Arabshahi, Singh, and Anandkumar (2018) propose a method for creating a dataset of symbolic mathematical equations for the tasks of symbolic equation verification and equation completion. Unfortunately, a dataset constructed using the method they propose will suffer from two serious flaws. First, the class of true equations that the procedure can generate will be very limited. Second, because true and false equations are generated in completely different ways, there are likely to be artifactual features that allow easy discrimination. Moreover, over the class of equations they consider, there is an extremely simple probabilistic procedure that solves the problem of equation verification with extremely high reliability. The usefulness of this problem in general as a testbed for AI systems is therefore doubtful.

Recursive neural networks have shown an impressive performance for modeling compositional data compared to their recurrent counterparts. Although recursive neural networks are better at capturing long range dependencies, their generalization performance starts to decay as the test data becomes more compositional and potentially deeper than the training data. In this paper, we present memory-augmented recursive neural networks to address this generalization performance loss on deeper data points. We augment Tree-LSTMs with an external memory, namely neural stacks. We define soft push and pop operations for filling and emptying the memory to ensure that the networks remain end-to-end differentiable. In order to assess the effectiveness of the external memory, we evaluate our model on a neural programming task introduced in the literature called equation verification. Our results indicate that augmenting recursive neural networks with external memory consistently improves the generalization performance on deeper data points compared to the state-of-the-art Tree-LSTM by up to 10%.