Thank you for the points raised! We will respond in the same order below:

How to validate?

Without the ground truth, validation in this sense is impossible by definition. As restated in the general remarks, the aim of this work is to provide a method that can guide research by providing independent feedback for hypotheses.

That said, the model architecture used as the learning mechanism is structured to encode actually meaningful properties of the data, which has been extensively shown on the closest dataset possible where ground truth is available - raw human speech. Please note that in that case, the learning was done in exactly the same way as here - raw audio, without any domain knowledge provided whatsoever. Furthermore, the model is shown to uncover structural relations that are present in whale communication in general, but not in the training dataset (Section 4, Paragraph 3). The odds of this happening due to a model artifact are extremely low.

Comparison with the existing approaches

The relations to other disentangled representation learning methods are discussed in Section 1.2, with $\beta$-VAE specifically being cited as reference number 17.

We feel that the pros and cons of GAN vs VAE-based disentangled representation learning have been discussed in enough detail elsewhere (e.g. reference number 35). What is pertinent to our case is that we have a relatively small training dataset (Section 1.1., Paragraph 2). Additionally, we do not require the posterior latent distribution, nor do we necessarily wish to enforce strict independence between the factors. To illustrate, our model encodes both the mean frequency as well as the acoustic regularity (Section 5), which might not be independent depending on the true ground truth distribution (which we, of course, do not know). However, both properties are salient for e.g. human speech - eg. general pitch vs. dynamics of a phrase, and it has been shown that whales have the capacity to deliberately control both of them.

In figure 4 and 6, it seems that only 1 bit is different

Disentanglement in this work refers to a process observable in the causal effect, as defined in Section 3: "which lends credence to interpreting this as a process of disentanglement: with higher values, the primary encoded effect in each bit starts to dominate, leading the other bits to lose their secondary effects on the number of clicks. Thus, we propose that bit 1 primarily encodes the number of clicks"

As stated in another response: within the training range, the bits remain entangled in their effect; moving outside the training range, the primary encoded effect begins to dominate, singling out one bit as the carrier of the encoding, while the others return to a baseline value in unison. This phenomenon is replicated across different observable quantities and estimators and is further examined in detail via an unrelated method in the Appendix, section A.6, which shows that the effect of the bits not encoding the property becomes close to random (in any particular observation) once sufficiently disentangled.

Hence the bit that is "different" is the one that disentangles and whose primary effect is the property tested, while the others return to a baseline.

Limitations, future research directions, and generalizations

The limitations are discussed in the third paragraph of Section 2.

As mentioned in another response and throughout the paper: the overall approach - using a generative model to independently encode properties salient to believable data generation, then treating it as a black box and uncovering these encodings in a causal experimental setup is completely model-agnostic. There is, therefore, no general impediment to applying the technique to other datasets, be it animal communication or not. In the latter case, one might want to replace the architecture used as the "learner" with another that has been tailored to the nature of the data (and verified on a close dataset with ground truth, as is the case here with human speech). This is one area of future research, with a way to test whether combinations of encodings carry meaning being another area.

In the specific case of animal communication, there is some impediment in the form of the availability of good and open datasets, which should be understandable given the quite frequent difficulty in collecting such data.

Dear reviewer,

Thank you for again for the time dedicated to reviewing our paper and the points you raised! We'd like to let you know that we've updated the paper with a new section (Section A.1.1.) in the Appendix that shows the findings to be robust to the model fit, since they replicate across independently trained models (with different sizes of the encoding space and random initializations). This adds additional evidence that the effects discovered are not artifacts of the model and should answer your concern expressed in Question 1.

When you had opportunity to read our responses (incl. the general remarks in the overall comments), please let us know if you have any further questions or comments! If you found our responses satisfactory, please consider increasing your score.

Thank you providing a clear structure to the points raised in your review. For clarity, we will address the points in the same order below.

Regarding the remark about the model being closed: while the original training set is, unfortunately, not yet available, the model, the experiment data, and reproduction code are all provided in full - see Appendix, section A.1 for details

Weaknesses

Narrow application of proposed methods

(i) modeling assumptions ...

