Venue: NeurIPS 2022 Conference

Reviews:

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: In this work, the authors have proposed Bayes predictive coding network (PCN), a model inspired by predicting coding literature from Rao and Ballard. They offer the inclusion of hierarchical associative memory, capable of performing continual one-short memory writes without the need for meta-learning heuristics. This mechanism also helps the model gradually forget partial least important information to free memory. Experiments are performed on cifar and tiny-imagenet to show the efficiency of the proposed method. 
strengths_and_weaknesses: # Strengths
* Well-written paper. However, writing can be improved. Since this paper can be easily understood researchers working on predicting coding and bio-inspired approaches. But for people outside the field, it's difficult to understand.
* Incremental approach 
* Model section is well defined.

# Weakness
* Experimental section needs more details
* Related work is missing some citations
* Ablation study is missing
questions: * Can authors comment on how the current approach compares/differs against, the neural coding network [1-3] which is proposed to be a stable predicting coding network that works on a wide variety of networks. 
* Ablation study with varied value of Sigma_w and Sigma_x is required, current approach uses Sigma_w = 1 and Sigma_x = 0.01
* Can authors report results with deeper BayesSPCN
* How are baseline models trained and did the authors conduct hyperparameter optimizations of those? Can authors report all these ranges?
* Hyper-parameter optimization- No detail about hyper-parameter optimization, authors should provide reasoning how these parameters were chosen. 
* Statistical significance: - Experiments should be conducted for K trials and average performance and the standard error should be reported.
* Can authors comment on the robustness and stability of the given model?
* Can authors provide computational overhead using temporal weights both during train and inference?

* [1] https://ojs.aaai.org/index.php/AAAI/article/view/4389
* [2] https://www.nature.com/articles/s41467-022-29632-7
* [3] https://arxiv.org/pdf/1905.10696.pdf
limitations: Authors have failed to include Broader Impact and Societal or negative impact sections. Please refer to the NeurIPS deadline, before submitting your manuscripts.
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 proposes the BayesPCN, an associative memory model that is trained with predictive coding (in contrast to Hebbian learning employed by Hopfield networks). It seems to be an extension of a similar recent work, the generative predictive coding network (GPCN). Rather than using the GPCN's offline write mechanism, this work alters the weights W by Bayesian inference, enabling continual learning in the network. In tandem they propose a forgetting mechanism that incorporates the Bayesian prior. They then compare recall errors for CIFAR10 and Tiny ImageNet across the GPCN, BayesPCN, and the modern Hopfield network (MHN).
strengths_and_weaknesses: The introduction and explanation of the model details, such as the write algorithm, are clear enough. Recasting the GPCN as a Bayesian network is interesting, and to my knowledge the proposed forget mechanism is a novel idea. However, the experiments are the weak point of this paper. Many details on experiment parameters are missing, which I list in the questions below. This makes it challenging to interpret some of the findings. Finally, the claims of novelty in the introduction of the paper are not well-supported by the experiments.

In the first claim, the authors emphasize that the model is continually learnable unlike the GPCN. However, they do not show any results for any common continual learning evaluations, such as class-incremental continual learning. Second, they say that "BayesPCN is the first parametric associative memory model to continually learn hundreds of very high-dimensional observations (>10,000 dimensions) while maintaining good recall performance." While my area of expertise is not in associative memory models, it is my understanding that the capacity of modern Hopfield networks is quite large. The authors do not show any experimental evaluations which result in high error for MHNs and relatively low error for the BayesPCN. They only show an example in Figure 3 of the MHN failing with high dropout and masking. By contrast, this is something more thoroughly evaluated by the GPCN paper (see their Figure 9 and Table 1), though even their work does not provide a good summary comparison between the two.

The authors then state that BayesPCN is "the first hierarchical memory which after repeated forgetting recovers its original memory state." While this third claim may be technically true, it does not seem a particularly significant or notable addition to the literature. If I understand correctly, the authors are saying that a dedicated forget mechanism (other than overwriting old memories) does not exist in models like the GPCN or hierarchical temporal memory (HTM) networks. And the authors show in Figure 4 that BayesPCN recall error is actually smaller later in a sequence, suggesting that it recovers the original images quite well. However, why is it notable or useful to have a *hierarchical* memory that can do this? I assume if it were the first associative memory model to do this, the authors would have claimed that instead.

This is not my area of study, so perhaps I am missing some context that would make this paper's significance more apparent. As is, I am rating it a borderline reject.
questions: * What are the details of the MHN models used in the experiments for Table 1? What is the size of the MHN? What hyperparameters were searched over?
* Which hyperparameters were best for each model in Table 1? For example, was the forgetting \beta set to 0.0 in these experiments? These hyperparameters could be included in a Supplementary document.
* Lines 242-245 claim that BayesPCN recall quality deterioriated relatively evenly across time. Where is the evidence for this?
* In Table 1 and in Figure 4, is the MSE the average across all datapoints thus far in the seqeuence (e.g. sequence length 512 averages 512 datapoints, whereas sequence length 128 averages 128 datapoints)? Or is it just showing the average across the most recent datapoints?
* What is the standard deviation of MSE across seeds? i.e. can you add these to Table 1 & Figure 4? While the checklist answer does not include these because "we are not necessarily claiming that BayesPCN obtains a better score than the baselines", the discussion does assert that "BayesPCN's recall performance is comparable to its offline-learned counterpart even though it is continually learned." Error bars would be useful to evaluate how comparable they are.

