AGRO: A DVERSARIAL D ISCOVERY OF E RROR - PRONE GROUPS FOR R OBUST O PTIMIZATION
Anonymous authors
Paper under double-blind review
A BSTRACT
Models trained via empirical risk minimization (ERM) are known to rely on spurious correlations between labels and task-independent input features, resulting in poor generalization to distributional shifts.
Group distributionally robust optimization (G-DRO) can alleviate this problem by minimizing the worst-case loss over a set of pre-defined groups over training data.
G-DRO successfully improves performance of the worst-group, where the correlation does not hold.
However,
G-DRO assumes that the spurious correlations and associated worst groups are known in advance, making it challenging to apply it to new tasks with potentially multiple unknown spurious correlations.
We propose AGRO—Adversarial Group discovery for Distributionally Robust Optimization—an end-to-end approach that jointly identifies error-prone groups and improves accuracy on them.
AGRO equips
G-DRO with an adversarial slicing model to find a group assignment for training examples which maximizes worst-case loss over the discovered groups.
On the
WILDS benchmark, AGRO results in 8% higher model performance on average on known worst-groups, compared to prior group discovery approaches used with
G-DRO.
AGRO also improves out-of-distribution performance on SST2, QQP, and
MS-COCO—datasets where potential spurious correlations are as yet uncharacterized.
Human evaluation of ARGO groups shows that they contain well-defined, yet previously unstudied spurious correlations that lead to model errors.
I NTRODUCTION
Neural models trained using the empirical risk minimization principle (ERM) are highly accurate on average; yet they consistently fail on rare or atypical examples that are unlike the training data.
Such models may end up relying on spurious correlations (between labels and task-independent features), which may reduce empirical loss on the training data but do not hold outside the training distribution (Koh et al., 2021; Hashimoto et al., 2018).
Figure 1 shows examples of such correlations in the MultiNLI and CelebA datasets.
Building models that gracefully handle degradation under distributional shifts is important for robust optimization, domain generalization, and fairness (Lahoti et al., 2020; Madry et al., 2017).
When the correlations are known and training data can be partitioned into dominant and rare groups, group distributionally robust optimization (G-DRO, Sagawa et al., 2019) can efficiently minimize the worst (highest) expected loss over groups and improve performance on the rare group.
A key limitation of G-DRO is the need for a pre-defined partitioning of training data based on a known spurious correlation; but such correlations may be unknown, protected or expensive to obtain.
In this paper, we present AGRO—Adversarial Group discovery for Distributional
Robust Optimization—an end-to-end unsupervised optimization technique that jointly learns to find error-prone training groups and minimize expected loss on them.
Prior work on group discovery limits the space of discoverable groups for tractability.
For example, Wu et al.
(2022) use prior knowledge about the task to find simple correlations—e.g. presence of negation in the text is correlated with the contradiction label (Figure 1).
However, such task-specific approaches do not generalize to tasks with different and/or unknown (types of) spurious correlations.
Approaches using generalizable features are semi-supervised (Sohoni et al., 2020; Liu et al., 2021) in that they assume access to group information on a held-out dataset.
However, obtaining supervision for group assignments is costly and can lead to cascading pipeline errors.
In contrast, AGRO is completely unsupervised and end-to-end while making no assumptions about the nature of the task and availability of additional supervision.
[Figure]
To address these challenges in AGRO, we construct a new parameterized grouper model that produces a soft distribution over groups for every example in the training data and is jointly trained with the task model.
We introduce two key contributions to train this model.
Firstly, the grouper model does not make task-specific assumptions about its inputs.
Instead, it relies on computationally extracted features from the ERM model including: (a) predictions and mistakes of the ERM model on training and validation instances, and (b) pretrained dataset-agnostic representations and representations fine-tuned on the task data.
Secondly, AGRO jointly optimizes the task model and grouper model.
We formulate a zero-sum game between the grouper model that assigns instances to groups and the robust model which seeks to minimize the worst expected loss over the set of inferred groups.
Specifically, while G-DRO optimizes the robust model to minimize the worst group-loss 1 , the grouper model adversarially seeks a probabilistic group assignment such that the worst group-loss is maximized.
On four datasets in the WILDS benchmark (Koh et al., 2021) (MultiNLI, CivilComments, CelebA, and
Waterbirds), AGRO simultaneously improves performance on multiple worst-groups 2 corresponding to previously characterized spurious correlations, compared to ERM and G-DRO with known group assignment.
AGRO also improves worst-group performance over prior approaches that find spurious correlations and groups by 8% on average, establishing a new SOTA for such methods on two of the WILDS datasets.
On natural language inference, sentiment analyses, paraphrase detection and common-object classification (COCO), AGRO improves robustness to uncharacterized distributional shifts compared to prior approaches, as demonstrated by gains in out-of-distribution datasets for these tasks.
Ablations on different parts of the framework underscore the need for a generalizable feature space and end-to-end optimization.
We develop a novel annotation task for humans to analyze the discovered AGRO groups—distinguishing group members from random examples and perturbing them to potentially change model predictions.
We find that humans can identify existing and previously unknown features in AGRO groups that lead to systematic model errors and are potentially spurious, such as the correlation between antonyms and contradiction in MultiNLI, or the correlation between hats, sunglasses and short hair with non-blondes in CelebA.
R ELATED W ORK
Group distributionally robust optimization G-DRO is a popular variant of distributionally robust optimization (DRO) (Ben-Tal et al., 2013; Duchi et al., 2016) that optimizes for robustness over various types of sub-population (group) shifts: label-shifts (Hu et al., 2018), shift in data-sources or domains (Oren et al., 2019), or test-time distributional shifts due to spurious correlations in training data (Sagawa et al., 2019).
Santurkar et al.
Koh et al.
(2021) introduce a benchmark for robustness to group shifts for measuring progress in this space.
There has been significant recent progress on this benchmark using optimization techniques apart from G-DRO — Zhang & Ré (2022);
Zhang et al.
; Piratla et al.
; Kirichenko et al.
However, all these techniques assume that groups or environments are available.
Recent work that focuses on group discovery include: (a) GEORGE (Sohoni et al., 2020), which clusters ERM representations to discover groups, (b) JTT (Liu et al., 2021) and LfF (Nam et al.,
2020), which use misclassified classes as groups, (c) Nam et al.
(2022) use annotations for spurious features on a small subset to build a learned group identifier, and (d) EIIL (Creager et al., 2021) and
PGI (Ahmed et al., 2020), which infer groups that maximally violate the invariant risk minimization (IRM) principle (Arjovsky et al., 2019).
