS): Similar to DRW, but we resample examples from class with probability inverse the true number of training examples in class i.
Among all the combinations of loss functions and training strategies, we discover that LDAM + DRS typically does the best, and combining GIT with it gives an additional boost in performance.
For GIT classifier training we set the class size cutoff parameter to K = 25 for GTSRB-LT, K = 500 for CIFAR-IO-LT. K 100 for CIFAR- and TinyImageNet-LI and K 20 for iNaturalist.
C.2 K49-LT
When constructing the synthetic datasets we used one of three transformation families and applied a randomly sampled transformation to each image in the dataset. For rotation, we rotated the raw image by a randomly sampled angle [0, 2xT) ). For background intensity, replaced the original black background with randomly sampled pixel value between 0 and 100, where 255 is the maxi- mum intensity. For dilation and erosion. we randomly either applied dilation with 60% probability or erosion with 40% probability, using OpenCV's dilate and erode functionality. For dilation we used an n x n kernel of 1's, where Unif( (2, 3, 4)), and for erosion we used an m x m kernel of I's, where ~
The per class eKLD curves on the K49-LT variants were calculated for a ResNet20 architecture, but to verify that the results are not specific to ResNet we repeated these experiments on a simple CNN, which consists of four blocks of 3 x 3 convolutions, batch normalization, ReLU, and max pooling with stride 2. A final linear layer produces the output logits. Figure 6 shows the resulting per class eKLD for both architectures. We see that classifiers struggle to transfer learned invariances to the tail classes regardless of architecture, and that GIT can help mitigate this problem in both cases.
16

---

Published as a conference paper at ICLR 2022
eKLD vs class size for different architectures
K49-ROT-LT (Rotation)
K49-BG-LT (Background Intensity)
K49-DIL-LT (Dilation/Erosion)
2.5
0.125
Method
ERM
Resnet-20
CE+DRS
1.5
CE+DRS+GIT
0.4
0.050
0.2
0.5
0.025
eKLD
0.0
0.125
2.0
0.100
Simple
0.075
1.0
0.050
0.025
10 0.000
10
102
10
Class size
Figure 6: Per-class eKLD curves three K49-LT variants for classifiers trained by different meth- ods using two different architectures: ResNet20 (top) and simple CNN (bottom). In each case wee that classifiers learn invariance to the nuisance transform unevenly, with poor invariance for the tail classes. We also see that adding GIT helps reduce eKLD and improve invariance on the tail. Shaded regions indicate 95% CT's over 30 trained classifiers.
C.3 GTSRB-BE AND CIFAR-LT
Table 3 and Table present more comprehensive set of experiments GTSRB-LT and the two CIFAR-LT benchmarks, comparing how GIT performs with wider combinations losses and train- ing schedules. Overall see that GIT works best when paired with resampling method (such as DRS), and offers less benefit when applied to reweighting schemes or the standard training process. Intuitively, resampling boosts the probability of sampling examples from the small classes, which GIT can then augment, providing the classifier with more diversity for the small classes. Without resampling, the classifier is rarely sees examples from the small classes at all, minimizing the impact that GIT can have. In fact, without resampling, GIT will be applied primarily to images from the larger classes, and we saw in Section that using GIT on larger classes can hurt the performance of the classifier. This is also confirmed on Table and where GIT often hurts the performance for non-resampling training schedules.
C.4 NNTURRALIST-2015
We use the 2018 version of the iNaturalist dataset and report validation accuracy different base- lines in Table 5 Note that similar to Kang et al. (2020), we could not reproduce the numbers for various baselines from Cao al. (001)).
17

---

Published as a conference paper at ICLR 2022
Kc9-DIL-LT
Real samples
K49-BG-LT
Real samples
Largest
Largest class
Smallest class
class
K49-ROT-LT
Real semples
GTSRB-LT
Real samples
C
Largest class
Largest class
50
50
O
Smallest
Smallest
20
20
20
20
20
CIFAR-10-LT
Real somples
CIFAR-100-LT
Real samples
Largest class
Largest class
Smallest class
Smallest
class
Figure 7: Random training examples from each of the datasets considered this work, with examples from both the largest and smallest classes in each dataset.
eKLD due to transformation only on K49
Rotation
Background Intensity
Dilation/Erosion
Method ERM
1.25
0.08
CE+DRS
1.00
eKLD
0.06
0.75
0.25
0.0
0.00
0.00
10P
10a
Class size (# of transformations)
Figure 8: The expected KL divergence (eKLD) synthetic K49 datasets that contain the number of original K49 examples across all classes. These datasets long-tailed only the amount of transformations observed, and are designed to isolate the effect the transformation. Each class starts with examples from the original Kuzushiji-49 dataset. Larger classes are created by repeatedly sampling more transformations of the same 5 originals. This design ensures that the only difference between large and small classes is the amount of transformation diversity. These datasets easier to learn, but show the qualitative trend Fig. Shaded regions show 95% CIs over trained classifiers.
