Infusing Lattice Symmetry Priors in Attention Mechanisms for
  Sample-Efficient Abstract Geometric Reasoning
Mattia Atzeni Mrinmaya Sachan Andreas Loukas
The Abstraction and Reasoning Corpus (ARC) (Chollet, 2019) and its most
recent language-complete instantiation (LARC) has been postulated as an
important step towards general AI. Yet, even state-of-the-art machine learning
models struggle to achieve meaningful performance on these problems, falling
behind non-learning based approaches. We argue that solving these tasks
requires extreme generalization that can only be achieved by proper accounting
for core knowledge priors. As a step towards this goal, we focus on geometry
priors and introduce LatFormer, a model that incorporates lattice symmetry
priors in attention masks. We show that, for any transformation of the
hypercubic lattice, there exists a binary attention mask that implements that
group action. Hence, our study motivates a modification to the standard
attention mechanism, where attention weights are scaled using soft masks
generated by a convolutional network. Experiments on synthetic geometric
reasoning show that LatFormer requires 2 orders of magnitude fewer data than
standard attention and transformers. Moreover, our results on ARC and LARC
tasks that incorporate geometric priors provide preliminary evidence that these
complex datasets do not lie out of the reach of deep learning models.