EIIL is especially relevant to our work: it adversarially maximizes the IRM objective to discover groups.
However, the approach is currently limited to two-class problems, and moreover, is challenging to apply for large datasets of the kind we study in this work.
Importantly, all these techniques are at least partially supervised, as they assume group memberships are available on a validation set for hyperparameter tuning or model selection.
This is a crucial resource, since an ERM-optimized model with access to such a set is also a competitive baseline (Gulrajani & Lopez-Paz, 2020).
Another closely related work on distributional robustness for group fairness is ARL (Lahoti et al., 2020), which adversarially trains a network to find instance weights for re-weighting of training examples.
One of the core difference between AGRO and ARL is the instance- vs group-based re-weighting.
Model errors have been found to be systematic, i.e., occurring in groups (Oakden-Rayner et al., 2020).
ARL precludes post-hoc analysis of such patterns due to instance-level modeling.
Slice Discovery Methods (SDMs)
A related problem to robust optimization is automatic slice discovery (SD)—identifying underperforming data slices for error analysis of deep-learning models.
Prior work on SD has used data with tables and metadata (Polyzotis et al., 2019; Sagadeeva & Boehm, 2021).
SDMs on unstructured data (Kim et al., 2019; Singla et al., 2021; d’Eon et al., 2022) rely on embedding inputs, dimension reduction, and clustering.
Recently, Eyuboglu et al.
(2022) propose
DOMINO, an error-aware mixture-model based clustering of representations on the evaluation set.
While SDMs can help determine patterns in model failures and making them human-comprehensible, they have not been applied for distributional robustness to group (slice) shifts.
M ETHOD 3. P RELIMINARIES
Problem Setup We consider the typical image/text classification problem of predicting labels y ∈ Y from input x ∈ X .
Training data D is drawn from the joint distribution P ( X , Y ) .
In state-of-the-art classification models, inputs are typically encoded using multi-layered pretrained transformers (Vaswani et al., 2017;
He et al., 2021; Bao et al., 2021)
We use g ( x ) and h ( x ) to represent input encoding before and after fine-tuning these encoders on D .
ERM principle Given a model family Θ and a loss function l : Θ × X × Y → R + , empirical risk minimization aims to find a model θ ∈ Θ that minimizes empirical loss over data drawn i.i.d from the empirical distribution P .
ˆ θ
ERM :=
argmin θ ∈ Θ E ( x,y ) ∼ P [ l ( x, y ; θ )] .
While ERM models achieve high accuracy on i.i.d.
evaluation data on average, they often underperform when the test distribution shifts significantly from the training distribution (Madry et al., 2017).
ERM also underperforms on a biased sample of the test set where a spurious correlation is absent (Koh et al., 2021).
G-DRO for Robust optimization Group-DRO (Sagawa et al., 2019) is a category of distributionally robust optimization (DRO, Duchi et al., 2016), where training distribution P is assumed to be a mixture of m groups, and each training point ( x, y ) comes from one group g ∈ G .
G-DRO minimizes the empirical worst-group risk
ˆ R ( θ ) i.e. worst (highest) empirical loss over m groups:
[Equation]
,y | g )
[ l ( x, y ; θ )] } , where p ( x, y | g )
∀ g is the empirical distribution of training data over groups.
With sufficient regularization over θ , G-DRO enables training models that are robust to test-time worst-group distributional shifts.
In practice, prior work adopts the efficient and stable online greedy algorithm (Oren et al., 2019) to update θ .
Specifically, worst-group risk ˆ R ( θ ) :
=
max q ∈Q E g ∼ q, ( x,y ) ∼ p ( x,y | q )
[ l ( x, y ; θ )] .
The uncertainty set Q are categorical group distributions that are α -covered by the empirical distribution over groups p train i.e. p train ( g ) :
= | 1 ( g i = g ) ∀
i ∈ D | / | D | and Q = { q : q ( g ) ≤ p train ( g ) /α
∀ g } .
Effectively, this algorithm up-weights the sample losses by 1 α which belong to the α -fraction of groups that have the worst (highest) losses, where α ∈ (0 , 1) .
Details of this algorithm are presented in Appendix A.2.
G-DRO is limited to scenarios where both spurious correlations and group memberships are known, which is often not the case.
[Table]
Error slice discovery DOMINO (Eyuboglu et al., 2022) shows that systematic mistakes made by models due to reliance on spurious correlations can be exposed via clustering of the model
’s representations X , predictions ˆ Y and reference labels Y .
DOMINO learns an error-aware mixture model over { X, Y, ˆ Y } via expectation maximization, finding m error clusters over the evaluation set.
Such a clustering can potentially be used for group assignment since the examples in a cluster are coherent (i.e. united by a human-understandable concept and model prediction) and suggestive of a specific feature that the model exploits for its predictions.
However, overparameterized neural models often perfectly fit the training data, resulting in zero errors (Zhang et al., 2021), i.e. Y =
ˆ Y .
3. AGRO: A DVERSARIAL DISCOVERY OF G ROUP FOR R OBUST O PTIMIZATION
AGRO combines insights from group distributionally robust optimization and error slice discovery, introducing a novel end-to-end framework to accomplish both objectives.
We formalize the problem of group discovery for robustness , where g is an un-observed latent variable to be inferred during the training process.
We replace discrete group memberships 1 ( g i = g ); g ∈ G with a soft-group assignment, i.e. a probability distribution over groups
P i,g := p ( g | f i ; ϕ ); g ∈ G .
P i,g refers to the probability that the i -th example belongs to the g -th group and is realized by a neural network q with parameters ϕ .
This enables modeling co-occurring spurious features and overlapping groups.
The input to the grouper model q is a high-dimensional feature vector f i ∈ F that can potentially encode the presence of spurious correlations in example
i (described in section 3.3).
AGRO jointly trains the parameters of the robust task model, θ , and the grouper model, ϕ , by setting up a zero-sum game between the robust model and the grouper model.
The optimization occurs over
R alternating game rounds—the primary round that updates the task model θ and the adversary round that updates the grouper parameters ϕ .
Parameters that are not optimized in a given round are frozen.
In the primary round, the optimizer seeks to minimize the worst-group loss (exactly the GDRO objective), while in the adversary round, it seeks to find a group assignment that maximizes the worst-group loss.
In doing so, the adversary finds a group assignment that is maximally informative for the primary, since it produces a loss landscape over groups that is highly uneven.
This forces the primary model, in the next round, to aggressively optimize the worst empirical loss to even out the landscape.