Suggestions
* The PDF appears to be rendered as an image, and it is not possible to search the document or highlight text. Please fix.
* In Section 4.2 line 137, the text refers to the particle model described in Section 3. There is no explicit reference to a particle model in Section 3.
* Line 45: is 'combing' supposed to be 'combining'?
limitations: Limitations of the model are discussed briefly. e.g. that the model can return nonsensical output for a memory query that is too far away, and that there is not a good biologically plausible implementation of the locally conjugate Bayesian weight update.
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 extends upon predictive coding neural networks by making the weights Bayesian and using this relationship to make connections to associative memory models within a deep learning framework more broadly. The model is also able to forget over time. 
strengths_and_weaknesses: Fig. 1 add labels to the rows and columns rather than putting everything in the caption. 

I think you should cite the paper http://proceedings.mlr.press/v80/marino18a/marino18a.pdf because of its relations to predictive coding. Discussing relations between your model and VAEs could be interesting in general. 

The Kanerva Machine should be added as a benchmark? Also a standard VAE as per the results of: https://www.pnas.org/doi/abs/10.1073/pnas.2005013117 . I would also cite the follow up to the Kanerva Machine: https://proceedings.neurips.cc/paper/2018/file/6e4243f5511fd6ef0f03e9f386d54403-Paper.pdf 

Line 119 difference between hetero and auto associative is confusing. Line 188 talking about SDM as non hierarchical -- this descriptor should apply to the other models mentioned too like MCHNs. Another sentence on the differences between your model and the Kanerva Machine could be helpful. 

The images in App. H generated from the BayesPCN are not impressive. Some commentary on this as a limitation in the main text should be present. A limitations section more broadly would be good. 

Can you control for the continual learning abilities? E.g. can you learn offline with BayesPCN and see if it outperforms the GPCN?

I'd like to see more experimental results and examples where BayesPCN performs better than existing approaches. You also note that MHN does worse for more heteroassociative tasks but dont show this in Table 1. Also what heteroassociative approach are you using here? The correct one is probably to concatenate the key and value into one large vector as is done in https://arxiv.org/abs/1606.01164 

Regarding forgetting it would be useful to know the memory capacity and performance and potentially benchmarking in general against a method like: https://proceedings.mlr.press/v162/sharma22b/sharma22b.pdf 

Where does eq. 33 come from? 
questions: See above. 
limitations: No I have requested that they add a clear limitations section.
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 proposes an interesting extension of PC-based memory models, that tackles an existing problem of the original generative network: the inability to remember stored memories when presented with new ones, i.e., to write new memories without resetting the model. Generative predictive coding networks were, in fact, trained only once using full batch training on the whole dataset. This work tackles this problem by introducing a new method to write memories in the database. Additionally, it allows to use a similar method to implement a 'forget' operation, that cancels memories from the database. 
strengths_and_weaknesses: Strengths:

1) The model works well, and is indeed able to store memories sequentially without the need of re-training the model from scratch, or without a loss in performance on memories stored multiple 'write' operations before;

2) This method could be potentially interesting in context that are more general than a generative model to perform associative memories, such as continual learning;

3) The literature and related work is well covered.

Weaknesses:

1) I personally found the description of the 'write' operation to be unclear, and it took me a couple of readings to fully understand it: The role of the n-th particle weight $\omega^{n}$ is not well explained, and the same applies to the n-th model $p^{n}$. Hence, a better and clearer explanation seems needed. It also says that these concepts are introduced in Sec.3, where exactly? 

2) The experiments seem to not really show the potential and limitations of the model on the task that concerns this paper the most: continual 'writing' of memories. I will list below a couple of questions I have about the performance of the model that are both a personal curiosity, and a tip on some experiments that would make the paper more (in my opinion) interesting. 

These are my main concern, and a rebuttal that addresses the above two points would make me increase the final score. 


questions: In Table 1, you show the average MSE of every data point, under specific kinds of corruption. However, what is the MSE of the first stored datapoints when all the patterns are stored? What is the MSE of the last ones? 
Particularly, I have the feeling that the reported MSE only show the weakness of the model when confronted with the other baselines, and no experiment shows the advantages. You could perform the same experiments using the standard generative network trained via running inference, and make it memorize one datapoint at the time, exactly how you did for BayesPCNs. I would guess that your model would perform much better on the retrieval of past memories. Why is something like that not included?



Line 237: "A surprising discovery from this experiment was how good MHN’s recall is compared to GPCN and BayesPCN when the memory read input has a moderate amount of noise."
This follows as the induced Gaussian noise has mean zero, and hence the expected normalized dot product between a memory + Gaussian noise and the original memory is 1. As MHNs use dot products to perform similarity scores, they actually perform quite well under this very specific task. This, however, does not happen if the vector of the pixels is not normalised before performing the MHNs operation: in this case, the model will often return the 'whitest' image of the dataset, as the colour white is the one with the highest norm in the rgb collar system. 


Fig.1 is slightly confusing: the description reads nicely and well explains the point, but the image is just a bunch of pictures. I would improve it by adding some pointers directly in the Figure, as well as removing the forth line. 
limitations: Yes they have.
review_title: null

Meta-review: metareview: This paper proposes a bayesian extension to predictive coding neural networks, serving as a form of associative memory. The response from reviewers was lukewarm, but almost unanimously erred on the side of acceptance. The only review arguing for borderline rejection was not as substantial as I would have liked, and did not reply to the authors after their rebuttal. Ultimately, I would have preferred to have a clear champion amongst the other reviewers, arguing more strongly for the paper, but having read the discussion I will take the tepid approval as a sign that the reviewers recommend acceptance, and recommend that the paper be included in the proceedings.
confidence: Certain
Decision: Accept