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The paper studies the capabilities of Recurrent-Neural-Network sequence tosequence (RNN seq2seq) models in learning four transduction tasks: identity,reversal, total reduplication, and quadratic copying. These transductions aretraditionally well studied under finite state transducers and attributed withincreasing complexity. We find that RNN seq2seq models are only able toapproximate a mapping that fits the training or in-distribution data, insteadof learning the underlying functions. Although attention makes learning moreefficient and robust, it does not overcome the out-of-distributiongeneralization limitation. We establish a novel complexity hierarchy forlearning the four tasks for attention-less RNN seq2seq models, which may beunderstood in terms of the complexity hierarchy of formal languages, instead ofstring transductions. RNN variants also play a role in the results. Inparticular, we show that Simple RNN seq2seq models cannot count the inputlength.

Learning Transductions and Alignments with RNN Seq2seq Models