18

---

Published as a conference paper at ICLR 2022
Loss Type
Training Schedule
Without GIT
With GIT
CE
None
68.88 + 1.75
65.90 = 0.66
CB RW
41.31 + 6.45
49.46 6.33
CB RS
= 4.55
61.67 3.43
RS
55.06 = 1.28
59.66 1.78
DRW
69.57 + 0.99
71.30 1.17
DRS
64.45 + 1.15
66.22 1.12
Focal
None
69.07 1.14
66.93
1.19
CB RW
+
43.22 2.09
CB RS
55.30
60.60 2.67
RS
4.60
56.09 1.61
DRW
66.73
66.80 0.99
DRS
65.68 2.09
68.92 1.15
LDAM
None
76.68 + 1.76
76.87
0.61
CB RW
53.81 4.61
59.69
2.92
CB RS
63.10 1.32
74.58 0.44
RS
66.05 + 0.63
73.61 1.22
DRW
7 1.26
77.53 = 0.44
DRS
77.25 + 1.29
78.51 + 1.29
Table 3: Full experimental results for the long-tailed GTSRB dataset. In this table, we report the average balanced test accuracy and the standard error of the mean of 3 runs for each entry. Note that we use GIT for all classes as opposed to only minority classes, in contrast to Table [ but still we see improvements for most of the methods when combined with GIT. Section 6 shows that using GIT only for minority classes outperforms using GIT for all classes, but since that requires one more hyper-paraan apper-parameter be tuned (class size threshold, K), we chose use GIT for all classes in this table.
19

---

Published as a conference paper at ICLR 2022
Dataset
CIFAR-10LI
CIFAR-100 LT
Loss type
Training Schedule
Without GIT
With GIT
Without GIT
With GIT
CE
None
70.74 + 0.13
67.05 + 0.37
38.69 0.32
40.09 + 0.27
CB RW
71.90 0.14
73.73 0.92
30.06 1
31.70 0.59
CB RS
69.85 + 0.08
74.20=0.22
$2.13=0.77
35.46 - 1.32
RS
69.15 0.62
74.10 +.21
33.08 + 0.21
34.48 0.40
DRW
75.22 + 0.50
75.77 0.09
41.05 + 0.10
41.90 + 0.32
DRS
74.28 0.56
76.29 + 0.20
40.97 = 0.40
42.73 - 0.22
Focal
None
70.22 0.56
07.31
38.41 0.27
40.60 0.32
CB RW
69.22 0.70
66.73 0.54
26.80 0.85
25.16 1.43
CB RS
68.64 0.62
+ +.39
33.04 0.36
34.72 0.60
RS
69.30 + 0.20
#.111
32.73 = 1.13
34.03 0.05
DRW
75.41 0.87
+
39.65 + 0.36
40.14 0.16
DRS
73.51 0.50
76.44 = 0.34
40.77 = 0.21
40.87 0.46
LDAM
None
73.06 0.28
69.00 0.38
40.45 0.26
40.88 0.73
CB RW
73.06 + 0.28
+
40.45 + 0.26
40.88 + 0.73
CB RS
70.38 0.41
75.46
30.68 0.43
32.37 0.39
RS
70.45 0.43
30.84
33.50 + 1.01
DRW
77.13 0.27
77.98 + 0.50
43.11 0.33
43.33 0.36
DRS
76.73 : 0.74
78.00 = 0.14
43.21 = 0.31
44.35 + 0.21
Table 4: Full experimental results for long-tailed CIFAR-10 and CIFAR- 100 datasets. In this table, we report the average balanced test accuracy and the standard error of the mean of 3 runs for each entry. Bold numbers represent superior results for each dataset. Note that augment all classes in- stead of only the minority classes for CIFAR-10 LT, and show that even without the eyper-parameter class size threshold, K.
most (Loss type, training schedule). For CIFAR- 100 LT, using GIT to augment all classes often hurts the performance compared to not using GIT, we only use GIT for classes with number of training samples 100.
major improvements
Baseline
Strategy
Top-1 Accuracy
Top-5 Accuracy
ERM
47.265
72.063
CE + DRS
57.574
78.707
+GIT
54.986
76.578
Focal DRS
52.567
75,276
+GIT
49.375
73.314
LDAM DRS
57.545
77,487
+GIT
53.051
73.946
Table 5: Validation accuracy with without GIT iNaturalist-2018. We report the numbers from a single run due to long training times. We use GIT with class size cutoff K 20.