With p train ( g ) :
= (cid:80) i ∈
D P i,g / | D | and uncertainty set Q is defined as before, the AGRO optimization objective is:
[Equation]
Primary Round
In round r , the primary classifier finds the best parameters θ that minimize the worst-group loss based on the current dynamic group assignments provided by ϕ in round r − 1 .
Updates to θ are similar to the online greedy updates used by Oren et al.
(2019) i.e. up-weight the loss of α fraction of groups with the highest loss, then minimize this weighted loss.
Adversary Round
In round r + 1 , the adversarial grouper updates ϕ and learns a soft assignment of groups that maximizes the loss of the worst-group (highest loss group).
In practice, we adopt the converse of the greedy updates made in the primary round, i.e. down-weight the loss of α fraction of groups with the highest loss, and then maximize this weighted loss.
For stable optimization, we iterate over T 1 minibatches of training data to update θ in the r th round and iterate over T 2 minibatches to update ϕ in the r +1 th round.
Algorithm 1 presents the pseudo-code for AGRO.
Implementation details, along with hyper-parameter values for T 1 , T 2 , α, m and R , are described in Appendix A.2.
In the first primary round, we start with a random group assignment (i.e. random initialization for ϕ ), which amounts to training an ERM model.
θ is initialized with a pretrained transformer-based encoder and MLP classifier.
In the first adversary round, we adopt a different initialization for ϕ , which is explained in Section 4.
The grouper model ϕ takes as input a feature vector f i ∈ F for each training example x i .
Next, we describe our choice of F .
3. F EATURES FOR G ROUP D ISCOVERY
Most prior work uses some knowledge about the task (Wu et al., 2022; Gururangan et al., 2018), data collection process (Poliak et al., 2018) or metadata information (Koh et al., 2021) for group discovery.
Instead, we develop an unsupervised end-to-end group discovery method that does not rely on any task-specific knowledge.
We do so using general purpose features f i ∈ F that can potentially indicate the presence or absence of a spurious correlations.
ERM features and errors We use features from weaker ERM models (i.e., under-trained, smaller capacity ones), which have also been used in prior work for automatic group discovery Creager et al.
(2021); Sohoni et al.
DOMINO (Eyuboglu et al., 2022) additionally clusters model representations and errors to generate coherent error slices on held-out data.
However, overparameterized models often perfectly fit training data.
To estimate model errors on training data, we apply K-fold cross-validation to get model predictions on held-out training instances in every fold.
Specifically, for a training example x i assigned to the k -th fold’s held-out set, we compute the following features: the model’s fine-tuned representations h ( x i ) , the reference label y i , and the vector of prediction probabilities over labels { p (ˆ y i | x i ; θ k ) ∀ ˆ y i ∈ Y} , where θ k is the fold-specific ERM classifier.
Pretrained features Recent work has shown that large transformer-based models trained on web-scale data learn general features for images which improve on out-of-distribution data (Wortsman et al., 2022a;b).
Pretrained models are less likely to encode dataset-specific features in their representations.
Following this observation, we also include pretrained representations g ( x i ) of the input x i .
In sum, the group discovery features f i for a training example x i are: the representations g ( x i ) and h ( x i ) , the label y i and the probabilities { p ( ˆ y i | θ k ) ∀ ˆ y i ∈ Y} .
E XPERIMENTAL S ETUP
Datasets with known spurious correlations We evaluate performance on four datasets in language and vision from the popular WILDS benchmark (Koh et al., 2021) to study in-the-wild distribution shifts.
We select tasks that contain more than one known worst-group and report on the top three known worst-groups (referred to as KWGs) from these datasets, chosen based on the rate of correlation between feature and label.
Table 1 briefly describes these known worst-groups by dataset.
More details about tasks descriptions, statistics, and pre-processing can be found in Appendix A.3.
Datasets without known spurious correlations Our main contribution is a fully unsupervised end-to-end technique for group discovery and robustness, which can be applied off-the-shelf on a new dataset with no additional annotation.
To evaluate this, we train AGRO for robustness to spurious correlations in datasets with possibly unknown biases and evaluate its generalization on OOD datasets, where such correlations may not hold.
We train models on two datasets from the GLUE benchmark (Wang et al.
, 2018)—Stanford Sentiment analysis (SST2) and Quora question paraphrase detection (QQP), and a modified version of image classification on the MS-COCO dataset (Lin et al., 2014),
COCO-MOD.
We evaluate on out-of-distribution (OOD) datasets for these tasks, like IMDb (Maas et al., 2011) for SST2, PAWS (Zhang et al., 2019) for QQP, and SpatialSense (Yang et al., 2019) for
MS-COCO.
Hyperparameters For θ , we use transformer-based (Vaswani et al., 2017)
pretrained models that have been shown to be robust to rare correlations (Tu et al., 2020), including DeBERTa-Base (He et al., 2020) for text classification and BEIT (Bao et al., 2021) for image classification.
ϕ is an 2-layer
[Table]
MLP with a softmax activation layer of size m (the number of groups).
Appendix A.4 and A.6.
further detail hyperparameter tuning, particularly for AGRO-specific hyperparameters α and m .
Initializing ϕ
A random initialization to grouper ϕ can result in a degenerate group assignment, where all examples are assigned the same group.
Such an assignment still results in a small proportion of groups ( one group) having the maximum loss.
This reduces to the ERM solution.
To mitigate this behavior, we initialize the grouper model’s parameters ϕ in the first adversary round to predict the same group memberships as the clusters from DOMINO (Eyuboglu et al., 2022), which was described in Section 3.1.
Our ablation results in Section 6 show that AGRO improves over directly using DOMINO slices as groups for G-DRO.
Details about the pretraining of ϕ are in Appendix A.2.
Model Selection Unlike prior work on automatic group discovery (e.g, Liu et al., 2021; Creager et al., 2021), we do not assume access to group annotations on the validation set based on a known spurious correlation to tune hyperparameters or to choose the best model checkpoints.
We develop a new strategy for model selection based on the learned grouper model ϕ .
We select the best model based on the combined performance of α -fraction of the worst-performing groups discovered by AGRO.
For a fair comparison with the baselines described below, we similarly use the worst-group available to each baseline.
In Section 6, we relax this assumption for all methods (AGRO and baselines) and use KWG1 of each dataset for model selection.
Baselines We compare against previous automatic group discovery approaches used with G-DRO:
JTT: Liu et al.
(2021) retrain on training data errors made by a weaker ERM model.
Model selection is based on errors made on the validation set.
GEORGE: Sohoni et al.
(2020) cluster the training and validation sets based on ERM features and loss components.
