Paper:
Recurrent Neural Networks (RNNs) facilitate prediction and generation of structured temporal data such as text and sound. However, training RNNs is hard. Vanishing gradients cause difficulties for learning long-range dependencies. Hidden states can explode for long sequences and send unbounded gradients to model parameters, even when hidden-to-hidden Jacobians are bounded. Models like the LSTM and GRU use gates to bound their hidden state, but most choices of gating functions lead to saturating gradients that contribute to, instead of alleviate, vanishing gradients. Moreover, performance of these models is not robust across random initializations. In this work, we specify desiderata for sequence models. We develop one model that satisfies them and that is capable of learning long-term dependencies, called GATO. GATO is constructed so that part of its hidden state does not have vanishing gradients, regardless of sequence length, and so that its state does not explode. We study GATO on copying and arithmetic tasks with long dependencies and on modeling intensive care unit and language data. Training GATO is more stable across random seeds and learning rates than GRUs and LSTMs.

Review:
The paper proposes a new RNN architecture designed to overcome vanishing/exploding gradient problems and to improve long-term memory for sequence modelling. The main ideas are (i) to split the hidden state into two parts, one of which does not influence the recurrence relation, and can therefore not blow up or contract by self-feedback; and (ii) to use periodic functions, in particular the cosine, as non-linearity in the decoder, so that the output is bounded but does not saturate.
The paper puts forward a fairly systematic analysis of the gradients in RNNs. The analysis appears correct, and is in fact quite similar to considerations in earlier RNN work (which is correctly cited), and forms the basis for the proposed GATO unit. There are two loose ends in this part:
1) the cosine non-linearity results from a purely negative selection - the function should be bounded, but not saturating. The paper does not even ask the question which periodic function might be a good choice.
2) While the method is presented as a grand theory, with the only constraint that a part of the hidden state does not influence the recurrence function; the actual implementation and experiments are limited to the narrow special case of "non-interacting" GATO, where the "passive" variables make up exactly half of the hidden vector, and the update of each individual hidden variable is influenced only by a single variable from the previous state. So there are in fact no empirical results, not even on toy data, for the general case that the paper claims to introduce.
In the experiments, there are two artificial problems (copying, adding) for sequences of symbols. These are illustrative and sensible to verify and analyse  the behaviour of GATO in a controlled setting, but rather far from most real sequence modelling tasks. In a third experiment the task is to classify whether or not patients will stay in intensive care for >1 week, based on a (seemingly private) database of time series of vital parameters. Unfortunately, the results for that experiment do not go beyond the usual "ours is better". While the numbers clearly support GATO, it would have been nice to look a bit closer and pinpoint what makes the difference. Also, the comparison is a bit loose. It would have been better to add additional baselines where also LSTM and GRU are restricted to "non-interacting", element-wise recurrence (as far as technically feasible). As it stands, it is unfair to claim "we can do it with much fewer parameters" - perhaps LSTM / GRU could, too. In fact, it could even be that the task is just simple, so that more restricted model with fewer parameters generally perform better - I do not claim this is the case, but the experiments do not rule it out and, hence, do not confirm that the clever GATO recurrence makes the difference.
A small gap is also that even the "real" experiment might not be completely realistic. Nowadays it is a popular strategy to use deep LSTMS / GRUs, i.e., stack multiple levels of recurrence, possibly with temporal sub-sampling, to better capture long-term relations. While this is potentially even more brittle, because of the additional gradient flow across layers, it does seem to work. But deep RNNs are not tested (in fact, not even mentioned) in the paper.
Overall, in spite of a few loose ends, I find both the design and the practical performance of the proposed GATO unit very interesting, and potentially valuable for the ICLR crowd. This is one of the more convincing RNN papers I have recently read.