  A key feature of human intelligence is the ability to generalize beyond the
training distribution, for instance, parsing longer sentences than seen in the
past. Currently, deep neural networks struggle to generalize robustly to such
shifts in the data distribution. We study robust generalization in the context
of using recurrent neural networks (RNNs) to learn regular languages. We
hypothesize that standard end-to-end modeling strategies cannot generalize well
to systematic distribution shifts and propose a compositional strategy to
address this. We compare an end-to-end strategy that maps strings to labels
with a compositional strategy that predicts the structure of the deterministic
finite-state automaton (DFA) that accepts the regular language. We
theoretically prove that the compositional strategy generalizes significantly
better than the end-to-end strategy. In our experiments, we implement the
compositional strategy via an auxiliary task where the goal is to predict the
intermediate states visited by the DFA when parsing a string. Our empirical
results support our hypothesis, showing that auxiliary tasks can enable robust
generalization. Interestingly, the end-to-end RNN generalizes significantly
better than the theoretical lower bound, suggesting that it is able to achieve
at least some degree of robust generalization.
