Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task

Summary

The paper studies compositional generation abilities of conditional diffusion models. The main contributions of the paper are the concept graph framework, which is used to examine compositional abilities in a simplified setting, and insights on the learning dynamics of diffusion models.

Strengths

The paper is very well written, motivated, and easy to follow. The problem the authors are investigating is relevant to know the limitations of compositional generation of the current diffusion models.

Weaknesses

Even though the paper provides a very pleasing framework to investigate compositional capabilities of diffusion models through simple and highly controllable interventions, I think the submission is incomplete. This is mainly because the paper considers only a single architecture and does not provide guidelines how insights from concept graph framework could be further studied or provide validation that they hold in a large scale setting. Additionally, I would like to see a summary answering the questions from the abstract: “What are the reasons underlying this behavior? Which concepts does the model generally find difficult to compose to form novel data?”

Questions

1. When does the sudden emergence of compositionality occur during training, can this be somehow predicted? Does it happen at the same time for different architectures and training configurations (noise schedules, augmentations etc.)? Providing answers to these questions would be valuable to researchers designing inductive biases to models. 2. How is the critical threshold for learning new capabilities in Fig. 8 determined? Is there a practical way of estimating critical thresholds for learning harmful concepts based only on the given training dataset? 3. Why Fig. 8 results could not be interpreted as if you have even a slight amount of harmful concepts in the dataset, then the model can eventually learn these given sufficient amount of training/capacity? From this point of view even a small amount of harmful samples leads to unwanted behavior and filtering training data is very important. Minor points on improving the clarity: 4. Potential typo at line 188, “0010” corresponds to a sample in the training set. 5. Fig. 5 duplicate sentence. For clarity Fig. 5 b) and c) would benefit having the same units in the x-axis (either optimization steps or epochs). 6. I would remove the bullet point: “if so, under what circumstances does it fail?” from the beginning of Sec. 4 to Sec. 5 because that is where this question is assessed. 7. Figure 8 lattices are potentially flipped. The lattice of (b) should be the lattice of (a) because in (a) the number of samples from “001” is modified, and vice versa. The lattice (b) is also redundant, I suggest refactoring the figure to contain three subfigures (a) showing the lattice and (b), (c) showing the interventions. Additionally, the x-axis shows the number of samples and the text discusses frequencies. I would switch the x-axis to show frequencies instead of the number of images to improve interpretability in a more general case. 8. Fig. 9 says “In this example, large objects are red, and small objects are blue.”, however in (a) there are large objects in both blue and red. In general, figures would benefit if they were converted to vector graphics format (pdf, svg etc.) because they need to be zoomed in order to view.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

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.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

The authors adequately addressed the limitations of their work.

Summary

This paper proposes to empirically studied how compositional structure emerges in diffusion model. The paper proposes the abstraction of concept graphs, and illustrates how diffusion models first learn to fit the training data before compositionally generalizing. The paper illustrates how diffusion models have difficulty disentangling data and modeling low data concepts

Strengths

- The paper is clearly written and the color coding through the text and figures greatly helped comprehension of the paper - I enjoyed the introduction of concept graphs and the illustration of compositional distance with respect to graph - The analysis in the paper is quite enlightening, illustrating how diffusion models first fit in distribution before generalizing out of distribution, as well as its struggles on finding confounding factors between variable and low data variables.

Weaknesses

- The evaluation setting is rather simple and focuses on a single synthetic dataset with 3 classes of attributes - It would be good to study generalization both to more complex images (for instance photorealistic synthetic scenes rendered using something like Kubric) as well as to more factors larger than 3 - In practice, a lot of concepts in the world follow the Zipf distribution -- it would be interesting to analyze that - It would also be interesting to see how syntatic form would effect compositional generalization - Some theoretical analysis on compositional generalization would also be interesting

Questions

See above

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

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.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

Yes

Summary

The authors try to understand the compositionality aspects of generative models by training a conditional diffusion model in a toy setting on synthetic data. They show that the models indeed learn to be compositional if we train longer. They also hypothesize that the sudden emergence of compositionality in the later parts of training is due to multiplicity of how the model learns the underlying factors. They also show that it is hard to disentangle and generalize to new concepts if the underlying factors are highly correlated.

Strengths

The paper is easy to follow. The study of compositionality in diffusion models is a crucial problem to understand. The authors studied it in a controlled setting which is novel.

Weaknesses

The authors chose a very simple synthetic dataset to study this problem. The dataset has only 3 attributes. Even though some of the observations make sense, we have no guarantees that any of the results will extend to the real world. The figures are quite confusing. Especially the colors. Blue (albeit a different shade), was used as an attribute and to denote the training data. In Section 4, the authors used a bit of sensationalist language, such as “sudden emergence” etc, while such terms are not defined nor appropriately cited. They can improve the writing in this section.

Questions

1. Did you try or have results with synthetic data with > 3 attributes? 2. Why did you not use synthetic data with real objects instead of colors and shapes? Verifying your claims on even a small real-object dataset would make the paper much more robust and useful. 3. I might have missed this detail, what is the size of the test set, did you look at only the “pink” examples in the figures?

