Neural Networks for Learning Counterfactual G-Invariances from Single Environments

Despite -or maybe because of-their astonishing capacity to fit data, neural networks are believed to have difficulties extrapolating beyond training data distribution. This work shows that, for extrapolations based on finite transformation groups, a model's inability to extrapolate is unrelated to its capacity. Rather, the shortcoming is inherited from a learning hypothesis: Examples not explicitly observed with infinitely many training examples have underspecified outcomes in the learner's model. In order to endow neural networks with the ability to extrapolate over group transformations, we introduce a learning framework counterfactually-guided by the learning hypothesis that any group invariance to (known) transformation groups is mandatory even without evidence, unless the learner deems it inconsistent with the training data. Unlike existing invariance-driven methods for (counterfactual) extrapolations, this framework allows extrapolations from a single environment. Finally, we introduce sequence and image extrapolation tasks that validate our framework and showcase the shortcomings of traditional approaches. INTRODUCTION Neural networks are widely praised for their ability to interpolate the training data. However, in some applications, they have also been shown to be unable to learn patterns that can provably extrapolate out-of-distribution (beyond the training data distribution) (