Summary and Contributions: The authors propose to construct a semantic memory module based on Prototypical Networks in order to boost the performance of few-shot recognition. Specifically, they model the memory recall part as a variational inference framework, such that the latent memory and class prototypes are stochastic. The experimental results suggest that the proposed method improves on the base Prototypical Networks on various standard benchmark datasets for few-shot classification.
Strengths: The main strength of this paper is that it provides a novel perspective on few-shot classification that we need a semantic memory module to better structure the previous experiences. In my opinion, although not discussed in the paper, this intuition can be useful for the combination of continual learning and meta-learning, as an external memory module could help avoiding catastrophic forgetting by structuring and well preserving the past experiences. And the experimental results show that the proposed method is competitive with some of the recent few-shot recognition methods on various benchmark datasets and architectures.
Weaknesses: The main weakness of this paper is correctness and clarity. The detailed discussions are provided below. In my opinion, the correctness part is below the NeurIPS acceptance threshold, and it should be improved a lot. The second but less significant limitation is that, from Table 1 and 2, the major performance improvements come from "Variational prototype network", which is quite orthogonal to the main argument of this paper that making use of semantic memory is important for few-shot recognition.
Correctness: As mentioned above, I am a bit skeptical about the technical correctness for the variational inference framework. Specifically, - I think the latent z in Eq.(2) does not properly represent the class prototypes as z is conditioned on each individual x, not a entire class set (But on the other hand, Figure 1 shows that the latent z is conditioned on each of the class sets, and I'm confused which one is right). - Also in Eq.(2), it seems that the prototype variable z is conditioned on the query instances, which is weird because prototype should represent each support set. (In my opinion, in order to properly represent the variational inference framework for meta-learning, it would be better to use the framework of Neural Processes .) - In Eq.(3), I don't understand how the approximate posterior q(z|S) can have dependency on S, because according to the generative process defined by Eq.(2), the true posterior p(z|x,y) does not have the dependency on the entire class set S except for each individual point (x,y). - In wonder whether the intermediate variable m in Eq.(4) is included in the generative process as well, or not. If it is not included, then the inference of m should be based on semi-implicit variational inference [2,3] as the intermediate stochastic variable m is only for the approximate posterior. However, such a discussion has not been discussed in the paper and the ELBO expression Eq.(13) seems not to represent the SIVI procedure as well. Same for Eq.(5). - In Eq.(6), I don't understand why the first summation term appears. Also, I guess p(m|M_a, S) corresponds to q(m|M,S) in Eq.(5)? - I cannot find the definition of q(z|S,m)? - In Eq.(13), I don't understand how the second KL term appears. = Reference =  Garnelo et al., Neural Processes, arxiv 2018.  Yin et al., Semi-implicit Variational Inference, ICML 2018.  Molchanov et al., Doubly Semi-implicit Variational Inference, AISTATS 2019.
Clarity: I think the clarity of this paper is below the acceptance threshold as I guess many parts in the approach section are incorrect. - Also, in the motivation side, it would be good to add more discussions and intuitions about why making use of semantic memory module should produce better results than the traditional Prototypical Networks. - I guess that the graphical model in Figure 1 represents the computational graph, which consists of both generative process and posterior inference part. It would be better to distinguish between the two (e.g. bold vs. dotted line) for better readability. - I would be good to discuss a little bit in more detail about the form of each diagonal gaussian distribution.
Relation to Prior Work: There seems no significant problem with this part.
Additional Feedback: I have some more questions. - Do the query instances also refer to the memory module? In other words, are the two inference pipelines for support and query set the same? - What is the use of batch normalization? Is it transductive via batch normalization or not? - Figure 3 suggests that the performance can be further improved if the memory size increases further. Why did you stop at 64? Is it because of some computational issue? - In Figure 2, the shape of the distributions are all unimodal, although the hierarchical posterior distribution defined in earlier sections implies that it would be multimodal. Could you explain about this? Overall, I think the submission is below the acceptance threshold. I suggest the authors to revise the correctness of the variational inference part.
