Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: summary: The article proposes a continual learning method that innovatively improves on an existing algorithm. Precisely, the current work takes GPM (Gradient Projection Memory) which they show is good at preserving performance on old tasks (good stability), but it's not that efficient at learning new ones (low sensitivity) and modifies it in two ways: by dynamically adjusting the importance of the various bases such that the less important ones can be dropped to increase sensitivity. In addition it improves the stability by employing a form of adversarial parameter perturbation to flatten the loss landscape.
The contributions of the paper are:
- an analysis that shows the loss landscape and its "flattness" / "sharpness"; this analysis is used to support the idea that flatter minima tend to forget less in continual learning setups;
- changing the GPM such that it has an increased sensitivity while also improving the stability by flattening the loss landscape around the current solution

main_review: The current work is novel and relevant to the continual learning literature. It identifies a weakness in a competitive algorithm from the literature (the low "sensitivity" of GPM = low performance on new task) and improves it with a well motivated modification.

The article is well written, the formulas and the pseudocode are clear, and the experiments support the claims made.

The algorithms used for comparison are relevant and diverse. The only weakness of the approach is its limitation to the "known task boundaries" setup and the lack of large-scale or reinforcement learning experiments. Although they are not the most challenging, the set of tasks are adequate and common in the continual learning literature.

Given the originality of the analysis of the sharpness of the loss landscape, the well-motivated changes to GPM, and the empirical results, I consider the paper should be accepted.

Minor observation: Humans are animals.

limitations_and_societal_impact: Limitations: not really. The approach is applicable to a subset of continual learning scenarios with assumptions such as known task boundaries, control over the times the data is used, etc.
Societal Impact: Not applicable.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: The paper proposes a new continual learning method that promotes the loss shapes to be flattened. The main idea is to optimize the worst case perturbed loss function at every gradient step, and the empirical investigation of the loss values around the learned parameter corroborates their assertion. Also, experimentally, they showed promising results compared to other recent baselines. 
main_review: First of all, I think the paper misses an important reference that also had a similar motivation of attaining the flat minima, or the wide local minima (WLL), in the context of continual learning:

Cha. et al., CPR: Classifier-projection regularization for continual learning, ICLR 2021. 

While the approach is different, I think it definitely need to be cited. 

Having said that, the proposed method of the paper seems novel in the context of attaining flat minima in the continual learning context. Followings are what I think about the paper:

Pros:
(+) Framework of minimax optimization and empirically showing that the loss function becomes flat seems to be novel. 
(+) Provided theoretical explanations, although the connection with the proposed method is not very straightforward.
(+) Experimental results tend to be thorough, providing ablation study and memory usage, time complexity comparisons. 

Cons:
(-) Missing the reference mentioned above. 
(-) The computational complexity of the method seems to be a limitation. At every task, one needs to carry out the SVD for obtaining M matrix, which could become quite expensive if large network model is used. 
(-) In Eq.(4), using sigmoid should be more explicitly explained. I believe the sigmoid is applied at the end of the gradient update, but is \lambda appearing at the right-hand side of (4) also the one with sigmoid, or not? Also, this step seems to be a heuristic, and it's not clear whether this is the best option. 
(-) Experiments on larger datasets would show more compelling results. 

Overall, despite some weakness mentioned above, I am leaning toward weak accept, but I will also see what other reviewers think about the paper. 

-------

I have read the author's rebuttal and other reviewers' reviews, and I would like to keep my score to 6. 
limitations_and_societal_impact: N/A
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: The paper studies catastrophic forgetting and continual learning from the loss landscape perspective.
The primary motivation is that from the plasticity/stability view, stable networks tend to have flatter minima.
While this has been observed before in [1], the paper studies the problem in more depth. Also, it proposes a solution to reduce the sharpness of minima for each task based on the gradient projection memory work.  
Overall, I like the paper, and I think it is an influential continual learning paper. However, I think the paper can be even better if the authors can address a few shortcomings.
main_review: 
### Overall
**Originality**: The significance of minima sharpness has been studied before in CL literature [1], but the work is novel enough regarding the depth and the approach of analysis.   
**Significance**: The paper is a significant contribution since it gives a better understanding of catastrophic forgetting and continual learning in general.  
**Quality**: I believe this is a high-quality work both theoretically and empirically.  
**Clarity**: The paper is well-written, aside from a few problems regarding the appendix (see below).

