NeurIPS 2020

Evidential Sparsification of Multimodal Latent Spaces in Conditional Variational Autoencoders

Review 1

Summary and Contributions: This paper introduces a technique for sparsifying the discrete latent space of a CVAE. The method is grounded in evidential theory and is applied post-training: a mass function equivalent to the softmax transformation is constructed such that the mass over singleton sets is sparse. Singleton sets (i.e. latent classes) with mass 0 are then filtered out and the distribution is normalized. They demonstrate that their method effectively sparsifies the latent space while maintaining more modalities than other sparsification techniques in the domains of image generations and trajectory prediction. --- Post-rebuttal update --- The authors adequately addressed my concerns in their rebuttal, and I've increased my score to a 7. I think a discussion about tuning the level of sparsity is important (also pointed out by another reviewer) and should be included in the main text. Some results about static thresholds for MNIST would also be great to have in the appendix.

Strengths: 1) Strong empirical results - the method seems to be on-par with softmax while also sparsifying the latent space, whereas sparsemax clearly drops modes and performs worse. Multiple domains are evaluated. I appreciate the proof-of-concept experiments with MNIST to build intuition. 2) The paper is well motivated and very well written. I’m not too familiar with evidential theory, but I was able to follow along in section 2. This is an interesting perspective of classification / supervised learning that I haven’t encountered previously.

Weaknesses: 1) The biggest difference between this and sprasemax is that this is applied post hoc whereas sparsemax is differentiable and applied during training. Shouldn’t a fair comparison also consider other sparsification methods that can be applied post hoc? For instance in Figure 2 for the MNIST experiment, it looks like the method selects the top k largest probability masses. Could you also consider a naive baseline method where the probabilities below a certain threshold are set to 0 and redistributed? Of course you will need additional tuning of the threshold and the method is not as theoretically grounded, but I’m just curious how this naive method would perform. 2) There are also other sparsification techniques that are differentiable and can be applied during training, such as the ones in [1]. The paper can be strengthened by comparing with more techniques (either in discussion or additional experiments, or both). [1] Laha et al. On Controllable Sparse Alternatives to Softmax.

Correctness: Yes

Clarity: Yes

Relation to Prior Work: Missing reference to [1].

Reproducibility: Yes

Additional Feedback: - In Eq. 8, what’s \hat{\beta_{jk}} ? - Is there a typo in Eq. 21 in the appendix? Should the second term be the mean of all bias parameters? - A brief summary of sparsemax would help (maybe in the appendix)

Review 2

Summary and Contributions: The paper introduces a methodology for reducing the dimensionality of the discrete latent space in variational auto-encoders. The approach is based on the principles of evidential theory, that authors use to filter out the latent classes that do not capture evidence of the data.

Strengths: In general the paper is well-written, and demonstrates a high-consistency and robustness in the flow of technical explanations. I particularly appreciate the motivation and introduction of the work, something that was not easy to do that well in this case. Moreover, the authors did a great job in the synthesis of evidential theory in the beginning of section 2. The idea of using the evidence formulation of Dempster (2008) for a posterior decision-making of what latent classes can be removed is definitely interesting and introduces a new brach of work in the design of discrete latent spaces. This last point is the one that I remark as the most important and novel in the work. I did not find or remember a similar approach on this, and neither the paper is super-conditioned to some other previous work. Last but not least, authors dedicated 4 pages to experiments, evaluation, figures and discussion, something that is valuable and proves the spirit of the authors for demonstrating the performance of the solution.

Weaknesses: I find three points of weakness that decrease the potential impact of the work: i) References are too focused on “application” papers and evidential theory, while authors want to present a new methodology for reducing the discrete latent space dimensionality in auto-encoders. Why do I say this? Well, if authors include more references or comments about theoretical papers of VAEs, this work could be better contrasted with other similar works, and will potentially facilitate its disclosure.. ii) Apart from the references, authors fail on the fact of not including a short paragraph or subsection about the CVAE with a few details to refresh the ideas and having a work that is totally self-contained. They could have sacrificed half-page of experiments to described the conditional auto-encoder better. What a pity! iii) I appreciate the effort dedicated to the experiments, however, I have a few questions that I would like to see answered: the error with the number 9 as “even” in Figure 2 is partially explained, ok. could the approach amplify errors or mistakes in the discrete latent space? that is, the good part of uncertainty is that it is never too certain or the opposite. So, if the number 9 was badly compressed in the latent space, and then so many other dimensions removed, after re-normalising, the number 9 gets importance? is that what is happening? The other question is about Table 1 and the accuracy performance under the 50% in classification, pretty bad, right? why is this? how could be improved?

Correctness: I do not detect any mistake or error in the paper, but I would like to see the latent classes z_k and its domain explained a bit better. I know authors refer very well to the softmax transformation, but, the reader does not know if the z_k are one-hot-encodings, natural numbers, real values, etc. This fits in the paragraph of L58 or later in the description of L68.

Clarity: The paper is clearly written and amenable to be read. The last sentence of the conclusions (L309) could be reformulated or omitted. “We leave the investigation of evidential latent space … to future work…” sounds a bit unmotivated. Why not “In future work it would be interesting to explore the dimension or the characterization of the ev. latent space”, something like.

Relation to Prior Work: My concerns about the prior work related to theoretical or more “pure” VAE papers where described in the previous sections of the review.

Reproducibility: Yes

Additional Feedback: Minors: L58: lack of information from conflicting information? information from information? Paragraph L58-L65 a bit repetitive wrt the end of the intro. Could it be elaborated a bit more? L95: what is “j”? what is indexing? L93—L102: more dense part of the paper, some extra information in the appendix perhaps? for helping non-familiar readers? L146: “these real-world (…) require high degrees of distributional multimodality”, ok, I trust the statement, but why? elaborate a bit please. Figure 2: your columns in the histogram should appear in a darker color when printing in grey-scale. otherwise there is no difference and I had to go to the original colored pdf. ###### [Post-rebuttal update] ######## I appreciate the time dedicated by the authors to answer the 3 points of weakness that I commented in the initial review. Looking again to the paper, I find the idea definitely interesting and the advances on the design of discrete latent spaces will have an impact in the future. In general, I think that it is a good paper and my concerns have been addressed in the response, so I revised my score upwards.

Review 3

Summary and Contributions: This paper presents a method to sparsify the latent representation of a Conditional Variational Autoencoder. Experiments show the presented method outperforms sparsemax and it is competitive to softmax while sparsifying the latent space.

Strengths: The paper presents a nice theoretical grounding of the method. The technical experiments appear to be correct and they show the presented method outperforms the current sparsemax method.

Weaknesses: The presented method outperforms sparsemax in terms of accuracy, but sparsemax is reducing the latent space by a larger %. In experiment 3.1 sparsemax reduces it by 99% while the presented method reduces it by 89%. Is it possible to adjust what % of the embedding space we want to reduce? In that case I would encourage the authors to present an analysis of how the performance of their method drops as the reduction of the embedding space increases. And then analyze which method provides a better trade off of accuracy vs reduction. In case it is not possible to tune the reduced % of the embedding space and it is just a consequence of the method itself, I would encourage the authors to state that in the paper. If the authors give a convincing explanation to this I am eager to increase the rating of the paper.

Correctness: The methodology appears to be correct.

Clarity: The paper is well written and easy to follow. The evidential theory section was harder to follow to me, I was not familiar with it.

Relation to Prior Work: The work is properly contextualized.

Reproducibility: Yes

Additional Feedback: