Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper is motivated by the formal concepts of coherence and consistency in neuro-symbolic AI, and the fact that such concepts have not been formalized in the connectionist paradigm. It claims that these concepts are important for assessing transfer learning performance. This is demonstrated by formalization of these concepts for neural networks, proposal of the "relation-decoder" model, and transfer learning experiments to show that good transfer performance is associated with coherence being maintained across domains and can be predicted by ability to maintain consistency over unseen inputs. 
strengths_and_weaknesses: *Originality*: to my knowledge, this paper is original. Beyond the labels, I'm not familiar with these specific formulations being used as metrics for neural networks. This paper spends time formally defining predicate logic concepts that may not need defining (at least not in the main paper) as they are very fundamental, but the soft structure formalization is technically new to me. 

*Quality*: this paper takes a well-scoped problem and lays out a clear strategy to show it. The goals seem to be to present formal definitions of consistency and coherence that are meaningful in the connectionist paradigm, create a transfer learning framework from which these metrics can be calculated, and show that they are useful indicators of transfer learning ability - presumably, that they predict standard performance metrics while also providing more insights. I think this is done successfully - the setup and experiments are very much called for by the aims. 

The only area for improvement I would bring up is usefulness beyond the relation-decoder framework - if the metrics only work for not only a narrow set of architectures but specifically the architectures in this paper, then it seems the paper should be more about the architecture than the metrics (though this would require different experiment analysis and to some degree different experiments). 

*Clarity*: This paper is quite well-written. Unlike most papers, the paper roadmap is clear early on in reading. I felt I had a pretty good mental model for the contributions after the intro, and could consider the rest of the paper from that perspective.

Some areas for improvement include a less dense and better-illustrated formalization section - this may be more about the paper than the research, but a lot of space is devoted to formalization steps prior to the structure and soft-structure definitions that may not be necessary for someone familiar with basic predicate logic, which is likely most of the audience. Some of the more composite concepts (signature, interpretation) would benefit from examples and intuitive explanation, since they seem to be more familiar and easy to grasp than they are presented as being. 

*Significance*: This paper presents novel (to my knowledge) metrics for assessing transfer performance. As machine learning moves toward scale and ubiquity, transfer performance and robust evaluation are both important areas in my opinion, so these are posed to be valuable contributions. My primary concerns about significance are related to my comments in quality - it's unclear to me how far these metrics can apply. While other architectures may fall under the same framework mathematically, I think the burden of assessing scope is on the paper since the message is ultimately about the value of the metrics. 
questions: - In the space of transfer learning architectures, and NN architectures in general, what all falls under this formalization paradigm?
limitations: The paper is upfront about its technical limitations. Based on the last couple sentences of sec7, it is likely that the authors and I disagree on the importance of having other architectures considered in this paper, but the acknowledgment is valuable nonetheless. 

The discussion of social limitations leaves something to be desired, but I commend the authors on engaging with it at all when a lot of core theoretical papers get away with a generic sentence. The mention of logic, biases, and disentanglement are interesting and merit development; the claim about trustworthiness of coherent concepts is also intriguing and would benefit from examples and some investigation. 

To go deeper, there are theoretical and empirical STS-type works that would engage further with the ideas of logical validity and absolutism as well. However, that would be getting beyond the scope of this type of statement. Ultimately these are **not** knocks on the paper - I only have words for this section because the authors chose to say something (anything) more than "N/A".
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: This paper addresses the problem of how logical predicates (e.g. isGreater, isSuccessor, etc.) can be learned from real-world data in a manner that transfers from one domain (e.g. images of handwritten digits) to another (e.g. images of stacked blocks). Focusing on ordinal relations, the paper first proposes a formal theory that relates first-order logic to 'soft structures' which can be learned directly from real data. This theory is then leveraged to derive formal definitions of 'consistency' (consistency of learned logical concepts within a domain) and 'coherence' (consistency of learned concepts between domains). Finally, a neural network architecture and training procedure are proposed. A particular variant of the architecture, with a novel comparator function, performs well on the transfer evaluation, and performance on this transfer evaluation is generally shown to align with the proposed definitions of consistency and coherence.
strengths_and_weaknesses: I have reviewed this paper before, and after reading through the new manuscript in detail, it appears that the authors have not made any changes to address the concerns that I raised in my previous review. Therefore, I am including that review below. I look forward to hearing the author's responses:

I am not familiar with any other work that attempts to build a rigorous theory connecting first-order logic with concepts learned from real-world data, so this aspect of the work was highly novel. The proposed neural architecture is well-motivated on the basis of the preceding theoretical considerations, but in the end is not particularly novel -- it amounts to an autoencoder paired with supervised training of relational concepts. The proposed comparator function is novel, but I worry that it is over-engineered for ordinal relations studied in this work, and the generic neural network relation decoder performs surprisingly well by comparison.