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

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.

Soundness

3 good

Presentation

2 fair

Contribution

3 good

Limitations

N/A

Summary

This work proposes a framework for studying the compositional generalisation abilities of diffusion models (or generative models more broadly). To that end it introduces the notion of a concept graph which the authors use to manipulate simple synthetic datasets. These concept graphs arrange different combinations of concept values and variables in a way that perseveres a notion of distance between different combinations (based on bit flips). By studying how performance changes as models are required to reconstruct concept value combinations that are further apart from the training data, they can draw inferences regarding the emergence of generalisation capabilities in diffusion models.

Strengths

1. The article is very well written and easy to follow. The idea of the concept graph and the manipulation of the dataset is clearly explained and well motivated. 2. The use of a hypothesis driven research as opposed to the standard benchmarking approach is welcomed change compared to most of the research in AI. That the way the authors present it makes it seem as particularly novel is more a reflection on the field than this particular work (but see later on some suggestions regarding this point). 3. The point correlations between concept value make learning difficult for the models is important since it highlights how much model still rely on correlations in spite of the fact of their superior generative capabilities.

Weaknesses

There are no substantial weaknesses, but there are some errors and omissions when discussing the literature which I will discuss below.

Questions

1. Is Multiplicative Emergence unsurprising when the authors are forcing accuracy to be 0 if at least one concept value is incorrect during out-of-distribution generation? 2. I find it weird that colour takes longer to learn than the other properties. Since the reconstruction error must be very high even if the shape and scale are correct, I would expect cooler to be learned quicker. Do the authors have some insight into why this happens? 3. Is the relation to grokking really that strong? In grokking, models still exhibit high validation error even if the test error is high. But here

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.

Confidence

5: You are absolutely certain about your assessment. You are very familiar with the related work and checked the math/other details carefully.

Soundness

3 good

Presentation

4 excellent

Contribution

3 good

Limitations

1. It is incorrect to characterise some of the work discussed in lines 120 and 121 as merely performing benchmarking. Indeed at least [94], [95] and [99] perform manipulations of the training and dataset in much the same way as this present work. Thus, while I definitely like that the authors took a more hypothesis driven approach to their work, it is not by any means the case that this is has not been done before. Other works that do this include [1] and [2]. While these may not be based on generative models, they are still relevant examples of the kind of study that the authors are advocating for. 2. Relatedly, the authors should discuss the relation of their work with [3] and [4]. Unlike the previous references, these do involve compositional generalisation capabilities of generative models. The former also provides one characterisation of compositional generalisation in generative models that is similar to the one used in this work. Thus it is indeed not the case that there have been no previous proposals and that [101] is the only noteworthy attempt (which by its own admission, just summarises previous definitions anyway). 3. The latter uses an approach based on transforming input images which allows it to identify the concepts that vary between images in a way that resembles the example presented in Figure 2, panel b. Their results show a similar pattern as the one in this work where combinations that are close to the training data are easier for the models. I believe that both this work and the previously discussed ones deserve a slightly deeper discussion. 4. Lines 291 and 292 are very close to each other which makes the caption of Figure 7 and the main text hard to distinguish. [1] Hermann, K., Chen, T., & Kornblith, S. (2020). The origins and prevalence of texture bias in convolutional neural networks. Advances in Neural Information Processing Systems, 33, 19000-19015. [2] Geirhos, R., Jacobsen, J. H., Michaelis, C., Zemel, R., Brendel, W., Bethge, M., & Wichmann, F. A. (2020). Shortcut learning in deep neural networks. Nature Machine Intelligence, 2(11), 665-673. [3] Montero, M. L., Ludwig, C. J., Costa, R. P., Malhotra, G., & Bowers, J. (2020, October). The role of disentanglement in generalisation. In International Conference on Learning Representations. [4] Montero, M., Bowers, J., Ponte Costa, R., Ludwig, C., & Malhotra, G. (2022). Lost in Latent Space: Examining failures of disentangled models at combinatorial generalisation. Advances in Neural Information Processing Systems, 35, 10136-10149. ** note that I used the same citation numbers the authors used for the other references i.e. [95] above corresponds to reference [95] in the main text.

Typo: Please replace "cross-entropy" with "probabilistic accuracy"

Dear Reviewer kruN, We would like to clarify a typographical error in our earlier rebuttal. In our discussion pertaining to Figure R3, please replace "cross-entropy" with "probabilistic accuracy." Initially, we experimented with cross-entropy loss, but for consistency with the notion of accuracy, we transitioned to this updated measure. We apologize for any confusion and direct you to our general response for further details.

Thank you for the rebuttal

Thank you for the response. The rebuttal answered my questions. I am updating my score.

Rebuttal Response

I thank the reviewer for their rebuttal response -- I will maintain my current score as I think the paper would be strengthened much more if a different dataset other than CelebA is considered (for instance attributes of CLEVR or rendered Kubric datasets). The CelebA dataset is very biased and its difficult to access the accuracy in which concepts are correctly generated.