The worst-group on the validation set is used for model selection.
EIIL: Creager et al.
(2021) propose to train a group discovery model to adversarially maximize the invariant risk minimization objective.
Upon examination of their experimental details, we find that for all large datasets (that we report on), they use labels as groups, since EIIL is hard to scale.
We follow the same procedure to compare EIIL with AGRO.
For small datasets Waterbirds and SST2, we use EIIL as is.
The class with the worst validation performance is used for model selection.
G-DRO : Following (Sagawa et al., 2019), we optimize G-DRO based on a group assignment for a known spurious correlation, and use the same assignment on the validation set for model selection.
G-DRO serves as an upper bound on the worst-group performance for this spurious correlation.
Specifically, we use KWG1 to run G-DRO on all datasets.
ERM: ERM models trained for longer and with larger batch size already improve worst group performance (see Appendix A.6), making for a strong baseline.
R ESULTS 5. AGRO IMPROVES ROBUSTNESS TO MULTIPLE SPURIOUS CORRELATIONS
AGRO learns a soft group assignment over training data, with the goal of improving worst-group accuracy over multiple co-occurring correlations.
We evaluate this hypothesis on the selected datasets from WILDS (Table 1).
Table 2 reports accuracy on the full evaluation set and on multiple worstgroups.
Additional results using weaker pretrained models are in the Appendix A.6.
Across datasets, AGRO improves worst-group accuracy by 25.5% on average over the ERM baseline without hurting the overall task accuracy.
In particular, it improves across multiple known worstgroups for each dataset.
On all datasets except CelebA, for KWG1, AGRO gets within 2% of the accuracy obtained by G-DRO with ground truth groups.
This shows that ARGO’s unsupervised
[Table] [Table]
[Table]
group discovery and robust optimization performs nearly as well as using the best manually designed groups.
No other baseline consistently improves worst-group accuracy over all tasks.
Approaches like
GEORGE, JTT and EIIL have mixed results across datasets.
Their performance depends on specific properties of the test datasets, such as high spurious correlation ratio (in CelebA) or severe label imbalance (in Civilcomments).
These results indicate that AGRO is most suitable for new datasets whose key properties are unknown.
Section 5.2 explores this further.
On MultiNLI , DeBERTa-based models achieve the best reported worst-group performance by both the ERM model and the G-DRO model (trained using KWG1 assignments).
The relative gap between worst and average accuracy persists with a weaker model like RoBERTa (see Appendix A.6).
AGRO has an 8% improvement over the next highest baseline on this task (EIIL).
GEORGE, which uses loss components for clustering groups and for model selection, underperforms even on in-domain data, potentially from over-fitting to groups with label noise.
The worst group performance of AGRO establishes a new state of the art for group robust optimization approaches that also find groups.
On
Waterbirds , the ERM model finetuned using BEIT has competitive worst-group accuracy, surpassing the performance gap of a weaker model like ViT(see Appendix A.6).
We hypothesize that a stronger pretrained model is generally less susceptible to spurious correlations (Wortsman et al., 2022a).
On both worst groups, AGRO outperforms ERM and has comparable performance with the next best baseline GEORGE, once again achieving SOTA.
CelebA and Civilcomments have overlapping groups i.e. images with multiple facial attributes and comments with mentions of multiple demography labels, respectively.
Consequently, the performance of G-DRO with ground-truth groups for KWG1 also improves performance on other worst groups.
On the Male-Blonde group in CelebA , AGRO outperforms the ERM model by 75%.
It also outperforms
GEORGE and EIIL on this group.
Owing to a high rate of spurious correlation in the dataset (male:non-male blondes ratio is 0.02), re-weighting misclassified points (JTT) proves to be an effective grouping mechanism.
Civilcomments has a significant label imbalance (a ratio of 0.
for toxic to non-toxic, the lowest for all datasets considered in this work).
Consequently, using the label-as-group heuristic (EIIL) performs the best among other baselines, followed by AGRO.
5. AGRO IMPROVES ROBUSTNESS TO DISTRIBUTION SHIFTS ON NEW TASKS
Since AGRO is fully unsupervised, it can be used off the shelf to improve distributional robustness on a new task.
To evaluate this, we apply AGRO to SST2, QQP, and COCO-MOD, datasets where spurious correlations and worst-groups are unknown.
Models trained on these datasets are tested on out-of-distribution (OOD) datasets, where spurious correlations learned in-distribution may not hold.
In Table 3, we report average and out-of-distribution accuracies achieved by AGRO and two best performing baselines, GEORGE and EIIL.
We also report OOD performance for MultiNLI.
A striking observation across tasks and datasets is that baselines generally underperform ERM on general out-of-distribution robustness.
We hypothesize that this may be because of over-fitting to noisy groups with high losses.
G-DRO can be effective at improving OOD robustness if distributional shifts in the groups correspond to distributional shifts at test time.
We hypothesize that the baselines overfit to groups in the in-domain data in unexpected ways due to their simplified grouping heuristics, resulting in poor OOD generalization.
On MultiNLI, AGRO outperforms ERM by 3.0% on average across OOD datasets.
On COCO-MOD, AGRO outperforms ERM by 2% on the OOD dataset.
On
SST2, AGRO improves performance over ERM on most datasets by 0.5-5.5% except on Senti (Twitter sentiment classification dataset).
On QQP, AGRO outperforms other baselines, including
ERM.
The JTT baseline on QQP gives us the best results on out-of-distribution data, but at the cost of in-domain performance.
We hypothesize that AGRO’s
OOD gains stem from reduced reliance on dataset-specific correlations.
A NALYSIS
We present detailed analysis to determine which aspects of AGRO contribute the most to its strong unsupervised performance and do a qualitative study of AGRO groups.
Feature Ablation Table 4 (right) reports the impact of adding different features used in AGRO on the MultiNLI dataset.
We find that using error-aware clustering of features (i.e. DOMINO in Row 3) as group assignments improves worst-group performance compared to clustering based on features alone (i.e. only using h ( x i ) ).
Using adversarial group discovery along with these features especially boosts performance on the worst group, underscoring the importance of our end-to-end framework.
Finally, adding pretrained features to AGRO gives us the best performance on MultiNLI.
Ablation results for Waterbirds are in Appendix A.6.4.
Model Selection Table 4 (left) reports the results on using knowledge of worst group during evaluation for model selection.
We report worst-group performance(of KWG1) of AGRO and all baselines for
MultiNLI by selecting model checkpoints based on that worst group.
The worst-group performance of all baselines increases.
