Paper:
We propose an unsupervised method for building dynamic representations of sequential data, particularly of observed interactions. The method simultaneously acquires representations of input data and its dynamics. It is based on a hierarchical generative model composed of two levels. In the first level, a model learns representations to generate observed data. In the second level, representational states encode the dynamics of the lower one. The model is designed as a Bayesian network with switching variables represented in the higher level, and which generates transition models. The method actively explores the latent space guided by its knowledge and the uncertainty about it. That is achieved by updating the latent variables from prediction error signals backpropagated to the latent space. So, no encoder or inference models are used since the generators also serve as their inverse transformations. The method is evaluated in two scenarios, with static images and with videos. The results show that the adaptation over time leads to better performance than with similar architectures without temporal dependencies, e.g., variational autoencoders. With videos, it is shown that the system extracts the dynamics of the data in states that highly correlate with the ground truth of the actions observed.

Review:
The authors propose an architecture and generative model for static images and video sequences, with the purpose of generating an image that looks as similar as possible to the one that is supplied. This is useful for for example frame prediction in video and detection of changes in video as a consequence to changes in the dynamics of objects in the scene.
The architecture minimizes the error between the generated image(s) and the supplied image(s) by refining the generated image over time when the same image is shown and by adapting when the image is changed. The model consists of three neural networks (F_Zµ, F_Zsigma, f_X|Z) and three multivariate Gaussian distributions P(S_t), P(Z_t) and P(X_t,Z_t) with diagonal covariances. The NNs do not change over time but they relate the three Gaussian distributions in different ways and these distributions are changing over time in order to minimize the error of the generated image(s).
The paper took a while to understand due to its structure and how it is written. A short overview of the different components of Figure 1 giving the general idea and explaining
* what nodes are stochastic variables and NNs
* what is trained offline/online
It would also help the structure if the links/arrows/nodes had numbers corresponding to the relevant equations defining the relations/computations. Some of these relations are defined with explicit equation numbers, others are baked into the text which makes it difficult to jump around in the paper when reading it and trying to understand the architecture.
There are also numerous language errors in the paper and many of them are grammatical. For example:
  Page 5, second paragraph: "osculations" -> "oscillations"
  Page 5, fourth paragraph: "Defining .. is defined as.."
The results seem impressive and the problem under consideration is important and have several applications. There is however not much in terms of discussion nor analysis of the two experiments.
I find the contribution fairly significant but I lack some clarity in the presentation as well as in the experiments section.
I do not find the paper clearly written. The presentation can be improved in several chapters, such as the introduction and the method section.
The paper seem to be technically correct. I did not spot any errors.
General comments:
- Why is 2 a suitable size of S?
- Why use two by two encoding instead of stride for the VAE baseline? How does this affect the experiments?
- How is S_0 and the Z_0 prior set (initialized) in the experiments?
- It would improve the readability of the paper, not least for a broader audience, if more details are added on how the VAE baseline architecture differ from the proposed architecture.
- In the first experiment: 
-- How many iterations does it take for your method to beat VAE?
-- What is the difference between the VAE basline and your approach that make VAE perform better than your approach initially (or even after a few iterations)? 
-- What affect does the momentum formulation have on the convergence rate (number of iterations necessary to reach VAE and your methods result at t=10)?  
- In the second experiment and Figure 5 in particular it was observed that some actions are clearly detected while others are not. It is mentioned that those that are not detected by the approach are more similar. In what sense are the actions more similar, which are the most prominent (from a humans perspective) such actions, what is making the model not detecting them and what can be done (within your approach) in order to improve or adjust the detection fidelity?
Please add more time labels under the time axis in Figure 4 and Figure 5. Also please annotate the figures at the time points where the action transitions are according to the ground truth.