While pretrained language models achieve excellent performance on natural language understanding benchmarks, they tend to rely on spurious correlations and generalize poorly to out-of-distribution (OOD) data. Recent work has explored using counterfactually-augmented data (CAD) -- data generated by minimally perturbing examples to flip the ground-truth label -- to identify robust features that are invariant under distribution shift. However, empirical results using CAD for OOD generalization have been mixed. To explain this discrepancy, we draw insights from a linear Gaussian model and demonstrate the pitfalls of CAD. Specifically, we show that (a) while CAD is effective at identifying robust features, it may prevent the model from learning unperturbed robust features; and (b) CAD may exacerbate existing spurious correlations in the data. On two crowdsourced CAD datasets, our results show that the lack of perturbation diversity limits their effectiveness on OOD generalization, calling for innovative crowdsourcing procedures to elicit diverse perturbation of examples.
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