Summary and Contributions: The paper proposes a latent variable memory that enables consolidation of concepts in a semantically similar manner. The memory improves the downstream task of few shot classification in a variety of standard few shot learning benchmarks. Overall the paper is presented in a clean Bayesian manner, incorporating a variational lower bound that captures the objective in a meaningful probabilistic manner.
Strengths: 1. The paper is well written and easy to understand. 2. The proposed method is SOTA on all tested tasks. 3. The use of graph based memory updates are a novel contribution as far as I can tell. 4. The proposed Bayesian framework is elegant. 5. The ablation against a non-distributional memory are appreciated.
Weaknesses: My main concern with this work is the lack of comparison to other (highly) similar memory models such as the Kanerva Machine (KM)  & Dynamic Kanerva Machine (DKM) . As far as I can tell there are no other memory models such as NTM / DNC / KM / DKM used in the baselines. The authors of [2, 3] show a drastic performance differential against non-memory models due to their ability to fuse information across an episode of samples (in the case studied here it would be fusing information across episodes). A fair evaluation of a memory model should include other memory models. ** I will be reading the author responses and will change my review given that the authors address / clarify the points from this review **  Wu, Yan, et al. "The Kanerva Machine: A Generative Distributed Memory." International Conference on Learning Representations. 2018.  Wu, Yan, et al. "Learning attractor dynamics for generative memory." Advances in Neural Information Processing Systems. 2018.
Correctness: 1. Is there a performance difference when approximating the addressing vector as a categorical (through VIMCO or the Gumbel-softmax estimator) instead of the softmax approximation? 2. I tried to run your code using a fresh anaconda environment with tensorflow-1.15 and the misc missing dependencies, but got a variable-reuse error. I was thus not able to directly validate the code. While code & the provided bash scripts are greatly appreciated, consider a docker container for the future to ensure a smooth workflow.
Clarity: The paper is well written and easy to understand. The biological parallels are interesting and aid in pushing the envelope of why we should use memory models, but some of the elucidations are a bit of a stretch. A few minor points should be addressed to make the paper cleaner: 1. How important is the EMA on the memory? Does setting the decay at 0.9999 vs 0.8 drastically alter performance? This can be added to the appendix, but is an important part of the memory updates and should be quantified. 2. While the ablation on variational memory / raw memory is informative, it is not clear if the same applies to the conditioned variable z. Does z need to be present? And if so, does it need to be stochastic?
Relation to Prior Work: 1. The paper is heavily related to  in its addressing mechanism (albeit in a smoother manner that linearly combines memory rows) and [2, 3] in its usage of latent variable memory, however  is only described in one sentence.  is not even referenced as a relevant work and  is incorrectly stated to have collapsing keys (see point 3 below). 2. While [2, 3] use a latent variable matrix gaussian, the addressing mechanism in practice becomes a linear combination of the read vector and the rows of the matrix gaussian mean (mentioned in ). While this paper presents SOTA in its target domain of few-shot learning there are no other memory models used as baselines. The authors of [2,3] showed that the Kanerva Machine drastically outperformed non-memory baselines and demonstrate its improvement over the DNC. 3. The KM and DKM models do not collapse to single slots as far as I'm aware since the keys have their own learned amortized approximate posteriors. Line 51 is correct for DNC, but not for KM/DKM.  Bornschein, Jörg, et al. "Variational memory addressing in generative models." Advances in Neural Information Processing Systems. 2017.  Wu, Yan, et al. "The Kanerva Machine: A Generative Distributed Memory." International Conference on Learning Representations. 2018.  Wu, Yan, et al. "Learning attractor dynamics for generative memory." Advances in Neural Information Processing Systems. 2018.
Additional Feedback: **Post Rebuttal Feedback** : I'm content with the author's responses and the addition of MANN, however I would recommend adding a comparison to DKM/KM as they are highly related. Thanks for the info regarding the EMA and Gumbel-Softmax estimator.
Summary and Contributions: The paper introduces a probabilistic modeling framework of the prototypical networks using variational inference. The model is augmented by an external memory, called variational semantic memory. The experiment results show the benefit of the proposed model in comparison to the previous models on mini/tieredImageNet and CIFAR-FS
Strengths: Overall clearly written although some improvements of the description structure would make reading easier. Probabilistic modeling of protypical representation is interesting. And the performance gain with the external memory is impressive. The experiment result is good overall.
