Summary and Contributions: This paper analyses new and existing VAE methods, finding that many do not naturally find irreducible representations, but that they can be improved by changing the loss landscape. This paper also proposes a new disentanglement metric that measures the independence of group actions on the learned representation. Finally the paper proposes a method to recover actions from transitions when no labelling is available, assuming the actions correspond to independent observational components of the environment. Rebuttal: Thank you for your response, I continue to support acceptance for this paper.
Strengths: This paper does an interesting follow up and analysis on existing methods, and then provide an interesting addition. The analysis itself is insightful; taking a very simple setting, how do various VAE/disentangling methods succeed and fail? The results are not extremely surprising but they provide more evidence, which is good. The novel algorithmic contributions of this paper are also interesting, in the sense that they add to the space of VAE. Although attempting to recover actions from observational data is not novel from an RL perspective, within the space of disentanglement literature this is a neat contribution. Another strength of this paper is that I found it to be very well written, clear & concise.
Weaknesses: It's not clear to me whether we're starting to overfit to such simple disentanglement cases as a blob on a 2d grid (well, in a sense we already have, see e.g. ) where we recover x & y, or whether it's valuable to pursue those simplest cases to the limit where we understand them and where our methods should pass these like sanity checks. I say this because while I see the value of such setups where we control and understand everything, the problems we care about in the end are not that clean, so is it worth pursuing the simple settings to the limit? Another weakness-that's-not-necessarily-a-weakness is that the algorithmic contributions of this paper borrow a lot from existing ideas, and are thus of limited novelty. Related to this is the lack of comparisons with such existing ideas. While the authors do a good job of referring to the disentanglement literature, parallels to the RL literature are lacking (see below).
Correctness: I could not find anything wrong.
Clarity: The paper is very well written and clear.
Relation to Prior Work: The second part of this work which aims at recovering the action space of an interactive agent is reminiscent of several prior works [1-5]. Although in this work the actions taken are unknown, the rewards used to recover which actions were taken is similar to ones use in some of these works [1,3,4] to reward disentangled feature/policy pairs. It may be interesting to compare to/consider them, especially considering that the proposed method seems to have the exact same weaknesses; an almost perfect disentanglement in simple environments such as gridworlds, the occasional suboptimal minima where learning gets stuck with redundant or mis-disentangled actions/policies, and an inability to deal with longer action sequences correctly. An interesting, if unsatisfactory conclusion from these works is that such approaches do not cleanly scale to more complex observation and action spaces. I wonder if the same is true here. Maybe less relevant, but I am also reminded of Independent Mechanisms .  Learning what you can do before doing anything, Rybkin et al, ICLR 2019  Contingency-aware exploration in reinforcement learning, Choi et al, ICLR 2019  Disentangling Controllable and Uncontrollable Factors by Interacting with the World, Sawada et al, NeurIPS 2018  Independently controllable factors, Thomas et al., 2017  Imitating Latent Policies from Observation, Edwards et al, ICML 2019  Learning Independent Causal Mechanisms, Parascandolo et al, ICML 2018
Additional Feedback: I do think it would be valuable to understand how brittle the proposed method is, or to conjecture more on its weaknesses. I don't think experiments on something like Atari are necessary nor would be valuable, but adding a bit of noise, confounders, or observational complexity would probably be quite informative as to the robustness of the various methods.
Summary and Contributions: The paper investigates how the concept of Symmetry Based Disentangled Representation Learning (SBDRL) relates to other popular disentanglement metrics and representation learning methods. In particular it demonstrates that 1) models such as the VAE do not learn linear disentangled representations, unless explicitly biased to, and 2) linear disentangled representations seem to improve already established metrics such as the mutual information gap (MIG). The authors build up on an existing Forward VAE model and describe an unsupervised method to train it.
Strengths: The paper clearly demonstrates some intuitive, but not explicitly shown so far results, regarding linear disentangled features. The authors provide substantial empirical evidence demonstrating that learning linear disentangled features requires explicit inductive bias. It also compares SBDRL with other popular methods using multiple disentanglement metrics.
Weaknesses: The paper presents RGrVAE which is essentially the same model as Forward VAE where the action is also treated as a latent variable. Given the discrete nature of the action space it is quite a natural step to model that latent variable through a categorical distribution and infer the parameters of that distribution through REINFORCE in an end-to-end fashion. However, one of the key questions in this approach is how do you choose the number of actions N (i.e. number of clusters?). Despite that the paper does not mention anything about that decision. Perhaps utilising a Dirichlet process might be beneficial. My biggest concern though is that the authors apply the proposed unsupervised method only to a single task which is the task introduced in the Forward VAE paper. Training with REINFORCE is known to be quite unstable so I definitely would like to see the behaviour of the algorithm with at least one other tasks. Perhaps considering the dSPRITE dataset can be another task to look into?
Correctness: Tthe empirical methodology adequately address the core hypotheses of the paper. Overall, I do not find any major issues with the correctness of the paper.
Clarity: The paper is written well, however, there are some places where a few things need to be clarified. For example: - Why is the order of the group 7? Where does this number 5 that you dived by come from? (line 140) - What does exactly the dot operator represent within the max operator of equation (2)? - I am not sure I can follow the reasoning in line 196. Why isn't MIG expressive enough? - Why is the reward proportional to the L2 norm of the difference between the previous and current latent codes? Don't you want the predicted post action code (based on applying the learnt group operator and the previous latent code) to be as close as possible to the actual post action code?
Relation to Prior Work: The presented paper fits well within the context of representation disentanglement. The authors explain clearly how their work differs from the related litarature.
Additional Feedback: Many, in my opinion, important results seem to presented in the supplementary material, however, the supplementary materials archive contains only the code and a copy of the paper.
Summary and Contributions: In this paper, the authors confirm empirically that irreducible representations are not naturally found in standard VAE models without biasing the loss landscape towards them. The authors determine that inducing such representations in VAE latent spaces garners improved performance on a number of standard disentanglement metrics. A novel disentanglement metrics to explicitly measure linear disentangled representations. Moreover, the authors propose a method to induce irreducible representations without the need for labelled action-transition pairs.
Strengths: This paper is well written and easy to read. The motivation is clear. The proposed method is novel and effective. The authors conduct extensive experiments and make this paper very solid.
Weaknesses: I do not find any obvious limitation of this this work.
Correctness: The claims and method are correct
Clarity: The paper is well-written.
Relation to Prior Work: The discussion about the differences from previous work is clear. A large number of comparative experiments have been carried out.