Orthogonal recurrent neural networks address the vanishing gradient problem by parameterizing the recurrent connections using an orthogonal matrix. This class of models is particularly effective to solve tasks that require the memorization of long sequences. We propose an alternative solution based on explicit memorization using linear autoencoders for sequences. We show how a recently proposed recurrent architecture, the Linear Memory Network, composed of a nonlinear feedforward layer and a separate linear recurrence, can be used to solve hard memorization tasks. We propose an initialization schema that sets the weights of a recurrent architecture to approximate a linear autoencoder of the input sequences, which can be found with a closed-form solution. The initialization schema can be easily adapted to any recurrent architecture. We argue that this approach is superior to a random orthogonal initialization due to the autoencoder, which allows the memorization of long sequences even before training. The empirical analysis shows that our approach achieves competitive results against alternative orthogonal models, and the LSTM, on sequential MNIST, permuted MNIST and TIMIT.
Summary:
The paper proposes an autoencoder-based initialization for RNNs with linear memory. The proposed initialization is aimed at helping to maintain longer-term memory and instability during training such as  exploding gradients (due to linearity).
Pros:
1. The paper is well written, the motivation and methods are clearly described.
Cons.
1. The authors claimed the proposed method could help with exploding gradient  in training the linear memories. It would be helpful to include some experiments indicating that this was the case (for the baseline) and that this method does indeed help with this problem.
2. The experiments on the copy task only showed results for length upto 500, which almost all baseline models are able to solve. I am not too sure how the proposed initialization helps in this case.
3. TIMNIT is a relatively small speech recognition dataset. The task/ dataset does not require long-term memorization. It is nice to see that the initialization helps in this case. However, it is still a little how this experiment corresponds to the messsage that the authors are attempting to deliver at the end of the introduction.
4. In general, it seems that the experiments could be more carefully designed to reflect the contributions of the proposed method. Some suggestions for future edits are, more analysis on gradients, maybe more experiments on the stability of training such as gradients could help.
Minor:
1. There are some confusions, on P2 "we can construct a simple linear recurrent model which uses the autoencoder to encode the input sequences within a single vector", I think the authors meant encode the input sequences into a sequence of vectors? Equation 1 and 2 suggest that there is a vector m^t per timestep (as oppose to having 1 for the entire sequence).
2. Although the copy task was used in ((Arjovsky et al., 2015), I believe the original task was proposed in the following paper and hence this citation should properly be the correct one to cite here,
Hochreiter, Sepp and Schmidhuber, Jürgen. Long short-term memory. Neural computation, 9(8):
1735–1780, 1997.