20


Reviews:
[{"review_id": "jrSACmLdWfF", "reviewer": "Reviewer_Zq9K", "summary": "", "questions": "", "limitations": "", "rating": 5, "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": "=== Strengnth ===\n1. The paper is mostly well-motivated, well-written, and very easy to read.\n\n2. The question raised by the authors in Section 1 is interesting. The experiments and metrics in Section 3 are inspiring and well-designed. They point out one direction for future research.\n\n3. Overall, I think the direction the authors proposed to approach imbalanced classification is quite interesting. Generative models have not been widely used in this task. The authors also make \"accurate\" claims: the proposed method is mainly to deal with task/dataset-specific (but class-agnostic) variation.\n\n=== Weakness ===\n1. The technical part of the paper (GIT) is not well-written, described, and justified. The authors only simply mentioned that they apply MUNIT but didn't have more discussion or provide formulations. For example, why is MUNIT the appropriate method to be used? Why can we learn anything meaningful (i.e., the class-agnostic variance) by turning MUNIT to learn the mapping between the \"same\" domains? Are there related works that learn to change the input image (e.g., style transfer) and can be applied here? Finally, the authors should have mentioned in section 1 that the generative model is conditioned on the input image. \n\n2. The experimental results are not enough. The authors only use small-scale datasets, but not large-scale ones like iNaturalist or mini/tiny-imagenet. The smaller improvement on CIFAR than on characters/traffic signs also raises a question --- could the proposed method be applied to natural, more complicated images/objects? Besides, the authors only compare to CB, LDAM, RS/RW, which are a bit outdated (though they are proposed in 2019). Finally, the proposed method seems to be not stable (according to Table 5).\n\n3. As the authors argue that the proposed method is not merely data augmentation, I would like the authors to empirically compare it to existing sophisticated data augmentation methods, e.g., Zoph. et al. Rethinking Pre-training and Self-training, NeurIPS 2020.\n\n4. From the paper description and the qualitative results (Fig 2 and Fig 4), it seems that the proposed method can only make the class-agnostic background, color, lighting, and dilation/erosion changes. However, in many large-scale datasets, there exists class-specific or semantically-related variation: for example, the appearance changes of cats might be similar to lions than to buses. Also, in many large-scale datasets, many tail classes seem to suffer from insufficient observations of their appearance changes (like from different viewpoints, insufficient instances (e.g., bag/airplane styles)). These can be found in Fig 7. It seems that the proposed method cannot effectively resolve these variances (see Fig 4). \n\n5. Some highly relevant works are missing (not cited and discussed). \n\nTransferring data variance from many-shot to few-shot data (e.g., to generate more data)\n\n[a] B. Hariharan et al. Low-shot visual recognition by shrinking and hallucinating features. In ICCV, 2017\n\n[b] X. Yin et al. Feature transfer learning for face recognition with under-represented data. In CVPR, 2019\n\n[c] Y. Wang. Low-Shot Learning from Imaginary Data. In CVPR, 2018\n\nLearning class-agnostic information\n\n[d] Y. Yang. Rethinking the Value of Labels for Improving Class-Imbalanced Learning, NeurIPS, 2020\n\nStyle transfer or image-to-image translation should be discussed in related works.\n\nFinally, based on the proposed method, I was wondering if the method proposed by Mariani et al. (2018) is applicable. If so, it should be compared.\n\n=== Minor weakness/questions ===\n1. The paper could cite and reference more existing works. For example, in Section 1, there are insufficient references (which dataset, which augmentation method?). \n\n2. When DR or DS is used, do the authors only apply the proposed augmentation to the final learning steps or the whole learning steps? As the proposed method does not simply over-or under-sample the examples in the original dataset, I think it could be applied to the entire learning process.", "summary_of_the_paper": "This paper works on long-tailed or class-imbalanced learning. The authors found that the learned classifier in such a setting cannot effectively transfer the class-agnostic (in)variance in a dataset from the head classes to the tail classes, which causes poor classification performance for the tail classes. The authors thus proposed to learn such class-agnostic (in)variance via a generative model, and then use it to augment the training data of minor classes. The experimental results on several small-scale datasets demonstrate the effectiveness of the proposed method in improving long-tailed or class-imbalanced classification.", "summary_of_the_review": "Overall, I enjoy reading the paper as it is well-motivated and well-written. The experiments designed in section 3 are quite interesting. However, the proposed method in section 4 is not well-described and justified; the experimental comparison in section 5 is not sufficient. I thus give a score \"5\" for now. More accurately, my score is between \"3\" and \"5\".", "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": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "SliPIFMQAcu", "reviewer": "Reviewer_PgZ2", "summary": "", "questions": "", "limitations": "", "rating": 8, "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": "Strengths:\n\n1. An extremely important problem: transferring invariances across classes opens up many avenues. For instance, to become invariant to any new transformation it would be sufficient to collect diverse data with only a few classes. This can help reduce resource required resources significantly. \n\n2. The approach of modeling nuisance parameters using generative model and then propagating them to low frequency classes is very interesting.