From: ICLR.cc/2023/Conference/Paper2358/Authors
title: Submission Withdrawn by the Authors

From: ICLR.cc/2023/Conference/Program_Chairs
title: Paper Decision
decision: Reject
metareview:_summary,_strengths_and_weaknesses: Summary: 
The authors propose two new disentanglement metrics and address the limitations of existing two metrics. The authors further show the existing disentanglement methods perform poorly under the proposed metrics.

Strength: 
Evaluating disentangled representations is an important and challenging area. The paper proposes novel metrics and few interesting ideas.

Weakness:
The paper can be improved in its clarity (e.g., definition, notations) and in supporting claims made in the paper. Potentially the paper would benefit by focusing on a subset of the contributions but with more experimental support.
justification_for_why_not_higher_score: The paper can be improved in its clarity (e.g., definition, notations) and in supporting the claims made in the paper.
justification_for_why_not_lower_score: N/A

From: ICLR.cc/2023/Conference/Paper2358/Reviewer_kR7C
title: Response to the authors
comment: I thank the authors for their detailed responses to my questions and comments.

Some of the responses satisfactorily answer my concerns. 

I agree that stronger definition of disentanglement has interpretability advantages over the weaker definition. However, it is still not sufficient to justify evaluating disentanglement methods for the stronger definition without a concrete downstream application. This makes the motivation behind SNC and NK metrics weak.

The additional clarifications in the response, e.g., the XOR example, NK accuracies for bad representations, how to pick a good method based on the proposed metrics, etc. would strengthen the paper significantly and should be added to the main paper as much as possible.

Overall, I think this paper presents some useful and interesting ideas. There are several contributions in the paper but all of them are weakly supported. I think the paper would benefit by focusing on only a subset of the contributions but with more experimental support. I agree with the authors that it is hard to make progress in this area because of the lack of a ground-truth and standard benchmarks, but even with that context in mind, in its current form, the quality of the paper is below the ICLR standards and the paper is not contributing significantly to the research community. Therefore, I am keeping my original rating.

From: ICLR.cc/2023/Conference/Paper2358/Reviewer_JbiH
title: Thank you for your response
comment: Thanks a lot for your rebuttal! I think the proposed evaluation methods still need to be applied to more semi-supervised and supervised disentanglement learning. Then the results are more convincing and solid. Thanks a lot!

From: ICLR.cc/2023/Conference/Paper2358/Authors
title: Adding mean and variance
comment: We have now uploaded these results as you suggest. For the SNC and NK metrics, we report the mean and standard deviation for five independent runs. Mostly, the std dev is reasonably low, with the high std dev of Parted-VAE on 3dshapes somewhat anomalous. This may be partly a random occurrence due to the number of figures we report, though we have observed this model to be the least stable of those that we report results on. 

For the NCFF task, we have added means and standard deviations across the different training runs corresponding to the different feature value combinations excluded. We have placed these results in the appendix. We do not include them in the main paper because we feel there is a natural variance in the difficulty of predicting certain value combinations. For example, the model often defaults to predicting all out-of-distribution data points as average size, and we are arguing that NCFF data points are treated as out-of-distribution. Therefore, if the excluded feature value for size happens to be the midway value (between highest and lowest), then the model will score highly, but this will not reflect it having learnt anything meaningful. Therefore, we feel a clearer picture is given by simply reporting the mean across all excluded combinations (as in the current version), so it can be noted that this average is at the level of random guessing.

From: ICLR.cc/2023/Conference/Paper2358/Authors
title: Author response
comment: **There is a typo above equation 1, where "z21" should be "z2."**
Thank you; we have fixed this.

**There is not enough description for equation 1.**
We have added further description.

**There is a typo in the last paragraph of sec3.2, where "Section 3.2" should be "Section 3.1".**
Thank you; we have fixed this.

From: ICLR.cc/2023/Conference/Paper2358/Authors
title: Author response
comment: We thank reviewer JbiH for their comments. Below are our responses.

