Venue: CLeaR 2022 Conference

Reviews:

final_score: rating: 6: Marginally above acceptance threshold
review_content: Summary: The paper considers representation identification in the setting where latent factors generate observations and labels for multiple tasks, and the latent factors are mutually independent. Within somewhat additional assumptions (compared with existing works), authors show that disentanglement (up to permutation and scaling) is possible in theory and also by experiment.
Main review: Overall, the paper achieves the identification goal by placing somewhat different (but possibly strong) conditions on the data generating process, so the identification becomes somewhat easier. Nonetheless, it should be a good addition to the current literature. 

I have some minor questions regarding the definition of *tasks*. 
-	In particular, what does it mean by “different tasks” and how they would affect the identity proof? For instance, if some tasks are redundant, then $k=d$ tasks may not be enough. There should be an explicit condition on how diverse the tasks are.
-	In the first two results, the theorem says the number of tasks is exactly equal to the number of latent confounders, i.e., $k=d$. What if $k>d$? How do we know the condition in practice? And how do we select $d$ in practical applications?
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review_title: null

final_score: rating: 7: Good paper, accept
review_content: Summary: This paper investigate the Nolinear Independent Component Analysis problem in a new setting, where latent factors cause auxiliary information, rather than auxiliary information cause latent factors. The authors prove that the latent factors can be recovered up to permutation and scaling with some excess assumption. When the dimension of label is at least equal to the dimension of factors, the assumption is weak. When the dimension of label is one, the assumption is stronger. To learn the latent factors from the observations and labels, the authors propose IC-ERM which constrains the representaion layer are mutually independent. To implement it,  the authors propose ERM-ICA.
Main review: The Nonlinear ICA problem is interesting. The authors investigate this problem in a natural setting, which is different from the previous. The theoretical result is complete and covers many situations. The experimental results confirm the effectiveness of the proposed ERM-ICA.
There are some confusing statement. 
In Page 8, I think "If the predictor is \theta^{\top}\Phi(X)=1^{\top}(\Phi(X)\odot\frac{1}{\theta})" should be "If the predictor is \theta^{\top}\Phi(X)=1^{\top}(\Phi(X)\odot\theta)". 
In Definition 2, I think the \Phi(X) should be V.
review_title: null

final_score: rating: 6: Marginally above acceptance threshold
review_content: Summary: This paper extends ERM paradigm with ICA under the setting of latents-generate-label process. Based on the assumption that all components of the representation layer are mutually independent, the authors provide proofs and experimental evidences to show the effectiveness of their method.
Main review: This paper is well written and easy to understand. I think the idea of constraining representations with i.i.d assumption would bring insights to the community.

1. It would be interesting to see some label-generate-latent rivals in the experiments. 
2. typos in the Proof sketch of Theorem 3: 'Baseed' -> 'Based'
review_title: null

Meta-review: I follow the recommendation of the three reviewers to accept this paper. I encourage the authors to address the questions and typos of the reviewers.


Decision: Accept (Poster)