\n\n3. The evaluation and experiment design is solid and rigorous.\n\n4. Paper is very well written. It is easy to follow and understand. \n\nMinor Weaknesses:\n\n1. I am curious how GIT compares to other methods attempting to specifically enforce invariance. One strength of GIT is that it doesn't require knowing the transformation. However, in the case of dilation/erosion and background intensity showed here, the transformation is known. So, it is possible to get an exact value for an upper bound of what GIT could have achieved. It would be good to include this upper bound to know how well GIT performs.\n\n2. Equation (1) is missing the superscript (i) for the image x. \n\n3. Missing literature: Some recent literature on the role of dataset size/diversity on invariances is missing which would be good to comment and connect to [1,2].\n\n4. I wonder where the most important contributions of the paper are. To me, it seems that bulk of the experiments are on quantifying their approach as a solution for class imbalance. So, I would suggest that the title and introduction should be adapted to focus more on this aspect. However, if instead the authors believe the main contribution to be the evaluation and solution for transfer of invariances, numbers mentioned in point 1 above should be mentioned.\n\nReferences\n\n1. Madan, S., Henry, T., Dozier, J., Ho, H., Bhandari, N., Sasaki, T., Durand, F., Pfister, H. and Boix, X., 2020. When and how do CNNs generalize to out-of-distribution category-viewpoint combinations? arXiv preprint arXiv:2007.08032.\n\n2. Yang, G.R., Joglekar, M.R., Song, H.F., Newsome, W.T. and Wang, X.J., 2019. Task representations in neural networks trained to perform many cognitive tasks. Nature neuroscience, 22(2), pp.297-306\n\n3. Achille, A. and Soatto, S., 2018. Emergence of invariance and disentanglement in deep representations. The Journal of Machine Learning Research, 19(1), pp.1947-1980.", "summary_of_the_paper": "The paper investigates if invariances learned by the model transfer across classes. Focussing on class-agnostic nuisance parameters, the interplay between per-class size and invariant representations has been explored. It is suggested that while networks can become invariant to these parameters for classes with many examples, it is unclear if this is also the case for classes with fewer examples. The paper shows this is not true i.e. invariances do not transfer well to small classes, and suggest that improving this can help increase performance on imbalanced datasets. And so, the paper proposes a two step solution to this problem. First, an image-conditional generative model is learned which learns to transform the image such that only the nuisance parameter changes. Secondly, this model for nuisance parameters is used for data augmentation. Using this approach, the authors are able to achieve a significant improvement on standard long-tail datasets.", "summary_of_the_review": "The paper investigates an extremely important problem: class-imbalance, and shows that part of the poor performance on classes with less samples stems from poor transfer of invariance to these classes despite good invariance building up for larger classes. Their proposed solution is thus very well motivated, and is a very nifty idea to model nuisance parameters. All in all, this is a solid applications paper in my opinion, and I think some minor changes in writing to focus more on fixing class-imbalance would make it a good paper for the computer vision community.", "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": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "IPPWQrrzs10", "reviewer": "Reviewer_k4Fm", "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": "Strengths\n\n+ Very interesting and fundamental research question \n+ Insightful analysis\n+ Well written, clear, and easy to understand\n+ The GIT solution improves\n\n\nWeaknesses\n\n- I find the empirical risk minimization setting strange: the paper assumes a different distribution of the training data from the test data.\n- I am not convinced of the main result in fig 1 (It could \"just\" be the class frequency; and not the transformation). See my detailed review below.\n- The abstract claims an \"explanation\" but this is actually what I miss. Why is this effect is happening? Sure, a generative model can remedy the symptoms to some degree, but what is actually the cause of these symptions?\n- Paper is not self-contained (I need the appendix for essential parts, thus, the appendix becomes part of the page limit?). See my detailed review below.