**Results should be reported as central as mean and variance from multiple runs.**
Thank you. We are working to include these as you suggest. We will add them to the paper as soon as possible, hopefully, in the next days.

**Results should be reported on more feature combinations.**
As can be seen in the full results, now uploaded in the supplementary materials, the volume of experimental results is already large. There are about 1500 figures recorded for various combinations of feature values, methods, datasets, and metrics. If we were to also explore different combinations of features, this could mean anything from 10-30x the number of figures to report. We believe that it gives a clearer picture to focus, for the present work, on a single feature combination, and take the time to explore this combination in more depth. In future work, we will test how performance on our proposed task varies with the choice of feature combination.

**The evaluation method should be applied to supervised/semi-supervised DE since prior work has shown DE is not possible without inductive bias.**
We already test on one fully supervised method, MTD, and show that it too is unable to recognize novel combinations of familiar features (NCFF). In future work, we will apply our framework to more supervised and unsupervised models.

From: ICLR.cc/2023/Conference/Paper2358/Authors
title: Author response (continued 2)
comment: **In Table 1, SNC and NK1 provide opposite trends -- for dSprites, beta-tcvae performs the best according to SNC but it performs the worst according to NK1. How can I use these two metrics to choose the best method for a given dataset?**
If we were forced to give a short and simple answer, we would say that SNC is more important than NK. A very high SNC would mean that, for each feature, there is a single unique neuron that well represents that feature, and, in our opinion, this more directly quantifies the spirit of DE than showing that the other neurons do not well represent this feature (which is what low NK would mean). However, the more complete answer to your question is that it depends on the use case. While it would be ideal to be able to assign each model a single scalar value quantifying the degree of disentanglement in a general way, we would argue that, unfortunately, this may not always be possible. DE has multiple components, each of which needs to be quantified separately. This is also the opinion of prior works that have decomposed DE into multiple components, and computed a separate figure for each, e.g., DCI, SAP, and JEMMIG. These different components can, as you have observed in our case, exhibit opposite trends. In such cases, there is no objective universal answer as to which model is better. This is similar to familiar trade-offs in machine learning: precision vs. recall, accuracy vs. model size, training time, or inference time etc. 

To take an example use case, when using DE for domain adaptation, SNC would likely be a more important metric, because we would only care that each feature is well represented by the neuron(s) that it is supposed to be represented by, as this is all that will be transferred to the new domain (as, e.g. in [1,2]). Whether it is also represented by other neurons is less important. On the other hand, if the goal for DE is interpretability, where we want to be able to understand how a given feature is represented by a model, NK would be relevant. For a model with high NK, we could not make inferences about a given feature by looking at the neuron(s) supposed to be encoding that feature, because much of the information for that feature could in fact be encoded elsewhere in the representation.

So, while we feel that SNC is probably a more important metric than NK, we also feel that this is a somewhat subjective opinion. To keep our presentation in the paper as correct and objective as possible, we opted instead to present both metrics side by side and let the user decide how much weighting to place on each, depending on their use case.

[1] Cai, R., Li, Z., Wei, P., Qiao, J., Zhang, K. and Hao, Z., 2019, August. Learning disentangled semantic representation for domain adaptation. In IJCAI (Vol. 2019, p. 2060). [2] Yang, J., Dvornek, N.C., Zhang, F., Chapiro, J., Lin, M. and Duncan, J.S., 2019, October. Unsupervised domain adaptation via disentangled representations: Application to cross-modality liver segmentation. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 255-263).

From: ICLR.cc/2023/Conference/Paper2358/Authors
title: Author response (continued)
comment: **The proposed metric SNC assumes that the dataset contains an equal number of instances for each of the feature values for the metric to work correctly, however, this is often not true for realistic datasets.**
It is possible to extend this technique to a non-uniform distribution by simply adjusting the bin widths to match the distribution: if, for N data points, the ith feature value occurs with relative frequency n_i/N, then we construct the ith bin to contain n_i data points. 

