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Despite -- or maybe because of -- their astonishing capacity to fit data,neural networks are believed to have difficulties extrapolating beyond trainingdata distribution. This work shows that, for extrapolations based on finitetransformation groups, a model's inability to extrapolate is unrelated to itscapacity. Rather, the shortcoming is inherited from a learning hypothesis:Examples not explicitly observed with infinitely many training examples haveunderspecified outcomes in the learner's model. In order to endow neuralnetworks with the ability to extrapolate over group transformations, weintroduce a learning framework counterfactually-guided by the learninghypothesis that any group invariance to (known) transformation groups ismandatory even without evidence, unless the learner deems it inconsistent withthe training data. Unlike existing invariance-driven methods for(counterfactual) extrapolations, this framework allows extrapolations from asingle environment. Finally, we introduce sequence and image extrapolationtasks that validate our framework and showcase the shortcomings of traditionalapproaches.

Neural Networks for Learning Counterfactual G-Invariances from Single Environments