Please refer to the overall comment for clarification regarding the choice of the dimension of t.

(ii) an unconventional GAN setup called fiwGAN ... / domain knowledge appears to be a substantive input ... (i) the model itself

Regarding the generality/conventionality of the model: as outlined in the general remarks, the main reason for choosing this setup is that it provides the following: the synthetic data is independently verified, the encodings $t$ are consistent and completely unsupervised, and the space available to them is limited, allowing us to, together with the preceding two properties, argue for their saliency for believable generation.

The fact that similar models uncover known rules on human speech is used as support of the relevancy of the encodings after they’ve been identified via CDEV; in other words, the procedure itself does not require domain knowledge.

CDEV is, indeed, a novel contribution of this work; regarding its generality - the reason for using causal inference methods is precisely to establish relationships between the encodings and observable properties without additional assumptions or need for external knowledge: e.g., the value of bit 1 has an effect on the number of clicks. What that can suggest, however, is reasoned about following the argument in the preceding paragraphs.

(ii) the data selection process,

The data selection was driven by the fact that whale codas (naturally) come in the context of dialogue, thus a significant part of the data featured interleaving codas. Thus, the reason for keeping only the top five "classes" is simply that after removing the codas with dialogue, the remaining classes had too few examples left - often one or none. As such, this process was not really driven by any goal obtained from domain knowledge. Conversely, we posit that a more diverse dataset would be even more beneficial to the generator’s ability to uncover salient properties.

(iii) the determining of appropriate extreme values

As outlined in Appendix, Section A.4., the limits of the range of the values used as treatment are determined by the quality of output of the generator. This is pointed out as a potential shortcoming in the case that these are too narrow, however, there is no domain knowledge involved in that determination - noise is reasonably close to an universal phenomenon. All values within this range are tested; additionally, the ICE estimator is "location-invariant" as it estimates the effect of an infinitesimal perturbation.

(iv) the outcome functions used to measure average treatment effect.

Please refer to the general comments.

Insufficient evidence to support claims

To continue on the points made in the general remarks: the purpose of this work is to present a procedure that can aid the scientific process in difficult problems without a ground truth. We do not claim to have proven any of the properties identified; however, the agreement of the method with the consensus on the more obvious properties, such as the number of clicks, can be used to bolster its credibility for more novel suggestions. Keeping this in mind, random sources of noise should even out with enough data, making the uncovered encodings more likely to be deliberately controlled by the whales.

Convergence of GANs is, as you’re most likely aware, a complex problem. We’d like to restate that we don’t need perfect convergence for this use case; as is illustrated in Figure 3 for an almost worst-case example, the output still looks like a whale coda, meaning that the GAN did not fail to fit the data to the extent that would make such analysis worthless. As stated in Section 2: "[noise] might, in part, be due to the network training not having converged completely; since the goal is to discover what observable properties are encoded and not high-fidelity whale communication generation, this is not a significant impediment."

In the hypothetical case where one would not be even able to tell when the output is noise (we previously argue that this is hard to believe), one could simply employ a fail-safe on the overall deviation from the data, for example using something in the vein of the Wasserstein estimators presented in Section 5.

Continuing from the previous comment:

Questions

Why is the fiwGAN structure necessary?

The reasoning for this particular model setup has been outlined in the general remarks and previous points. The incompressible of noise lacks the additional properties outlined of the encoding t, and is often "over-parametrized": please see paragraph 2 of Appendix, Section A.8 for an example of a use on bird vocalizations, as well as for more details.

The key difference between using a generative model vs. just testing a hypothesis directly...

Please refer to the general remarks; as mentioned in another comment - the gist is that we’re interested in what an independent "learner" under the constraint of believability considers salient to a communication system, not whether any given feature is present in the data, which would be trivial for, e.g. the number of clicks.

How might we extend this method ...

The overall approach - using a generative model to independently encode properties salient to believable data generation, then treating it as a black box and uncovering these encodings in an causal experimental setup is completely model-agnostic. The extension to diffusion models is an intriguing problem, about which we're still thinking.