For AGRO, our selection strategy from Section 4 is as effective as using the known worst group for selection (the results remain unchanged).
AGRO and the baselines EIIL and
GEORGE have competitive worst-group accuracies.
These observations hold on the Waterbirds data as well (A.6).
Our selection strategy can potentially also be used with other group robust optimization techniques, which we will explore in future work.
Small-scale human study Appendix A.8 has examples of slices discovered by AGRO on several datasets.
The core goal of AGRO is to discover error-prone groups without prior knowledge of
[Table]
WG1:
Qualifiers like “all, only, solely" with Neutral class.
P: Chapter 5 focuses on synergistic combinations of control retrofits on a single unit.
H:
Chapter 5 focuses solely on synergy (Neutral → Entail) P:but that that’s my that’s probably my main hobby that sewing and reading books that’s about it H:
Sewing and reading books are my only hobbies.
(N → E) P:Nuns are in their habits and Israeli women in military uniforms.
H:All Israeli women are in the military, which is why they wear military uniforms.
(N → E) WG2: Antonyms in P and H with Contradiction class.
P: Stand behind it.
H: Stand so that it is in front behind of you.
(Contradict → Entail)
[Table]
: Look for the
[Table]
Hotel on the western end of the square.
H:
You can see the Cecil
[Table]
from the centre west of the square.
(C → E)
[Table]
Get there
[Table]
the
[Table]
the crowds
[Table]
You should
[Table]
there shortly after
[Table]
they
[Table]
to beat the crowds.
[Table]
is needed to ascertain whether a model exploits any spurious correlations in the discovered slices (Eisenstein, 2022).
Soliciting human feedback is challenging since models may exploit spurious correlations that do not correspond to human-interpretable or identifiable features.
We design two annotation tasks to obtain feedback indirectly.
The first annotation task evaluates coherency .
Annotators are shown four instances from a group identified by AGRO, along with two other test instances, only one of which is from the same group.
The annotators are asked to identify the test instance that belongs to the group.
The second annotation task follows the first, where the annotators are asked to perturb the instance chosen to be part of the AGRO group in such a way that the task model’s prediction would change.
This exercise can implicitly surface the common feature humans think exists in the slice.
We conduct the human study on 5 slices each from MNLI, SST and CelebA. More details of the human annotation setup can be found in Appendix A.7.
For Task 1, we find that inter-annotator agreement has a score of 0.7823 Fleiss Kappa.
Humans were able to identify the correct group member 70.1% of the time.
Some examples of the flips provided by human annotators in Task 2 are presented in Table 5.
We often see specific patterns in the perturbations humans make within each group, which indicates that the perturbations may be automated in future work to interpret model behavior on a large scale, or for building harder evaluation sets.
C ONCLUSION
We studied the challenge of applying G-DRO to new tasks with multiple, unknown spurious correlations and groups and present AGRO—Adversarial Group discovery for Distributionally Robust
Optimization— an end-to-end approach that jointly identifies error-prone groups and improves model accuracy on these groups.
AGRO’s adversarially trained grouper model finds a soft group assignment that is maximally informative for G-DRO.
Compared to prior work, AGRO is a more effective off the shelf optimization technique for fully-unsupervised group discovery and robustness on new tasks.
Like other approaches that use G-DRO, AGRO’s improvement on test distribution shifts is limited if training and test distributions are very distant, which we will explore in future work.
A A PPENDIX A. A DDITIONAL R ELATED WORK Other Robust
Optimization
techniques
Other approaches for robustness to group distributional shifts include data augmentation and ensemble learning.
(Liu et al., 2022; Wu et al., 2022) (for
MultiNLI) and (Plumb et al., 2021) (for COCO
) use data augmentation.
However, they make task-specific assumptions about the types of features that can be spurious to generate additional data.
Product-of-experts(PoE)-based (Hinton, 2002)approaches like (Sanh et al., 2020; Mahabadi et al., 2019;
He et al., 2019) use a biased model to construct a robust ensemble.
The biased model is typically constructed using task-specific information.
Since Since AGRO finds error-prone groups that potentially encode model biases, these groups can be used for data-augmentation or PoE approaches in future work.
A. A LGORITHMS AND I MPLEMENTATION D ETAILS
G-DRO Algorithm 2 presents the online greedy algorithm used in G-DRO.
Note that group assignment over training data is based on a predefined spurious correlation.
EMA refers to exponential weighted moving average.
i.e. EMA ( v 1 , v 2) = γv 1 + (1 − γ ) v 2 , where γ ∈ (0 , 1) and α ∈ (0 , 1) .
A is the α fraction of groups with the highest loss.
Specifically, based on the group proportions ˆ p ( t ) train , A consists of those groups with high loss values that make up α -fraction of the dataset.
The greedy up-weighting scheme is based on the CVaR-style implementation of G-DRO from Zhou et al.
(2021) and Sagawa et al.
They seek to optimize:
[Equation]
The uncertainty set Q are group distributions that are α -covered by p train , which is the empirical distribution of groups in training data.
Specifically, p train ( g ) is the proportion of training examples that belong to group g .
[Equation]
, and
[Equation]
In their code, Zhou et al.
(2021) recognize that p train ( g ) can’t be exactly computed since optimization occurs in mini-batches.
| 1 ( g i = g ) ∀
i ∈ D | is therefor estimated based on the number of examples of group i in minibatch (of size B).
In order to have an unbiased estimate for p train ( g ) they maintain an expected moving average ˆ p train ( g ) .
Thus,
[Equation]
In implementation, the optimization up-weights the sample losses by 1 α which belong to the α -fraction of groups that have the worst (highest) losses, where α ∈ (0 , 1) .
This algorithm is presented in
Appendix A.2.
All the other groups are down-weighted by a minimum group weight, w .
We set w = 0 .
1 following prior work.
We tune α based on known worst-group accuracy on each dataset.
DOMINO (Eyuboglu et al., 2022) propose a mixture model that jointly models input embeddings, class labels, and model predictions.
This encourages s slices that are homogeneous with respect to error type (e.g. all false positives), while also being coherent with respect to human-interpretable features.
The model assumes that data is generated according to the following generative process: each example is randomly assigned membership to a single slice among k possible slices according to a categorical distribution S ∼ Cat ( p S ) with parameters p S ∈ { p ∈ R
k
+ : (cid:80) ki
=1 p i = 1 } .
