  Many experts argue that the future of artificial intelligence is limited by
the field's ability to integrate symbolic logical reasoning into deep learning
architectures. The recently proposed differentiable MAXSAT solver, SATNet, was
a breakthrough in its capacity to integrate with a traditional neural network
and solve visual reasoning problems. For instance, it can learn the rules of
Sudoku purely from image examples. Despite its success, SATNet was shown to
succumb to a key challenge in neurosymbolic systems known as the Symbol
Grounding Problem: the inability to map visual inputs to symbolic variables
without explicit supervision ("label leakage"). In this work, we present a
self-supervised pre-training pipeline that enables SATNet to overcome this
limitation, thus broadening the class of problems that SATNet architectures can
solve to include datasets where no intermediary labels are available at all. We
demonstrate that our method allows SATNet to attain full accuracy even with a
harder problem setup that prevents any label leakage. We additionally introduce
a proofreading method that further improves the performance of SATNet
architectures, beating the state-of-the-art on Visual Sudoku.