\n- I miss an analysis on GIS for \"rotation\" (fig 1 vs fig 3)\n- I find it strange that the effect only seems to hold for supervised learning. So, if the class labels are removed but the dataset is the same, does the effect no longer occur? (ie: the GIS is trained unsupervised and seems to not have trouble in learning these general nuisance effects..)\n\nDetailed review:\n\n- Minor detail in general: The paper is fond of using \"very\" very much. A small tip is to try to avoid \"very\" it achieves the opposite of what the writing aims to achieve: http://www.writerswrite.co.za/45-ways-to-avoid-using-the-word-very/\n\n- Minor detail: Abstract: \"In order to\" can nearly always be replaced by \"To\".\n\n- Abstract: \"much less invariant on smaller classes\", what does this mean? Isn't invariance to a transformation T a binary property? ie: T(f(x)) = f(x) or is some (relative?) distance/similarity measure implied? I also assume its not about the classes, but about the nuisance transformation T in those classes? Perhaps the word \"robust\" is better?\n\nPage 1: \"where withholding explicit class information\" so, is it then about the class information? Or about the occurrence frequency of the appearance of a class? Ie: this statement makes me wonder if class labels play a role here at all? Ie: in unsupervised settings there can also be an imbalance in the 'semantics' as measured by the nr of samples (but no explicit class labels are used). Basically: Why does this effect hold when using labels, and why does this effect not hold without using labels (but using the same dataset). It seems to me that the generative approach proposed later by this paper does not suffer from this effect?\n\nFig 1: How can we be sure that this effect is due only to the transformation and to nothing else than the transformation? I could pose an alternative explanation to this graph which is: Its generally more difficult to learn the classes that have fewer examples. This would also explain the shape of these curves, without relying on transformations. Ie: I miss a figure where there is no transformation at all, to see the baseline effect of having fewer examples (perhaps this can be achieved by measuring the eKLD for different initialized runs of the same model trained on untransformed data only? This would give an estimate of P_w || P_w ). I assume that this \"no transformation baseline\" would follow the same trend for ERM; yet perhaps be completely uniform for CE+DRS (?) So, generally, for this figure, I wonder how to investigate the exclusive effect of the transformation without measuring the confounded effect that \"classes with fewer samples are more difficult\".\n\nPage 2, minor detail: \"in long-tailed and class-imbalanced settings\", Its a bit unclear to me what the difference between these two setting is (?).\n\nPage 2: \"we find that combining resampling methods with GIT further improves\", it seems to me that GIT itself is another version of re-sampling? Perhaps a more specific method geared towards invariance?\n\nEq 1: Minor detail: shouldn't \"x\" be \"x^{i}\" ?\n\nPage 3: \"want our model to perform well across all classes\". This is strange to me. In ERM a strong assumption is that P_train is distributed identically as P_test. In the setting where performing well over all classes is required, thus changes P_test from P_train. Does it make sense at all to use ERM then? Put in another way: if some classes are rare in the considered problem setting (which is why they are rare in P_train) then why is it to be expected that suddenly they do occur frequently when deploying the model? (not rare in P_test) ? Ie: optimizing *average* risk seems not the final goal here?\n\nPage 4: About the conclusions about fig 1: see my earlier remark (how can we be sure that this effect is just because of the transformations, and not due to the small nr of samples?)\n\nPage 5: I'm a bit confused what conclusion is now given by \"Hence modeling the transformations directly is the more natural choice on imbalanced datasets\". This paragraph seems to argue that a generative model does *not* suffer from class frequencies? Is this the goal of the paragraph? And if so, is that claim then true?\n\nPage 6-7: All classifier/architecture information is missing. A paper should be self-contained. If it is mandatory to read the appendix to understand the paper then the appendix is an essential part of the paper and thus the paper is over the page limit.\n\nFig 3: Where is the \"rotation\" experiment from Fig 1? The paper is incomplete. (If the appendix contains such essential results, then, in my opinion, the appendix becomes part of the main submission and should adhere to the same page limits that hold for other authors)\n\n\n", "summary_of_the_paper": "The paper investigates if robustness (or \"invariance\") to nuisance transformations which do not change the class label such as lighting, rotation etc are learned across all classes or if such robustness is sensitive to the class size. The paper demonstrates that such invariances seem not to transfer across classes: ie the classes with fewer examples suffer more. THe paper proposes a generative model (GIT) to \"augment\" the less frequent classes which, to some degree, remedies this problem.\n", "summary_of_the_review": "I'm sorry if my review reads negative, but I really like the paper!  