Given membership in slice j , the embeddings are distributed normally as Z | S ( j )
= 1 ∼ N ( µ ( j ) , Σ ( j ) ) with parameter mean µ ( j ) ∈ R d and covariance Σ ( j ) ∈
S d ++ (the set of symmetric positive definite d × d matrices), the labels vary as a categorical Y | S ( j ) = 1 ∼ Cat ( p ( j ) ) with parameter p ( j ) ∈ { p ∈
R c + : (cid:80) ci =1 p i = 1 } , and the model predictions also vary as a categorical Y | S ( j )
= 1 ∼ Cat ( ˆp ( j ) ) with parameter ˆp ( j ) ∈ {
ˆp ∈ R c
+ : (cid:80) ci
=1 ˆ p
i
= 1 } .
The embedding, label, and prediction are all independent conditioned on the slice.
The mixture model is parameterized by ϕ =
[ p S , { µ ( j ) , Σ ( j ) , p ( j ) , ˆp ( j ) }
k j =1 ] .
The log-likelihood over the validation dataset D v is given as follows and maximized using expectation-maximization: l (
[Equation] [Equation]
, where γ is a hyperparameter that balances the trade-off between coherence and under-performance and h θ ( x i ) are the class logits predicted by the ERM model on example x i .
γ is set to 1 for all the datasets considered in this work.
AGRO The AGRO optimization objective is as follows:
[Equation]
The uncertainty set Q are group distributions that are α -covered by p train , similar to G-DRO.
However, p train ( g ) is the proportion of training examples that belong to group g .
[Equation]
In the case of AGRO, p train ( g ) is computed based on a group assignments probabilities output by the adversary model ϕ trained in the previous round.
Specifically, for minibatch B
[Equation]
, where p ( g | f j , ϕ ( t − 1) ) is the probability of example j in the minibatch belonging to group g, which is estimated by the adversary model ϕ .
Primary Round To optimize θ , we up-weights the mini-batch sample losses by 1 α which belong to the α -fraction of groups that have the worst (highest) losses, where α ∈ (0 , 1) .
All the other groups are down-weighted by a minimum group weight, w .
We set w = 0 .
1 following prior work.
We tune α based on known worst-group accuracy on each dataset.
Secondary Round
We compute probability distribution over m groups for instance i , P ( t ) i , using the grouper model of the previous iteration, ϕ ( t − 1) .
This soft group assignment is then used to compute weighted loss and soft group count for the minibatch in iteration t .
As described in 3.2, in order to train the grouper model in the adversary round, we reverse the greedy weighting procedure adopted in G-DRO.
Therefore, if A is the α fraction of groups with the highest loss, the α -fraction of groups in A are down-weighted by α , while all the other groups are up-weighted by a maximum group weight, w .
We set W = 1 . 0 , which we find works for all the datasets considered in this work.
Iterative optimization We set the number of rounds to R = 1 , since we found no further gains with more rounds of AGRO and high computational cost.
The computational cost for further rounds is considerable since the feature space F needs to be re-computed for the new robust model θ .
The optimization process is further simplified by setting T 1 and T 2 to a certain number of epochs.
Since we first begin with training the primary model in round 0, we start with a random group assignment, which basically amounts to training a weaker ERM model for T 1 epochs.
After this we train the adversary for T 2 epochs.
After one round of training the primary and adversary model, we again train the primary model for the same number of epochs that we use to train a strong ERM model baseline that we compare against.
Hyperparameters m and α are tuned for each dataset separately, which we explain in greater detail in Appendix A.4.
Initializing ϕ
In the adversary round, the grouper model learns a soft assignment of groups that maximizes the loss of the worst-group (highest loss group).
In practice, this means down-weighting the loss of α fraction of worst-loss groups and then maximizing this weighted loss.
If ϕ is initialized randomly, the maximization results in a degenerate solution — all examples are forced into one group.
This solution trivially maximizes the loss over a small α fraction of groups, since all examples are forced into those α groups.
In order to prevent this degeneracy, we provide an initialization to ϕ that already creates an uneven loss distribution over groups.
DOMINO clusters examples based on model errors, labels and representations.
Consequently, they possess two properties that can be a good initializing for ϕ — (a) Coherence, slices that have similar features are grouper together, and (b) Homogeneous errors, slices with the same predicted and reference label are generally grouper together.
Thus, we train the grouper MLP parameters ϕ to predict cluster memberships provided by DOMINO on training data (which we obtain using K-fold training).
Specifically, we minimize the KL-divergence between the probability distribution over groups generated by the grouper model and the probability distribution over groups predicted by the generative mixture model trained by
DOMINO.
We pre-train the grouper model for 10 epochs, with a batch size of 256.
Constructing F
Figure 2 is a visualization of the feature generation pipeline used to create features for the grouper model f i ∈
F∀ x i ∈ D .
[Table]
A. T RAINING AND E VALUATION DATASETS A.3. WILDS BENCHMARK
We experiment with 4 datasets from the WILDS benchmarkKoh et al.
(2021) with multiple potential spurious correlations.
Each is described in greater detail here.
For more detail on each task, we refer the reader to original paper that used them for G-DRO — Sagawa et al.
MultiNLI Williams et al.
(2017) task is to classify a pair of sentences as one of entailment, neutral, contradiction.
We follow the train/dev/test split in (Sagawa et al., 2019), which results in 206, training examples.
(Gururangan et al., 2018) identified that negation words in the second sentence are spuriously correlated with the contradiction labels.
Accordingly, examples are grouped based on if the second sentence contains any negation word in the list (nobody, nothing, no, never).
Test/validation data follows same group-class distribution as train.
In addition to the negation spurious correlation that is tested in the standard benchmark, we also test for the correlation between lexical overlap and the entailment label.
To construct groups for this correlation, we consider token-level overlap (number of common token-types between premise and hypothesis normalized by hypothesis length) > 0 .
9 to contain the lexical overlap heuristic.
In order to measure robustness to general distributional shifts on
MNLI, we also evaluate on the following out-of-distribution datasets following (Wu et al., 2022).
The
NLI adversarial test benchmark Liu et al.
(2020b) that tests for the following heuristics/short cuts that models may exploit: (a) Partial Inputs (PI) Heuristics Gururangan et al.
; Liu et al.
(2020a)
; (b) Inter-sentences (IS) Heuristics, specifically the syntactic diagnostic dataset HANS McCoy et al.
(2019); (c) Logical Inference Ability (LI) Glockner et al.
; Minervini & Riedel (2018); and (d) Stress-test (ST) Naik et al.
We also evaluate on other crowdsourced NLI datasets like
SNLIBowman et al. (2015), WaNLILiu et al.
and Adversarial NLI Nie et al.