Figure 1 shows 0, 1 for $t$ codes ...

Thank you for pointing this out, the typo in Section 2 has been fixed. More explanation is given in the general remarks.

Dear reviewer,

Thank you for again reviewing our paper and your useful comments! We'd like to let you know that we've updated the paper with a new section (Section A.1.1.) in the appendix that shows the findings to be robust to the model fit and the choice of the encoding dimension, since they replicate across independently trained models (with different sizes of the encoding space). This would be unlikely if "any interventional effects are simply a consequence of a poorly fit model?"

When you had opportunity to read our responses (incl. the general remarks in the overall comments), please let us know if you have any further questions or comments! If you found our responses satisfactory, please consider increasing your score.

Thank you for raising some interesting points! We'll respond to them in order below:

Order of bit indices

As mentioned in Section 2, and the newly added Section A.2 of the Appendix, the encoding is enforced to be consistent in a loose way, via an additional optimization loss - the variational lower bound between the generated data and the encoding value. Hence, we cannot reliably claim the rank ordering of the bits to indicate the properties’ importance in the vein of say, PCA. The focus of the approach, therefore, is more to identify (via causal estimators) what is encoded.

Factor combinations

Factor combinations, or "bit interactions", is indeed an area we’re examining for the extension of this method, in addition to adopting it to other architectures. As your motivating example shows, the presence of these is eminently plausible; additionally, the specific architecture has been shown to learn with compositionality on human speech, where the ground truth is available.

Weaknesses

The work lacks clarity at times

variable $t$ was not defined

Thank you for pointing this out, this has been fixed.

it would help to write down explicitly the loss that is optimized

The exact loss has been added in the Appendix, Section A.2.

The code t is binary, but the rest of the paper assumes t is Rademacher

Thank you for pointing this out, this has been fixed - see general remarks.

the meaning of "entanglement"

Please refer to the discussion regarding the use of the phrase "entanglement" in the previous comment.

Questions

Do we need 5 bits for the approach to work?

Please refer to the general remarks.

Thank you for a well-structured response; below, we'll respond in the same order of points raised.

Weaknesses

Unclear motivation

Please refer to the general remarks for a more complete restatement. The gist is that we’re interested in what an independent "learner" under the constraint of believability considers salient to a communication system, not whether any given feature is present in the data, which would be trivial for, e.g. the number of clicks. The disentanglement with CDEV is the method of uncovering these encodings.

Originality

We believe this is the first example of using causal inference methods for interpreting encodings in an unsupervised setting (please refer to Section 1.2 for more discussion on related work). We also believe that the method of disentanglement - CDEV - is also novel: we could find no prior work that forced extreme values on the input and measured the effect systematically with causal inference methods. We see no need for additionally inventing separate causal inference estimators since using proven ones adds credibility to the results obtained via CDEV. That said, we do believe that the ICE estimator might not be that well known and is a very good fit for this (and similar) use cases, which could be of broader interest.

Unclear use of the word “disentanglement”

The definition is given in Section 3: "We observe a high degree of entanglement of the learned encodings within the range seen in training ([1, 1]). However, when setting the treatment value above that range, all the bits but bit 1 stabilize at roughly a constant effect, which lends credence to interpreting this as a process of disentanglement: with higher values, the primary encoded effect in each bit starts to dominate, leading the other bits to lose their secondary effects on the number of clicks".

While we agree this definition might be relatively unusual, it was inspired by the phenomenon of Quantum (dis)entanglement, in which case the use of the phrase is well-established. In this view: within the training range, the bits remain entangled in their effect; moving outside the training range, the primary encoded effect begins to dominate, singling out one bit as the carrier of the encoding, while the others return to a baseline value in unison. This phenomenon is replicated across different observable quantities and estimators and is further examined in detail via an unrelated method in the Appendix, section A.6, which shows that the effect of the bits not encoding the property becomes close to random (in any particular observation) once sufficiently disentangled.

We thus think the name is still a good descriptor of the phenomenon observed; however, we are naturally amenable to renaming the method if the confusion is believed to be too great.