I think the question it asks is insightful, fundamental and important. \nYet, I am not fully convinced by how this question is then investigated (see my detailed review below).\nI find the \"GIS\" part not so interesting, although it indeed remedies the symptoms and gives \"bold numbers\". I would be much more interested in *why* this happens. And if, for example, lighting plays a role, then why dont the first layers (which presumably are shared between classes) to some degree deal with this?\nIf the authors can somehow convince me, either with some new insights, or by new argumentation, I would be very happy to upgrade my score.\n", "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": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "EGtNb3YvFjU", "reviewer": "Reviewer_4nAf", "summary": "", "questions": "", "limitations": "", "rating": 6, "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": "===================\nStrengths:\n+This paper provides a new perspective to understand the long-tailed problem of DNN models. They found that the class-agnostic invariances cannot automatically transfer from the head to tail classes, which means the models are simply memorizing the data without understanding it.  Since humans are able to disentangle the class-specific contents from class-agnostic transformations, they can easily learn new contents (categories) through a limited number of observations. Therefore, this paper pinpoints that the key to solving the long-tailed problem might be disentangling the class-specific features from class-shared features.\n\n===================\nWeaknesses:\n- Despite the good motivation of this paper, the technical details of the paper are not satisfactory. For example, I think the authors confused the classifier with the entire model. A DNN classification model is usually composed of a backbone (like ResNet) and a classifier (e.g, Linear classifier or Cosine classifier). In algorithm 1, you only mentioned the classifier updating, but I guess it means the entire model here. Such a description is confusing in the study of long-tailed classification (LTC) because a commonly used strategy in LTC is called decoupling[1], which learns the backbone and the classifier separately.\n- Second, according to Figure 3, the proposed method actually hurt the invariance of head categories while the CE+DRS doesn't, which means GIT is not a good method to transfer the learned class-agnostic invariances from head to tail classes. Unlike the head-tail trade-off in the accuracy, I don't think the learned invariances should be forgotten. The eKLD of the CE+DRS also proves that the trade-off shouldn't be existing in the given invariance metric.\n- Besides, I don't think the GIT is necessary to increase the invariances of tail classes and the current ablation study is too simple. For example, how about using RandAug[2] for tail classes during training? It's much simpler than learning a generative model and I'm pretty sure that it can increase the invariance.\n\n[1] Decoupling Representation and Classifier for Long-Tailed Recognition\n[2] RandAugment: Practical automated data augmentation with a reduced search space", "summary_of_the_paper": "=======================\nSummary: \nThis paper studies the problem of how well do neural networks transfer class-agnostic invariances from head classes to tail classes. They found that even a given transformation is class-agnostic, the DNN models still cannot disentangle it from class-specific features, which could partially explain the worse performances on rare classes. To solve this problem, they introduce a GIT method that uses a generative model to augment the tail categories with more diverse samples under certain transformations. It can empirically improve the long-tailed performances and transfer the knowledge of class-agnostic transformations from head to tail.\n", "summary_of_the_review": "===================\nJustification:\nThis paper provides a new perspective to understand the long-tailed problem of DNN models, yet, the technical details and the solutions of the paper are not satisfactory", "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": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper investigates how well properties invariant to changes such as lightening and background learned in the major class can be transferred to the minor class. In this paper, the authors reveal that invariances do not transfer well to small classes, and suggest that resolving this phenomenon can help increase the performance on imbalanced datasets. From this point of view, the authors propose a generative model-based augmentation technique.

Three reviewers suggested acceptance, and one reviewer judged borderline reject. It seems true that the method is not novel enough, but it is solid and well motivated. In particular, the finding of the paper is interesting and the design of the experiment is well done, so I think that it will have a great influence on research in this field in the future. As the negative reviewer mentioned, the lack of large-scale experiments is a major weakness of this paper. I strongly encourage the final version to supplement the promises made to the reviewer, including adding iNaturalist experiments.
Decision: Accept (Poster)