**A bad representation (that doesn’t encode a lot of useful information) would always have a low NK1 or NK2 accuracy, right? Does that mean that this metric should only be used to compare good representation learning methods?**
Yes, a very noisy/uninformative representation would have low NK1/2. NK is designed to measure whether a good representation is also disentangled, not whether the representation is good in the first place. To measure whether the representation encodes useful information, one could look at the accuracy of the full classifier, or the SNC metric. That is, both the SNC and the NK metric should be evaluated together to give a full picture of the extent of disentanglement. To use the framework of [1], NK gives a measure of compactness, not informativeness, whereas the full classifier gives a measure of informativeness, but not compactness. (The property that [1] calls disentanglement is ensured, in our evaluation method, by enforcing an injective function when aligning factors to neurons, as per equation (1) in our paper.)
[1] Eastwood, C. and Williams, C.K., 2018, February. A framework for the quantitative evaluation of disentangled representations. In International Conference on Learning Representations.

**If the focus of NCFF is the representation the encoder produces, shouldn’t the classifier be trained on perfectly balanced data so that it doesn’t learn any correlations in generative factors?**
The correlations that exist are non-linear. The fact that the linear classifier still fails to identify the novel combinations means that it cannot be the classifier that is learning the correlations, rather, it must be the encoding of the model itself. We remove the combination from the training set for the classifier in order to maintain consistency with the ‘normal test set’ setting.

**NCFF linear, NCFF excl 1/2 seem to perform better in predicting shape in many cases as compared to NCFF. What might be the reasoning behind that? Which of these numbers should I use to select the best method for a given dataset?**
This could be because, when predicting the first removed feature, the MLP receives a slightly confusing signal from the neuron representing the second removed feature (insofar as a single neuron does represent this feature, in general our results show that this occurs only weakly), because it is weakly correlated with the first. When this neuron is excluded, therefore, the MLP classifier has a better chance of predicting the first feature correctly. Note that the scores for the linear classifier and excl 1/2 are roughly the same on average, and slightly better than the full MLP. This suggests that, in addition to the entanglement learnt by the encoder, the MLP is learning some small additional correlation. The other models (excl 1/2 and linear) are not, and so they perform slightly better. However, they are still, on average, similar to random guessing, so the encoder must still be strongly entangling the two features.

With respect to model selection, the answer depends on the use case. If the goal is NCFF itself, that is, we want a model that can generalize to novel combinations of features, then it would make sense to pick the model with the highest NCFF score, across all the NCFF settings. If the goal is non-axis aligned DE, that is, each feature is represented by projection along some direction of latent space, then linear NCFF would likely be the most important figure. 

**The appendix is missing.**
Apologies for this. It is now uploaded.

From: ICLR.cc/2023/Conference/Paper2358/Authors
title: Author response
comment: We thank reviewer kR7C for their comments. Below are our responses.

**Both proposed metrics apply only to strong DE, whereas weaker DE can also be useful e.g. if the goal is robustness to distribution shift, then weaker DE is still good. Why is the strong definition better than the weak one?**
The stronger version of DE does have some advantages. A weakly disentangled representation is less compact, requiring multiple neurons per factor. It also loses much of the interpretability afforded by strong DE, because it may be infeasible to compute which of the exponentially many partitions (Stirling number of the second kind) is the correct one, and so we may never be able to tell which neurons represent which features. This point is discussed at the top of page 4, we can expand that discussion if you think it would be helpful.

This is not to say that weak DE cannot be valuable as well. For our proposed NCFF task, weak DE would work just as well as strong DE, so that part of our paper is also relevant to weak DE. In fact, one of the conclusions that might be drawn from the SNC and NK results, particularly the failure of the single-neuron classifier to properly encode the corresponding feature, is that the strong definition is too ambitious and that future research should focus more on the weaker version of DE.