WaterBirds WaterBirds task is to predict if an image contains water-bird or a land-bird and contains two groups: majority, minority in ratio 62 : 1 in training data.
The minority group has reverse background-foreground coupling compared to the majority.
Test/validation data has equal proportion of each group.
CelebA CelebA Liu et al.
(2018) task is to classify a portrait image of a celebrity as blonde/nonblonde, examples are grouped based on the gender of the portrait’s subject.
The training data has only 1 , 387 male blonde examples compared to 200 K total examples.
Test/validation data follows same group-class distribution as train.
CivilComments CivilComments-WILDS Borkan et al.
(2019) task is to classify comments as toxic/non-toxic.
Examples come with eight demographic annotations: (white, black, LGBTQ, muslim, christian, other religions, male and female) based on if the comment mentioned terms that are related to the demographic.
This leads to a significant group overlap, where the same comment will have several demography words at once.
Label distribution varies across demographics.
In the benchmark train examples are grouped on black demographic, and testing is done on the worst group accuracy among all 16 combinations of the binary class label and eight demographics.
In particular, we report on the three worst groups i.e. groups with rarest co-occurrence rate between demography label and class label — LGBTQ-toxic, other religions-toxic and black-toxic.
A.3. O THER DATASETS
To demonstrate the effectiveness of AGRO on new datasets where spurious correlations may be uncharacterized as of yet, we experiment with two additional text classification tasks and 1 image classification task.
Since the worst-group based on a known spurious correlations is not known, we instead measure performance on out-of-distribution data which can contain unknown group-shifts.
While AGRO does not target those specific group shifts and is only guaranteed to provide robustness over group distributions that it finds in-domain, we believe that generally reducing reliance on spurious correlations may lead to improvements on other group shifts as well.
SST2 SST2 task Socher et al.
(2013) from the GLUE NLU benchmark Wang et al.
(2018) is to classify 1-sentence movie reviews as positive or negative.
SST2 has an equal proportion of labels in training and evaluation sets.
For robustness evaluation, we use the same out-of-distribution datasets as those used by (Wu et al., 2021) — twitter sentiment analysis tasks (Go et al.
; Asghar, 2016), ImDB sentiment analysis Maas et al.
(2011), and counterfactual datasets constructed over ImDB Gardner et al.
(2020) (Contrast) and Kaushik et al.
(2021) (CAD).
QQP Quora question paraphrase detection task (QQP) from GLUE is to classify a pair of question extracted from the Quora platform as paraphrase or not-paraphrase.
The task consists of 400, label-balanced training instances.
For robust evaluation, we use (Zhang et al., 2019), a dataset consisting of a group distributional shift that tests for the spurious correlation of
COCO-MOD
We modify the COCO (Common Objects in Context)(Lin et al., 2014) image classification dataset into a 7-class problem instead of the more complex 80 object classification problem.
We select the following 7 classes: [Tie, Toothbrush, Bird, Frisbee, Tennis racket, Dog,
Fork].
These classes are specifically chosen based on the findings of Plumb et al.
(2021) (see Table 2).
They find that these 7 object classes are often associated with other spurious objects.
For example,
[Table] [Table]
ties with cats and toothbrushes with people.
We apply AGRO on the classification task for theseobjects to potentially rediscover these correlations.
A. H YPERPARAMETER SEARCH
Hyperparameter search for G-DRO are other baselines are discussed individually in A.5.
Here, we focus on hyperparamter search for AGRO.
The list of hyperparameters and the range of values used for search can be found in Table 6.
Since the hyperparamter space to explore is quite large, we use the following values for other hyperparameters that we keep fixed while doing a linear sweep over a particular hyperparameter.
The order of hyperparamter search is in the same order as the rows in Table 6.
In Table 7, we report the final set of hyperparameters used for each of the datasets we implement AGRO on.
The exponential weight decay parameter used in greedy G-DRO is set to a default value of 0 .
5 following prior work and is not tuned.
Hyperparameter search procedure : m (the number of groups) is set to 2 times the number of labels in the classification task.
This is based on the assumption that one spurious correlation divides training data twice as many groups as the number of labels (groups with and without the feature).
A default of 0.2 is used for α , following the value that was used for G-DRO on all datasets in Zhou et al.
T 1 i.e. the number of epochs used to train the primary model in the first round is set to 3 epochs, following Sanh et al.
(2020), where a bias-only model is trained on fewer epochs before using product of experts.
This basically amounts to training a weaker ERM model, since we start with a random assignment of groups in the first primary round.
The default value for T 2 i.e. the number of epochs used to train the adversary, is 1.
After one round of training the primary and adversary, we again train the primary model for the same number of epochs that we use to train a strong ERM model baseline that we compare against.
This is referred to as N in Table 7.
θ refers to the base pretrained model use for the primary model in each dataset.
The hidden-layer size of the two-layer
MLP used to instantiate ϕ , referred to as ϕ h is also tuned.
For batch size, we ensure that we use 16 × m , to ensure that an almost equal number of examples from each group can potentially get sampled.
Note that the minibatch is drawn uniformly from the training data.
A note on model selection For the performance gains reported in Tables 2 and 3, model selection is based on the predicted groups, and not known worst group.
For model selection, we use the combined performance of α -fraction of the worst performing groups discovered by AGRO.
When we tune α , we are tuning for the same value of α being used in training and validation.
Statistical significance We run AGRO and all other baselines with three different seeds, and report the average worst-group accuracies over these three trials in Table 2 and Table 3.
A. B ASELINES
We describe each baseline used in this work in greater detail, including describing choice of base-line specific hyperparameters and implementation details specific to individual tasks, that follows the details in prior work.
ERM
The ERM model is trained for N epochs (provided in Table 7).
We report on the same batch size as that used in the corresponding AGRO model to draw a fair comparison between them.
Learning rate and weight decay are tuned in that order similar to AGRO.
Model selection used to report performance in Table 2 and 3 is based on the entire development set .
G-DRO This baseline applies for the datasets where spurious correlation based groups are predefined (MNLI, Waterbirds, CelebA and CivilComments).
We report on a batch size of 6 × m , where m is the number of groups and as many epochs as used to train AGRO.
We use the value of α = 0 .since
it typically corresponds to 1 worst-group for all two class problems and 2 worst-groups for
MNLI.
We don’t use weight decay, and tune learning rate η similar to AGRO.
JTT Liu et al.
(2021) is a very simple up-sampling strategy where the errors made by ERM are upsampled by training for a second time on those examples.
However, hyperparameter tuning is based on access to a known worst group.
