From: NIPS.cc/2018/Workshop/Spatiotemporal/Paper23/AnonReviewer1
evaluation: - Studying the dynamics of LSTMs is important, but it is not quite related to spatiotemporal decision making. It would be appreciated if the authors can clarify the relevance of the paper to the workshop.

- Using homotopy continuation method to compute nonzero equilibria is novel.  Pls provide more details on how to compute the equilibria as well as the eigenvalues around these equilibria.

- The experiment results are quite interesting. Especially on the Nottingham datasets where the eigenvalues show clear patterns of moving towards unit circles. However, it would be helpful to provide insights into novel neural network design or training based on these observations.

From: NIPS.cc/2018/Workshop/Spatiotemporal/Paper23/AnonReviewer1
relevance: 2: low
impact: 3: borderline
novelty: 4: high

From: NIPS.cc/2018/Workshop/Spatiotemporal/Paper23/AnonReviewer2
relevance: 4: high
impact: 4: high
novelty: 4: high

From: NIPS.cc/2018/Workshop/Spatiotemporal/Paper23/AnonReviewer2
evaluation: Summary

The authors study the equilibrium solutions (roots) of the LSTM update equations. First, they formulate a homotopy function H(t,.), which at t=1 describes a root of LSTM(c.h) = 0. Given H, they then use standard techniques to derive a differential equation that implicitly defines H. They then solve this differential equation numerically using model weights observed during training on 3 standard learning tasks. They conclude that the solution shows that some equilbria are close to the unit circle, e.g. some eigenvalues of the update equations approach 1.

Overall eval

This approach is interesting and could contribute to more theoretical analysis of deep models. There are a few points to address in the future / full paper:

- The theory does not use inputs to the LSTM. In experiments, inputs are used. How do you adapt the formulas / homotopy analysis for this? This is not discussed.
- How does the LSTM sweep over a single MNIST image?
- The current work does not explain in detail how to empirically solve the differential equation for H, using empirical recorded weights/biases. 
- What object are the eigenvalues computed of? F(x)? This is not clearly explained in the text (although I assume they follow the related work). 

1. What did you learn from reading this paper that you did not know before?
Eigenvalues for LSTMs in practice show some equilibriating behavior on real data.

2. What was the most exciting part of the work?
Possible further analysis of behavior of sequence models.

3. What in your opinion makes this work stand apart from other papers in this area?
Potential for theoretical progress.

4. Does the paper fit into the scope of the workshop?
Yes.

5. Are you aware of relevant literature that you may want to make the authors aware of?
No.