**MIG values should be given for the for the XOR example in Table 1.**
For the model in Table 1, the MIG is 0.189 for each feature. For the other model, the MIG is 0.07 for shape, 0.189 for colour, and 0.129 on average. We will add these figures to the paper, with the calculations in the supplementary material.

The reason the other model is better is that it is closer to the ideal disentangled model.  In the ideal model, z_1 represents shape and shape only, and z_2 represents colour and colour only (WLOG on ordering of the neurons), and in the first model z_1 represents nothing and z_2 represents both, whereas in the second model z_1 represents shape and z_2 represents both. In the first model, z_1 needs to learn shape and z_2 needs to unlearn shape, in the second model all that needs to happen is that z_2 unlearns shape.

**Failings of existing metrics are shown only with respect to one metric (MIG) and on hypothetical data. We need additionally to show that the metrics fail on real-world data, as compared with a ground truth.**
We use MIG as an example, but, as we state, many other popular metrics, incuding JEMMIG, DCI, RMIG, and SAP, are also based on the idea of comparing neurons pairwise, so exactly the same argument applies. We cannot simply compare to a ground-truth disentangled representation, because it is not clear what such a representation would be, or how to recognize such a representation if we had it. It is also not clear how to compare a learned representation with a ‘ground-truth’ disentangled representation. The usual distance metrics of L_n, cosine similarity etc. would clearly not be suitable. This is part of the reason disentanglement is a tricky subject, and why the field is still coming to grips with how to define and quantify it.

We can’t experimentally validate a new metric, unless there is downstream task, and this is largely lacking in DE research. One could have made the same criticism of all the previous papers that introduced DE metrics, that the authors should have verified their metric experimentally.


**The example in Sec 3.2 considers an XOR relationship between two latent dimensions. Could the authors provide an example of a real-world data/setting where the learned representations might exhibit such a relationship?**
It is not so important whether XOR itself occurs as the relationship between some pair of neurons and some feature. The purpose of the XOR example is to illustrate that a given feature may have high MI with some subset of neurons, but low MI with any of those neurons individually. This is the essential property that existing metrics fail to account for, because they only consider the MI with each neuron individually. That this sort of representation (low MI individually but high MI collectively) occurs in practice is evidenced by comparing the accuracy for individual classifiers vs. full classifiers, as in Table 2. Accuracy is low when classifying with an individual neuron, meaning that neuron has low MI with the feature in question, and high for all neurons, meaning they have high MI. (MI is bounded above and below by a function of classifier accuracy [1].)
[1] Luxburg, U. V. "Relation between classification accuracy and mutual information in equally weighted classification tasks." PhD diss., Universität Hamburg, 2016.

From: ICLR.cc/2023/Conference/Paper2358/Authors
title: Author response (continued)
comment: **The NK metric is not novel,  a very similar metric was described in [Mathieu], the paper is not cited.**
(Mathieu et al., 2016) is similar but different in some important ways, not just, as you say, in the number of neurons that are removed. The most important difference is that it is a measure for supervised models. It only works if we are given a partition of the latent space into two parts that they call specified and unspecified, where the latter has been encouraged not to be informative about the class label. In contrast, our method applies to fully unsupervised models, and we identify the specific neuron to knockout using the alignment procedure. Another difference is that Mathieu et al. only train a single classifier, and only on a single subset of neurons. This is because their characterization of disentanglement is a representation in which all the class information is confined to a certain subset of neurons. That is the only requirement. The remaining neurons are free to represent anything as long as it is not class. In our metric, on the other hand, the neurons used to classify, e.g., g_1, are themselves supposed to be representing different features. So, when we show that z_2, … z_m can represent g_1 with high accuracy, this is a failing for two reasons. To use the language of [1], it is evidence both against compactness and disentanglement (the “D” and “C” from DCI). It is evidence against compactness, because it shows that the information about g_1 is not just confined to z_1 – this point is clear, and this is the property that is also investigated by the metric of Mathieu et al. It is also evidence against disentanglement, because it shows that each of z_2, …, z_m contains information not just about the factors they are supposed to be representing, i.e., g_2,..., but also about g_1. This point may be less obvious, but it is an equally important part of our NK metric, and it is not a part of the metric of Mathieu et al.

Really, our SNC and NK metrics are dual, and are also essentially related to the alignment procedure using the Kuhn-Munkres algorithm, because they both require the identification of the single neuron that is supposed to be representing a given feature. 

Note that there are multiple novel contributions in our paper: the identification and explanation of problems with existing disentanglement metrics, the proposal of two new metrics, the introduction of the task of classifying novel combinations of familiar features, and extensive experimental evaluation of our proposed metrics and task. The criticism of DhWb regarding novelty is directed only to one of the proposed metrics, and not to the entire rest of our paper, and even on this one metric, there is still significant novelty in what we propose. We agree that there is some similarity to the metric of Mathieu et al. -- we thank DhWb for the reference and will include it in the paper – but there are also important differences, which we outlined above. We strongly reject the claim that our paper lacks novelty.

[1] Eastwood, C. and Williams, C.K., 2018, February. A framework for the quantitative evaluation of disentangled representations. In International Conference on Learning Representations.

From: ICLR.cc/2023/Conference/Paper2358/Authors
title: Author response to review
comment: We thank reviewer DhWb for their comments. Below are our replies.

**"These are also sometimes called “generative factors”. In this paper, we mostly refer to them as “factors” or “features” "**
We are not sure what the criticism is here.

**Entanglement refers to functional relationship between gt factors and latent representation, and not to distributions (ie. not statistically independent).**
Entanglement is often spoken of in the literature in probabilistic terms: disentangled data are conceived of as the ground-truth distribution being composed of (at least some) statistically independent generative factors. The intention then is that the model learns the same independence in its representation. This is the characterization of (dis)entanglement in [1-3], to give just a few examples. Note that the latent space of a VAE defines a distribution, not just a single value. 
[1] Higgins, I., Matthey, L., Pal, A., Burgess, C., Glorot, X., Botvinick, M., Mohamed, S. and Lerchner, A., 2016. beta-VAE: Learning basic visual concepts with a constrained variational framework.
[2] Chen, R.T., Li, X., Grosse, R.B. and Duvenaud, D.K., 2018. Isolating sources of disentanglement in variational autoencoders. Advances in Neural Information Processing Systems, 31.
[3] Kim, H. and Mnih, A., 2018, July. Disentangling by factorising. In International Conference on Machine Learning (pp. 2649-2658). PMLR.
"Formally, let p(X,Y) be the empirical distribution from the data for the two features, q(X,Y) the distribution learnt by the model, and x, y the two feature values that do not appear together in the data" This part does not make sense for me. The learned model is a just a function. Disentanglement tries to learn a function that reverses the functional relationship between the gt factors and the data. If we are talking about the model output as random variables here, then the notation is wrong.
A generative model, like a VAE, learns a joint distribution q(X,Y), not just a conditional distribution q(Y|X). So, it is not correct to say that the learned model is just a function.

**"Firstly, the dependence that we introduce between X and Y is restricted entirely to one combination of values, with probability zero of this combination and otherwise the features being totally independent" A set of random variables are either independent or not. There is no "otherwise totally independent". So here I guess the X and Y are constructed as taking an independent joint distribution and removing the probability mass associated with some X=x and Y=y values. According to 6.2., this is the case, but it is unclear to the reader up until that point.**
Yes, that is how X and Y are constructed. We can formalize “otherwise totally independent” as P(X,Y|X!=x, Y!=y)=P(X|X!=x)P(Y|Y!=y).

**There is no equation defining the NCFF task**
The task is as follows: 
randomly sample values for size and shape, form a test set of points with those two values
train the VAE (or supervised model) on the training set
encode the entire dataset with the encoder from the VAE (this step is not needed for supervised models)
train and test the classifier on the training and test set, respectively, using the encodings as input
We have added some lines to explain this further; however, we do not feel that an equation would be useful to describe this task.

From: ICLR.cc/2023/Conference/Paper2358/Reviewer_DhWb
confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: The paper proposes novel disentanglement metrics, that
- address shortcomings of existing metrics
- they propose their own metrics to avoid the shortcomings
- according to the new metrics, existing disentanglement methods fail to disentangle factors of variation
strength_and_weaknesses: Strengths:

There is a good metric that is proposed and makes intuitive sense :Single-Neuron Classification (SNC). Previous metrics can assign multiple factors to one neuron, which is not desirable. The new metric resolves this by enforcing 1-to-1 assignment

Weaknesses:

The paper is written in a vary unclear way, up to the point where I did not understand what they do in one of the metrics (NCFF).

The Neuron Knockout (NK) metric is not novel.
clarity,_quality,_novelty_and_reproducibility: Clarity

The paper is very much unclear to me
- "These are also sometimes called “generative factors”. In this paper, we mostly refer to them as “factors” or “features” "
- "However, if there is entanglement between the different features, then the novel combination is out of distribution". As far as I know entanglement (and was used like this in the paper before) refers to functional relationship between gt factors and latent representation, (i.e. not one-to-one correspondence but e.g. XOR) and not to distributions (ie. not statistically independent).
- "Formally, let p(X, Y ) be the empirical distribution from the data for the two features, q(X, Y ) the distribution learnt by the model, and x, y the two feature values that do not appear together in the data" This part does not make sense for me. The learned model is a just a function. Disentanglement tries to learn a function that reverses the functional relationship between the gt factors and the data. If we are talking about the model output as random variables here, then the notation is wrong.
- "Firstly, the dependence that we introduce between X and Y is restricted entirely to one combination of values, with probability zero of this combination and otherwise the features being totally independent" A set of random variables are either independent or not. There is no "otherwise totally independent". So here I guess the X and Y are constructed as taking an independent joint distribution and removing the probability mass associated with some X=x and Y=y values. According to 6.2., this is the case, but it is unclear to the reader up until that point.
- " Our proposed task of correctly classifying NCFF is a more natural, realistic way to measure if the models are learning to encode features independently." So far in the text NCFF was not defined. It is not clear at all, what the task is here. What is the input and output to the classifier, what is the loss? There is no equation defining the terms there is no equation defining the task.

Novelty:

The Neuron Knockout (NK) metric is not novel. A very similar metric was described in [Mathieu]. The only difference is that in [Mathieu] they knocked out multiple neurons, not one.
[Mathieu]: Disentangling factors of variation in deep representations using adversarial training, NeurIPS 2016
The paper is not cited.

Reproducibility:

I would not be able to reproduce the experiments based on the text.


summary_of_the_review: There are two major issues with the paper, each alone would be too severe to accept:
1) lack of novelty/acknowledgement of a relevant paper
2) The writing is very unclear, there is no way to know what the proposed method is, as there is no formal definition/equation about what they do.
correctness: 2: Several of the paper’s claims are incorrect or not well-supported.
technical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
empirical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
flag_for_ethics_review: NO.
recommendation: 1: strong reject

From: ICLR.cc/2023/Conference/Paper2358/Reviewer_kR7C
confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
summary_of_the_paper: The paper focuses on the evaluation of disentangled representation learning. Its main contributions are: 
1. The paper presents two failings of existing metrics — incorrect alignment and distributed entanglements.
2. The paper then proposes two new evaluation metrics to address the above problems — Single-neuron classification (SNC) and Neuron Knockout (NK)
3. Finally, the paper proposes the task of recognizing novel combinations of familiar features (NCFF) as an additional evaluation metric for measuring disentanglement. 

Experimental results show that existing disentangled representation learning works perform poorly on both the proposed SNC and NK as well as NCFF task.
strength_and_weaknesses: Strengths
- The paper presents shortcomings of existing evaluation metrics that sound reasonable to some extent. The paper then proposes new metrics to try to fix these shortcomings. This direction of research should be useful for disentangled representation learning researchers.
- Experiments in the paper include 3 different datasets and various top methods from the research area.
- The paper does a good job of drawing connections with and citing many related works.


Weaknesses:
- The proposed metrics SNC and NK rely on the strong definition of disentanglement (DE) where there is a one-to-one mapping between the generative factors and a subset of latent dimensions. These metrics very clearly penalize the methods that satisfy the weaker definition where a generative factor can be represented by a combination of a few latent dimensions. But, there is no clear incentive why the stronger definition is better than the weaker one. The choice between the two definitions seems subjective and dependent on the downstream task, for example, generalization to distribution shift settings (where the test distribution has a different degree of correlation between factors as that of the training set) should work well with the weaker definition of DE. Are there any downstream tasks/applications that would require the stronger definition of DE and would not work with the weaker definition? 
- Both the failings of existing metrics are described with assumptions that are supported with one example of one metric on a hypothetical data instance each. I think this is not sufficient. I think these failings need solid experiments of their own to support the claims, e.g., realistic task/data settings where the existing metrics clearly fail as compared to a ground-truth or expected results.
    - Additionally, could the authors provide more details for the given example in Sec 3.1 — what would be the MIG values for the model in Table 1 and the other model in which z_2 is as Table 1 and z_1 represents shape to an accuracy of 70%? What about the other metrics? Also, how is it obvious that the second method is more desirable (as mentioned in the paper) without a downstream task/application in mind?
    - The example in Sec 3.2 considers an XOR relationship between two latent dimensions. Could the authors provide an example of a real-world data/setting where the learned representations might exhibit such a relationship?
- The proposed metric SNC assumes that the dataset contains an equal number of instances for each of the feature values for the metric to work correctly, however, this is often not true for realistic datasets.
- A bad representation (that doesn’t encode a lot of useful information) would always have a low NK1 or NK2 accuracy, right? Does that mean that this metric should only be used to compare good representation learning methods? 
- In Table 1, SNC and NK1 provide opposite trends -- for dSprites, beta-tcvae performs the best according to SNC but it performs the worst according to NK1. How can I use these two metrics to choose the best method for a given dataset?
- Both the proposed evaluation metrics need evaluations of their own to justify that they are good metrics, e.g., task settings where the proposed metrics rank methods in an expected order, examples of representations which would achieve the best and the worst scores for the proposed metrics. 
- If the focus of NCFF is the representation the encoder produces, shouldn’t the classifier be trained on perfectly balanced data so that it doesn’t learn any correlations in generative factors? 
- NCFF linear, NCFF excl 1/2 seem to perform better in predicting shape in many cases as compared to NCFF. What might be the reasoning behind that? Which of these numbers should I use to select the best method for a given dataset?
- There are multiple references to the appendix for detailed results and more details about the experimental settings but there is no appendix provided in the submission. Hence, the paper is insufficient in its current form.

clarity,_quality,_novelty_and_reproducibility: Clarity - The paper is not very clearly written and is difficult to understand at various instances. A lot of claims in the paper require further justifications or support from experiments, some of them are mentioned in weaknesses above.

Quality - The proposed metrics lack evaluation and claims about shortcomings of the existing metrics are unsupported with experiments, hence I consider the quality of the work to be low. 

Novelty - The contributions of the paper seem to be novel. 