Overall, the novelty and significance are primarily in terms of the theoretical foundation sketched in sections 2-4. I found these sections deeply stimulating, but in the end I have significant worries about the practical relevance of the overall paradigm. The general worry is that the approach seems well-suited to the ordinal concepts studied in this work, where the formal theory governing these concepts can be neatly defined. It's unclear how the proposed approach will scale to more complex, fuzzy, real-world concepts (such as those that figure in natural language), where the specification of such a formal theory is likely impossible.

The authors may argue that their approach doesn't actually require a formal theory to be specified for the concepts in question. Strictly speaking, all that is required for training the proposed neural network model is to have training examples corresponding to positive and negative examples of these concepts that can be used for supervised learning. This doesn't necessarily require a formal theory of how these concepts relate, and therefore is perhaps more easily scalable to more complex concepts whose meaning can't be neatly defined. But this then leads me to wonder, what is the purpose of connecting this approach to a theory in terms of first-order logic? Beyond being an interesting intellectual exercise (which it certainly is), does this suggest any particular directions for learning real-world concepts in a manner that transfers better between domains? On its face, the proposed neural network architecture and training procedure constitute a rather straightforward way of learning concepts through supervised learning, and it's not clear that their development depends in any way on the accompanying theory.

Another concern is that it's not even clear to me whether concepts (in the sense of logical predicates) are needed at all, and it isn't clear what we'll do with these concepts once we have a neural system that can obtain them from real-world data. It would be helpful if the authors could sketch out how they envision this approach fitting into the broader program of AI research, and in particular how these learned concepts can be useful for downstream functionality, e.g. applied problems in computer vision or NLP.
questions: My questions are outlined in the 'strengths & weaknesses' section above.
limitations: I do not envision any potential negative societal impact from this work.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: The paper formalizes coherence and consistency measures in ANN models that consist of an encoder ($\psi$) and relation ($\phi$) networks. To demonstrate the usefulness of these measures, they train autoencoders to additionally be coherent and consistent across two domains with respect to a single relation that was learned in only the source domain. They show that more consistent models, which implement a proposed DC model as a relation model $\phi$, are also better in zero-shot transfer to unlearned relations in the target domain. Thus, the paper demonstrates that coherence and consistency, as they formalize it, are useful for evaluating relation models.
strengths_and_weaknesses: Strengths:

1) Clear writing.

2) The DC relation-decoder seems promising for other applications.

3) The formal structure that was used to define coherence and consistency is interesting because it formally describes fundamental concepts.

4) An interesting main result, of consistency leading to better zero-shot transfer to other relations.


Weaknesses:
1) Missing supplementary materials don’t allow for a full paper evaluation.

2) The loss of eq. (9) is very similar to the established Relation Network (RN) loss [1, 2]. The paper ignores this similarity. Recognizing this similarity would have enabled comparison with results that were obtained using RN and its derivatives.

3) Following the previous point, I think that the formalism presented in the paper might not be justified. The paper could have been rewritten using only common machine learning terms such as the RN loss values and generalization errors.



[1] - Sung, F., Yang, Y., Zhang, L., Xiang, T., Torr, P. H., & Hospedales, T. M. (2018). Learning to compare: Relation network for few-shot learning. In Proceedings of the IEEE conference on computer vision and pattern recognition (pp. 1199-1208).

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[2] - https://en.wikipedia.org/wiki/Relation_network

questions: Request: the supplementary materials, and relating the work to Relation Networks.
limitations: The paper addresses its limitations well.
review_title: null

Meta-review: metareview: This paper has slightly mixed reviews, trending toward a weak accept overall. The paper's topic and approach are overall novel, supported by good experiments. It's an interesting paper that will likely spark further investigation and inspire other research. There is still some disagreement among the reviewers, with recommendations ranging from accept to weak reject. In particular, the reviewers believe that, while overall well written, the paper could still use some improvements in presenting the relationship among the ideas and the architecture. In particular, the authors are encouraged to revise their presentation to better present "the architecture as merely a testbed for the proposed losses", as suggested in the discussion below. These revisions are easily made. The reviews also suggested improvements in a working example, which the authors' stated already exists in Fig 3 and admit is rather dense. It would benefit the paper to include a more detailed and clear work-through of the example, possibly in summary in the main paper and then in detail in the appendix.

Side note: the authors' privately expressed concerns were taken into consideration by the meta-reviewer in evaluating this paper.
confidence: Less certain
Decision: Accept