Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: summary: The paper presents a generative view of attention: N hidden memory units each of which generates observed a query and a value. The memory units densely connected with each other. The paper shows that, given queries, the value of a memory unit, in a certain condition, is computed in a similar way as in attention, using EM. 

Applying this new attention, called probabilistic attention, to interactive image segmentation tasks (where users provide some ground-truth pixels' values on the fly), the paper shows better results than using traditional attention on GrabCut and Berkeley datasets. 

**Contributions** 
1. novel explanation of attention, leading to new attention mechanism relying on probabilistic 
main_review: **Originality** 

Explaining attention is not new but using probabilistic generative view in this paper is novel and very interesting. It will open a door to a new class of attention layers that have wider probabilistic properties. 

I particularly like the trick of letting beta -> 0 in section 3.3. This is counterintuitive to me as beta -> 0, eq 9 implies that v is more and more independent of all u_j. Turns out, in the end, we have traditional attention. Also, line 142, it is interesting that we just need to use one EM update, exactly like the attention. 


**Quality** 

The paper technically is sound. I found the maths correct (though some steps are missing, such as from B3 to B4 where beta1=beta2=...=beta is crucial). 

I would like to see more in the paper: 
1. What is the effects and use of EM? It's unclear to me whether EM is used together with training the networks for priors. If it is, how? 
2. Interactive image segmentation looks like a good tasks for attention. The authors claim this probabilistic attention is more generic applicable. Is there another successful story? Is it simple just to pickup a task, a model which uses attention, and replace that attention by the probabilistic attention? Is tuning precision prior important?

**Clarity** 

The submission is well written. 

**Significance**

The results shown in the paper is important as now we can have more freedom to extend attention, especially in probabilistic ways. 
limitations_and_societal_impact: I don't see any negative societal impact.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper describes an EM-based approach to propagating attention parameters, showing strong performance on an interactive segmentation task.
main_review: The paper describes a probabilistic attention model which contains standard transformer attention as a special case, along with an online value propagation method which allows humans to update attention weights in a principled manner. This is evaluated in the domain of interactive segmentation but could seemingly be applied to other domains such as interactive machine translation. This paper is not in my area, but to the best of my knowledge the approach for attention propagation is novel and potentially applicable to a wide number of human-in-the-loop tasks. Although the empirical gains are modest, both the theoretical and empirical sections are clearly written and motivated.

The empirical results show that:
 - Probabilistic attention outperforms standard attention in a low-click interactive segmentation domain and performs similarly to standard attention with a greater number of clicks
 - Unsupervised key adaptation (cf. Section 3.5) leads to significantly improved IoU in a non-interactive domain

The authors also released a Pytorch layer implementing their proposed approach. The paper is seemingly missing a comparison to other methods for interactive segmentation and does not justify its choice of the BoTNet50 architecture as a baseline model. Once again, though, the paper is out of my area and I am not familiar with the state-of-the-art in this domain. I will choose to defer to the other reviewers on my recommendation for acceptance.
limitations_and_societal_impact: N/A
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: This paper offers a new interpretation of standard dot-product
attention as a mixture model. The model assumes memory units are
latent variables that dictate the probabilistic interaction between
query and value vectors. The significance of this probabilistic
interpretation is twofold:

1. MAP inference under a carefully constrained Gaussian mixture model
   case of the model yields exactly the update rule of standard
   dot-product attention. Prior to this the most similar
   interpretation of attention was through modern Hopfield networks
   (Ramsauer et al., 2021).
2. The model admits an EM algorithm which allows for either online or
   offline learning in the precence of partial annotations. 

The paper applies this probabilistic attention approach to interactive
semantic segmentation by incorporating it in various ways within
BotNet. The probabilistic attention either replaces standard attention
or is used within the self-attention at the last part of the
network. Under various settings (e.g. full or axial attention;
factored or full relative positional encoding), the incorporation of
probabilistic attention improves over the corresponding baseline. 

The paper finally introduces a corrective self attention layer in
order to more effectively pass along information from an annotators
corrections of the model output. Results show that such a use of these
corrections is more effective than not.
main_review: Strengths:
- The paper presents a novel interpretation of standard dot-product attention as a probabilistic (mixture) model.
- Bayesian inference in the model enables online updating of the
  mixture parameters and corrections on a subset of values to be
  propagated.
- The results on interactive semantic segmentation suggest that the
  approach is a drop in replacement for attention that can improve
  over baselines without.

Weaknesses:
- From the initial description of the mixture model, it was a bit difficult to understand *why* it would make sense to have latent memory units at all. Only later upon thinking what these were being used for within the context of interactive semantic segmentation did this become clear.
- The probabilistic attention mechanism is only applied to one task (interactive semantic segmentation). It would be interesting to see its effectiveness in other settings.

limitations_and_societal_impact: Yes
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: Summary and Contributions

The authors study a probabilistic interpretation of attention mechanisms for interactive segmentation.  The goal is to show that self-attention is related to MAP and EM can be used to induce the posterior distribution over attention scores.  The main contributions are: probabilistic interpretation of attention as a generative model, interactive segmentation with the proposed attention model, and classification.  The study shows that the proposed model has competitive results compared to related work.

main_review: Strengths

Clear description of background knowledge, proposed model, and related work needed to understand the proposed model.  
The authors perform a comprehensive comparison across different tasks.

Weaknesses

It is not clear the motivation to  define attention as a generative model. 
It is not discussed the possible difference of the proposed models with variational attention models.

Questions to the Authors
Please address the following questions during the rebuttal:

Which is the relation of the proposed model and variational attention models used in NLP applications? e.g. Variational Attention for Sequence-to-Sequence Models
A possible extra contribution could be the discussion of the proposed model for text classification tasks. e.g. GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding

limitations_and_societal_impact: Yes, the authors addressed  limitations.
review_title: null

Meta-review: This paper builds and analyzes a probabilistic mixture model for which softmax attention mechanisms are a special case. Reviewers  find the construction enlightening, educational, and with high impact potential. They strongly recommend improving the presentation to make the "story" and motivation much clearer upfront: the reasons for the construction don't reveal themselves until the connections to attention. The constructions seem different, but uthors should discuss the relationship with other probabilstic attention work (e.g. variational attention by Deng et al, but also Heo et al, NeurIPS 19, Bahuleyan et al, Coling 19). The font sizes and line markers/colors in the plot should be changed to improve readability and skimmability of the paper.
Decision: Accept (Spotlight)