Reproducibility - The paper provides many experimental details, although some details that are supposed to be in the appendix are missing.
summary_of_the_review: The paper focuses on the important problem of evaluation in disentangled representation learning research. However, the contributions of the paper require further justifications or need to supported with relevant experiments. Hence, I would recommend the paper for rejection in its current form.
correctness: 2: Several of the paper’s claims are incorrect or not well-supported.
technical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
empirical_novelty_and_significance: 2: The contributions are only marginally significant or novel.
flag_for_ethics_review: NO.
recommendation: 3: reject, not good enough

From: ICLR.cc/2023/Conference/Paper2358/Reviewer_JbiH
confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
summary_of_the_paper: This work presented two new metrics, single-neuron classification and neuron knockout, to evaluate disentanglement of existing work. The proposed metrics illustrated the poor performance of prior work on learning the disentangled representations. Then it presented a new combination of familiar features to evaluate the disentanglement learning methods. The evaluation results also showed that the existing methods do not perform well.
strength_and_weaknesses: * Strength
1. This work provides a new perspective to evaluate the disentanglement performance of existing studies using two new metrics.
2. It also presented a new combination of familiar features to evaluate the disentanglement learning methods. 
3. Evaluation on multiple datasets illustrate the poor performance of existing work on disentanglement using new metrics.

* Limitations
1. It only adopted two features shape and size to evaluate the proposed NCFF. It would be better to explore more latent factors to verify the proposed method.
2. Please report the mean and variance of the accuracy using multiple random seeds in Table 2 and 3.
3. It would be better to evaluate the approaches about semi-supervised disentanglement learning, since the prior work has proved it is impossible to disentangle the latent variables in an unsupervised learning manner without inductive bias on the model and data.
clarity,_quality,_novelty_and_reproducibility: The paper is well written and organized. It is a bit novel to evaluate the performance of existing studies on disentanglement learning from a new perspective. The experimental results look like to be reproducible.
summary_of_the_review: It offers a new perspective to evaluate the performance of existing studies on disentanglement learning. I think the idea is a bit interesting. However, it would be better to explore more latent factors to verify the proposed method. In addition, please also evaluate the existing work on supervised disentanglement learning for better verifying the effectiveness of the proposed metrics.
correctness: 4: All of the claims and statements are well-supported and correct.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
details_of_ethics_concerns: No
recommendation: 6: marginally above the acceptance threshold

From: ICLR.cc/2023/Conference/Paper2358/Reviewer_HoHs
confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
summary_of_the_paper: This paper questions the current disentanglement approach. The authors point out that current metrics cannot reflect incorrect alignment of latent variables and distributed entanglements. Two new metrics are proposed to quantify the disentanglement and it also validate the failure cases concerned previously exists. The proposed metrics include the accuracy of classifying the feature using single disentanglement neuron or neurons other than the disentanglement neuron. A new task recognizing novel combinations of familiar features is proposed to evaluate disentanglement. The proposed metrics and task are reasonable, and it reflects the weakness of current disentanglement approach. It may inspire following works on designing better disentanglement approach.
strength_and_weaknesses: Strengths:
This paper is logically sound, and the proposed problem is crucial to evaluating the disentanglement approach. The designed experiments well show that the concerned problem exists, and the proposed metrics can reflect the failure case of previous metrics.

Weaknesses:
Some typos exist and more explanations are expected.
1. The z21 should be z2 above equation 1.
2. There is not enough description for equation 1.
3. Sec3.2 should be 3.1 in the last paragraph of sec3.2.

clarity,_quality,_novelty_and_reproducibility: The concerned problems of previous metrics on disentanglement seem to exist from the designed experiments. i.e., the distribution of neurons contains entangled information. So the quality of novelty and writing is good. The designed experiments and writing are clear. The concerned problem and proposed metrics are also original.
summary_of_the_review: This paper points out problems of previous metrics on disentanglement that seem to exist from the designed experiments, i.e., the distribution of neurons may contain entangled information. The authors proposed new metrics that can reflect the concerned problem, i.e., after knocking out certain neurons the classification of target features on other neurons should be inaccurate. The proposed metrics can be an inspiration to design better disentanglement methods.
correctness: 4: All of the claims and statements are well-supported and correct.
technical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
empirical_novelty_and_significance: 3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.
flag_for_ethics_review: NO.
recommendation: 8: accept, good paper