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The Abstraction and Reasoning Corpus (ARC) (Chollet, 2019) and its mostrecent language-complete instantiation (LARC) has been postulated as animportant step towards general AI. Yet, even state-of-the-art machine learningmodels struggle to achieve meaningful performance on these problems, fallingbehind non-learning based approaches. We argue that solving these tasksrequires extreme generalization that can only be achieved by proper accountingfor core knowledge priors. As a step towards this goal, we focus on geometrypriors and introduce LatFormer, a model that incorporates lattice symmetrypriors in attention masks. We show that, for any transformation of thehypercubic lattice, there exists a binary attention mask that implements thatgroup action. Hence, our study motivates a modification to the standardattention mechanism, where attention weights are scaled using soft masksgenerated by a convolutional network. Experiments on synthetic geometricreasoning show that LatFormer requires 2 orders of magnitude fewer data thanstandard attention and transformers. Moreover, our results on ARC and LARCtasks that incorporate geometric priors provide preliminary evidence that thesecomplex datasets do not lie out of the reach of deep learning models.

Infusing Lattice Symmetry Priors in Attention Mechanisms for Sample-Efficient Abstract Geometric Reasoning