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Logical reasoning tasks over symbols, such as learning arithmetic operationsand computer program evaluations, have become challenges to deep learning. Inparticular, even state-of-the-art neural networks fail to achieve\textit{out-of-distribution} (OOD) generalization of symbolic reasoning tasks,whereas humans can easily extend learned symbolic rules. To resolve thisdifficulty, we propose a neural sequence-to-grid (seq2grid) module, an inputpreprocessor that automatically segments and aligns an input sequence into agrid. As our module outputs a grid via a novel differentiable mapping, anyneural network structure taking a grid input, such as ResNet or TextCNN, can bejointly trained with our module in an end-to-end fashion. Extensive experimentsshow that neural networks having our module as an input preprocessor achieveOOD generalization on various arithmetic and algorithmic problems includingnumber sequence prediction problems, algebraic word problems, and computerprogram evaluation problems while other state-of-the-art sequence transductionmodels cannot. Moreover, we verify that our module enhances TextCNN to solvethe bAbI QA tasks without external memory.

Neural Sequence-to-grid Module for Learning Symbolic Rules