Weaknesses: - Memory 'M' is discussed from the 'memory recall and inference' but what it actually means is detailed only later in the 'Memory update and consolidation' section. It would be better to introduce it earlier. - For without memory version, how q(z|S) is implemented is not clear. - In the model in Eqn(2), why not condition the model (prior and likelihood) on S? Similarly, why not condition the variational posterior q(z|S) on (x_i, y_i) as well? - The memory is basically constructed using the class label because for a new class the representation is just appended to the memory. Only the updated of the semantic representation is learned while learning the sematic (clustering) is done by provided labels. In this sense, I'm afraid to say that the term "semantic" is a bit overly used. - The memory mechanism seems not that novel because its base is on variational memory addressing and with some update like graph attention. - In Eq 8, the distance function g(M_a, S), is not clearly described. M_a is a vector and S is a set. How do you define a dot product. - In Eqn (13), "L = argmin" should be "argmin L" - Lack of some analysis on how modeling uncertainty (without semantic memory) helps. Table 1. shows the overall performance improvements but it's not clear how uncertainty contribute to this. - Some ablation study, such as without using the graph attention for memory update (which I think become similar to VMA reading) would be informative. - Discussion and reference to some Bayesian approaches to Meta-Learning is missing, e.g. Bayesian MAML (J Yoon et. al., 2018) and Amortized Bayesian Meta-Learning (S Ravi - 2018) - Discussion about "Gaussian Prototypical Networks for Few-Shot Learning on Omniglot" is missing
Correctness: The model and empirical method is correct.
Clarity: Clear overall. The structure of the description can be improved though. (See weaknesses)
Relation to Prior Work: Discussion on some important related works are missing (see Weaknesses)
Summary and Contributions: This submission tackles to mitigate the data scarcity in the few-shot learning problem. This work proposes a variational memory-based prototype network that uses probabilistic prototype representation rather than deterministic one in ProtoNet . The proposed method can be viewed as a non-trivial extension of ProtoNet. This idea is reasonable because, in the scarce data regime, uncertainty would be non-negligible, and also rare class data can be effectively dealt with long term memory. The proposed algorithm derivation is clear and intuitive. Also, they demonstrate the effectiveness of the proposed method successfully. It would have been complete if the authors follow the standard benchmark protocol, e.g., 20-way experiments are missed. =========== updated after rebuttal =========== This reviewer has read all the other review comments and the rebuttal, and found that all the questions and concerns are well dealt with by the authors' rebuttal. I still believe that this work has its potential value sufficient to report in the community by showing that uncertainty modeling and latent parameterization by semantic memory effectively improve ProtoNet in the few-shot recognition. Thus, this reviewer votes for acceptance of this work, and increase the score. While this work is interesting, as pointed by other reviewers, the paper description, structure, and details should be improved because the missing details or ambiguous descriptions raise most of the concerns. Thus, the authors should reflect all the comments and put efforts to resolve the concerns in the camera-ready. Also, it would have been stronger if the analysis is more through to understand where the performance improvement specifically comes from.
Strengths: - Hierarchical and probabilistic design of ProtoNet - Noticeable performance improvement and favorable performance against the state-of-the-art methods. - The technical design is well-motivated
Weaknesses: - 20-shot experiments are completely missing, which have been evaluated from the prior arts. - Missing reference (see below)
Correctness: - The algorithm derivation is well developed.
Clarity: - The paper is written very well.
Relation to Prior Work: - Properly discussed the innovation compared to ProtoNet well. Missing reference: Although this submission is more general and extended work, the following work seems very closely related. [Variational Prototyping-Encoder: One-Shot Learning with Prototypical Images, CVPR2019]
Additional Feedback: - As a small suggestion, since the proposed method is good in uncertain data regimes, it may demonstrate more strong advantages of the proposed method if a zero-shot experiment is added as done in ProtoNet. - The authors only show the limited memory size cases. Since the performance trend does not show the saturation yet, it would be informative to show more experiments up to a saturation point. Does it have any computational burden problem? - The proposed method requires two MC samplings. How much do those samplings affect the training time and stability of the training?