----

### Strengths
**1-** I appreciate the fact that this paper aims to increase our understanding of catastrophic forgetting. In my opinion, the CL literature needs more works that try to understand the continual learning challenges.   
**2-** The proposed method and analysis seem novel and reasonable.  
**3-** The experiments are very well designed. However, they can be improved to make the contributions of the paper even more significant.  

 
### Weaknesses
**1-** Since the main objective of the proposed method is to reduce the sharpness of minima, and since the authors seem to be familiar with the impact of training regime on sharpness [1], I wonder why they have chosen to use a single hyper-parameter rather than integrate the findings of [1] regarding the training regime. Can the authors elaborate on this? Aside from that, I think it will be fairer if the results of Tables 1 and 2 were calculated using a grid-search over different hyper-parameters since using only one set of parameters might favor a specific method.

**2-** Figure 6 illustrates the effectiveness of FS-DGPM over other methods and shows that around the local minimizer, the loss landscape of FS-DGPM seems to be flatter than other methods. But, what about the Multitask method? What would the results look like compared to the upper-bound, which is the multitask training? Could the authors report the results in this regard?

**3-** While Figure 5 (c) shows the memory usage, it is unclear what would happen if the memory budget increases/decreases. Could the authors perform an experiment where they compare the results for ER and FS-DGPM when the memory size increases? For instance, an experiment similar to figure 1 in [2] can show the behavior of FS-DGPM over different scenarios. For instance, for Split CIFAR-100 (super), memory sizes of 100, 500, 1000 seem representative enough.

**4-** It seems like the appendix is not well-connected to some parts of the main text. For instance, in Section D.4 (L135), the paper mentions figure 5 (b) while it refers to figure 5 of the main text rather than figure 5 of the paper. Also, in the main text (L283), the paper mentions the training details hyperparameters are reported in Appendix D.4 while they are discussed in Appendix D.5 and D.6. Also, Figure 1 in the appendix does not have a legend.

**5-** Do authors plan to release their code for this paper?

----- Update after discussion period ------  
The authors have addressed my comments and I still vote accepting the paper. 


[1] *Mirzadeh, Seyed Iman, et al. "Understanding the Role of Training Regimes in Continual Learning." Advances in Neural Information Processing Systems, 2020*   
[2] *Chaudhry, Arslan, et al. Continual Learning with Tiny Episodic Memories. 2019. https://arxiv.org/pdf/1902.10486.pdf*
limitations_and_societal_impact: Yes
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: In this paper, the authors propose a method called Flattening Sharpness for Dynamic Gradient Projection Memory (FS-DGPM) for continual learning. The main idea is to investigate the effect of weight loss landscape on overcoming catastrophic forgetting. With the understanding of the weight loss landscape, the authors further propose a method based on the recently proposed Gradient Projection Memory (GPM) method to predict the importance of bases which span the subspace of old tasks. Less important bases can be dynamically released based on the proposed soft weight. Extensive experiments show that the proposed method can consistently outperform the state-of-the-art methods across a range of widely used benchmark datasets.
main_review: 
Originality: The idea of leveraging the flatness of the minima for continual learning is novel and interesting. However, the proposed method seems incremental. 

Quality: The paper is technically sound. 


Clarity: The writing of the paper needs improvement. The paper should include a clear introduction to GPM such that it is easier to understand the proposed method. Meanwhile, the proposed method is not clearly explained. There are also several typos in the paper.  


Significance: The improvements are not significant but meaningful which show the effectiveness of utilizing the loss landscape. 



Questions and suggestions:


1. Can the idea of leveraging the loss landscape be used for other continual learning methods other than GPM?

2. To show the effect of loss landscape on continual learning, maybe the authors should conduct a simpler experiment to remove the factor of continual learning methods themselves. For example, just train a vanilla network sequentially on all the tasks, then compare the performance of the network with or without enforcing flat minima. 

limitations_and_societal_impact: Yes
review_title: null

Meta-review: Echoing what the reviewers highlighted as well. I think the idea of this work is quite novel, and the paper is well executed, where there was due diligence in terms of explaining the hypothesis, and doing ablation studies. As it stands, I think the work is definitely interesting for the community and should be accepted. 
Decision: Accept (Poster)