Regarding Figure 5, the plots presented are for a single bit, stratified by the number of clicks. The bit proposed has a consistent effect no matter the number of clicks in the generated coda, while other bits (such as the one presented) do not present any consistency in their encoding. This is in line with the definition presented above.

Concerns with experiments

Re-initialization

The results of re-initialization are presented in Figure 8 in the Appendix, Section A.5.1, showing the results to be very robust to re-initialization.

Figure 4

As mentioned in Section 2 and the Appendix, Section A.2., the upper range was selected on the basis of the generator still outputting samples with low enough noise so that our algorithmic measurement of the observables was possible. To answer the question - extending the range would give us data that makes no sense, hence speaking of an effect above (roughly) that value is not possible.

Surprising findings

The evidence can be inferred from the relationships displayed in Figure 5. We see the presence of codas with click numbers up to 10, while the model infers the connection between the number of clicks and the regularity on its own: "Furthermore, [real] codas with more clicks are often more regular in their ICIs, regardless of their duration. The generator has thus inferred this connection without the codas with a high number of clicks even being present in the dataset."

Thus, regular 9R-like (the R denoting "regular") codas are quite common in the generated samples.

Unnecessary use of causal terminology

While this is true to an extent (and argued for in the Appendix, Section A.8), we believe the work shows that causal inference-derived estimators are a natural fit for this problem setup. This is the reason phrases like "methods from causal inference" are used in the work instead of a full causal argument. As an example of the fit, the ICE estimator neatly sidesteps most dilemmas with regard to the choice of the baseline and the range of "treatment", which are not self-evident in this case.

Dear reviewer,

Thank you for again reviewing our paper and your useful comments! We'd like to let you know that we've updated the paper to further address two of the points you raised, namely robustness to re-initialization, as well as robustness to the size of the encoding space. The results can be found in the Appendix, Section A.1.1. and should answer the questions in the affirmative: the approach is robust to both.

When you had opportunity to read our responses, please let us know if you have any further questions or comments. If you found our responses satisfactory, please consider increasing your score.

Thank you for providing more details regarding your concerns; we've striven to answer them as completely as possible given the additional information.

Motivation

Restating the clarification of our motivation from the general comment: we’re interested in what an independent learner under the constraint of believability considers most salient to an unknown communication system. K.P. Murphy's Probabilistic Machine Learning: Advanced Topics describes it thus in Section (32.3.2.1): "One criterion for learning a good representation of the world is that it is useful for synthesizing observed data. If we can build a model that can create new observations and has a simple set of latent variables, then hopefully this model will learn variables that are related to the underlying physical process that created the observations."

To answer the question directly regarding extracting the features from the data directly: we are naturally biased towards assigning meaning to features that appear meaningful to us in truly unknown data such as sperm whale communication. For example, we can count the number of clicks in a vocalization "by hand". Can we then simply pronounce this as a carrier of meaning? How are we sure it's not simply a side-effect of something else? To provide an analogy, surely bats hear "features" of our speech that carry absolutely no meaning to us since we cannot hear those frequencies - they are merely high-frequency artefacts.

As outlined in the general comment and the previous responses, the architecture gives us a way of letting an independent, unbiased learner suggest what it considers most salient. The learner has the following properties: (1) it has to be believable to an independent observer with access to real data, (2) the special encoding $t$ has to be consistent (3) it has to be salient else the model is wasting a precious encoding spot.

Thus, to answer your first question, this is in essence not about ensuring that $t$ is interpretable, us having already decided what it should be. We aim to answer what gets encoded in an unsupervised learning, no ground truth situation. Therefore, we believe there has been a misunderstanding about the basic aim of the paper.

Novelty & Causal terminology

As a reminder, for GANs, the "incompressible noise" $X$ also encodes information, that is, its values have direct effects on the outcome. Thus, "ordinary" GANs have just $X$ as their feature space. However, it does not have the above-mentioned properties (2) & (3). Thus, the goal here is to identify what gets encoded in $t$ as opposed to merely $X$.

