Title: Symbol-Shift Equivariant Neural Networks. Abstract: Neural networks have been shown to have poor compositionality abilities: while they can produce sophisticated output given sufficient data, they perform patchy generalization and fail to generalize to new symbols (e.g. switching a name in a sentence by a less frequent one or one not seen yet). In this paper, we define a class of models whose outputs are equivariant to entity permutations (an analog being convolution networks whose outputs are invariant through translation) without requiring to specify or detect entities in a pre-processing step. We then show how two question-answering models can be made robust to entity permutation using a novel differentiable hybrid semantic-symbolic representation. The benefits of this approach are demonstrated on a set of synthetic NLP tasks where sample complexity and generalization are significantly improved even allowing models to generalize to words that are never seen in the training set. When using only 1K training examples for bAbi, we obtain a test error of 1.8% and fail only one task while the best results reported so far obtained an error of 9.9% and failed 7 tasks.
