Continual Learning and Out of Distribution Generalization in a Systematic Reasoning Task

Abstract

Humans often learn new problem solving strategies from a narrow range of examples and generalize to examples out of the distribution (OOD) used in learning, but such generalization remains a challenge for neural networks. This impacts learning mathematical techniques, which can apply to unbounded problem spaces (e.g. all real numbers). We explore this limitation using neural networks trained on strategies for solving specified cells in $6\times6$ Sudoku puzzles using a novel curriculum, where models first learn two preliminary tasks, then we assess OOD generalization during training on a subset of the set of possible training examples of a more complex solution strategy. Baseline models master the training distribution, but fail to generalize OOD. However, we introduce a combination of extensions that is sufficient to support highly accurate and reliable OOD generalization. These results suggest directions for improving the robustness of models trained with the highly imbalanced data distributions in natural data sets.