Instead we do model selection based on the worst-performing group, i.e., the group consisting of all the errors of the ERM model.
We tune weight-decay and learning rate η similar to AGRO.
We start with the same ERM model used for AGRO.
GEORGE Sohoni et al.
(2020) generates groups via clustering of ERM model representations and loss-components.
However, implementation details for GEORGE showed that only the loss component was used for Waterbirds and CelebA. We follow the same heuristic for MNLI and
CivilComments as well.
We cluster this loss component via GMM and select number of clusters based on the parameter setting that achieves the highest average per-cluster Silhouette score, following
Sohoni et al.
Instead of finding global clusters and overclustering them, we only cluster once (since they didnt find overclustering useful).
We use the value of α = 0 .
2 since it typically corresponds to 1 worst-group for all two class problems and 2 worst-groups for MNLI.
We tune weight-decay and learning rate η similar to AGRO.
Model selection is based on the worst-performing group , discovered via the clustering approach.
We start with the same ERM model used for AGRO.
EIIL Creager et al.
(2021) generates groups via adversarially training a model that learns to maximally violate the Environment Invariance Constraint of Invariant risk minimization (IRM)
Arjovsky et al.
However, model selection is based on access to a known worst group.
Moreover, implementation details for EIIL showed that a simple heuristic like using labels as groups maximally violates EIC.
They find that for large datasets like CivilComments, the convergence time for gradient-based EI increases significantly.
Hence they use labels as groups.
We also follow this for all datasets except Waterbirds.
We use the value of α = 0 .
2 since it typically corresponds toworst-group for all two class problems and 2 worst-groups for MNLI.
We tune weight-decay and learning rate η similar to AGRO.
After group discovery (EI), we use G-DRO for robust optimization.
Model selection is based on the worst-performing group , discovered via the grouping strategy.
For implementation of EIIL on waterbirds, we follow hyperparamter setting from (Creager et al., 2021).
A. A DDITIONAL E XPERIMENTS
List of additional experiments:
• A.6.1 Experiments on Waterbirds using the ViT(Dosovitskiy et al., 2020) model and on MultiNLI using the Roberta(Liu et al., 2019) pretrained model.
• A.6.
Stronger ERM model experiments compared to weak models.
• A.6.3 Sensitivity of worst-group performance of AGRO to the hyper-parameters α and m .
A
[Table] [Table]
A.6. E XPERIMENTS WITH PRETRAINED MODELS
In Table
[Table]
we report results on using older pretrained models of smaller sizes and less effective pretraining strategies (less data, less effective pre-training tasks).
We report on the Roberta-base model (Liu et al., 2019) for MultiNLI and ViT (Dosovitskiy et al., 2020) for Waterbirds
. A.6. E XPERIMENTS WITH ERM MODEL
In Table
[Table]
we report average and worst group accuracies for MultiNLI using different pretrained models and batch sizes.
While model size and pretraining initialization improves both average and worst group accuracy, the gap between both does not change.
A.6. E FFECT OF α AND THE NUMBER OF GROUPS
We find that the most important (sensitive) hyperparameters to tune for AGRO are α and number of groups.
Figure 3 shows variation of worst-group performance on MNLI as a function of α (left) and m (right).
As the proportion of examples in worst groups increases (with α ), the model converges to the ERM solution.
For very small values of alpha, only one group is used for up-weighting, and this group may potentially contain noisy or outlier examples.
Consequently, we observe a drop in worst-group performance.
A similar pattern also holds with number of groups (keeping alpha fixed to 0 . 2 ).
As m increases, groups may contain noisy or outlier examples.
If m is very small, groups may not encode any meaningful correlation, thereby reducing to the ERM solution.
Note that we use a known worst group on MNLI for model selection for these ablation experiments.
Details about other hyperparameters and their values on different datasets and baselines are provided in Appendix
A.4.
A.6. F EATURE A BLATIONS ON W ATERBIRDS
Results in Table 10.
[Table]
Ablation of features in F and ablation for adversarial learning over clustering (right).
A. H UMAN E VALUATION
We do human evaluation on three datasets (MultiNLI, CelebA and SST2).
For each of these dataset, we use AGRO to obtain a large number of groups on the dataset (as opposed to the m < 25 groups used for optimization).
We do this for qualitative analysis to limit the number of instances in each group to fewer than 100.
This allows us to examine the slice in its entirety.
We pick the top 5 most underperforming (highest error-rate) groups for all 3 datasets.
For task 1 (Coherence estimation), we randomly sample 4 examples from a given group i and 1 additional example from another random group i ′ !
= i .
We recruit 10 annotators (graduate students familiar working on machine learning and
NLP).
Each annotator is presented with 3 examples from group i , and 2 examples—the 4th example from group i and the randomly chosen example from group i ′ .
They are asked to identify which of the two test examples belongs to group i .
Note that we only show the models’ predictions on all examples, since we want to get indirect feedback about model behavior from annotators.
We enforce that they provide a definitive choice and explain their reasoning in 1-2 sentences.
We solicit 3 different annotations for all 15 slices - a total of 45 different annotations.
For the two text classification tasks, we additionally ask annotators to minimally perturb the chosen test example in order to potentially change the model’s original prediction (this is not verified during the annotation process).
A minimal perturbation includes adding, deleting or substituting a word or 3-4 token phrase in the original instance.
Once again, annotators only see model predictions for all examples.
A. Q UALITATIVE E XAMPLES OF S LICES
In Figures 4,5 and 7, we present randomly sampled examples from the worst groups discovered by
AGRO, which we also used in the human evaluation study
[Table]
sixteen year old yep boy i had a surprise birthday party and a war started in Israel", Hypothesis: "I turned 18 when the war in Israel began.",
Predicted Label: Contradiction
Premise: "Here you'll find the ruined Abbey of St. Colm, founded in the 12th century and named for St. Columba, who had brought Christianity to western Scotland 600 years earlier.",
Hypothesis: "Christianity was brought to Scotland in the 6th century."
, Predicted Label: Contradiction
Premise: "Helms, who will be 81 when his fifth term ends, is increasingly frail."
, Hypothesis: "Helms will turn 91 soon.",
Predicted Label: Contradiction
Premise: "Nearby is the Monastery of Nea Moni, founded in 1049, and one of the most beautiful Byzantine religious sites in the Aegean.",
Hypothesis: "The Monastery of Nea Moni was founded in 1500 and it is very beautiful."
Predicted Label: Contradiction
Premise and hypothesis contain different numerical values or forms, correlated with contradiction
Women with short hair and eyeglasses, correlated with nonblondes
[Figure] [Figure]