The novelty compared with [1] is described in paragraph 2 of Section 2. To expand on that: [1] is fundamentally concerned with examining how neural networks learn features of data with ground truth - human speech. The forcing of extreme values is employed in a latent space interpolation problem setting (cf. chapter 20.3.5 in KP Murphy's book cited previously), with the architecture being an "ordinary" GAN. Thus specific, pre-determined phonetic features are focused on. Extreme values are employed in the context of manipulating single bits in $X$ while the rest are set at constant (random) values for a given, single, example in which the desired phonetic property has already been identified. This enables the author to examine, for example, how that specific phonetic feature morphs when one traverses the latent space outside the bounds of the training range. While the regression (not testing) methods employed are appropriate for an interpolation setting, there is no experimental setup with large samples of experimental units being tested.

Conversely, this work is in almost all aspects an inverse problem to the above. We are dealing with a structure discovery problem (Chapter 20.3.4 in the same book), where we have no ground truth. Thus we situate our methodology within an experimental setup and wish to test for what properties are encoded. The criterion of something being encoded in a bit of $t$ is it undergoing the process of disentanglement in the causal effect space with sufficiently large "treatment" values in the same bit. The extreme values technique is used here (in contrast to [1]) to force this process of disentanglement, which is not studied in [1].

Thank you for again singling out the points of disagreement; unfortunately, we still feel there has been a misunderstanding of the paper on some of them.

Motivation:
I'm not sure whether it is fair to conclude that, because the fiwGAN model extract some features, it means that these features are important for communication and not an artefact of the signal. This reasoning seems flawed to me. I don't see any reason why the model couldn't encode artefacts (i.e. features that are not relevant to communication)

We have never claimed that what the model encodes is guaranteed to be meaningful. The aim of this application is to provide a method of obtaining a second opinion that is derived independently and does not share human biases, yet it has to be believable (+ the other properties listed previously). This is spelled out in the introduction of the paper and has been re-iterated in the rebuttals. This second opinion can then be used, for example, by researchers to help decide which research direction to prioritize.

That said, we have very good empirical reasons to give credence to the model. As stated in the first general comment: "Additionally, the fiwGAN architecture has been shown to uncover linguistic rules on human speech (references 3; 5; 2), hence we suggest (but not claim) that the encodings uncovered here might play a similar role in whale communication. This is further bolstered by the fact that it independently learns a rule present in real-world codas, but not in its training data (Section 4), as well as determining that the number of clicks is informative, which is the basic consensus [among the experts] in the domain."

Causal terminology:
I respectfully disagree with the authors. I think introducing the jargon of causal inference here is "overkill" and does not serve the reader. What has been done here are standard latent traversals (with additional averaging over $X$ ). Sure you can always explain these in the language of causality, but I don't think this brings something new to the table.

It is precisely the ruling out of the effect of $X$ that is needed for identification of the effect of $t$. Thus, the "additional averaging over $X$", which is what this amounts to when (and only when) using the ATE estimator (one of three approaches presented) is a crucial feature. A standard latent traversal does not work here since you cannot proclaim the effect to be encoded in the "special" $t$ space without ruling out the possibility of it being an artefact of $X$. Any restatement of these requirements in other language would, in practice, amount to re-inventing causal inference for randomized experiments, making it less clear to the reader.

Robustness: I was talking about rerunning the learning phase multiple times. I saw that you added an extra rerun in the appendix A.1.1 showing the same results. My point is that this is only two runs, I think this is not enough. Could you show 10 runs? What fraction of these 10 runs shows the desired behavior?

This should be clarified in light of the misunderstanding regarding the motivation of the paper discussed above. We aim to present a methodology of extracting a "second opinion" from independent learners that don't share human biases. The methodology replicates perfectly, since a virtually identical disentanglement phenomenon can be observed and quantified after using the CDEV method on an independent model.

We feel that the requirement for an ensemble of 10 (or 100) of independent learners to agree 100% on all of the salient features is overkill and missing the point of the paper. Even in that case, we would still not proclaim these to be the true carriers of meaning of in whale communication, as explained in the motivation rebuttal above.