Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The authors propose to constrain lipschitz constant  for the Continual Learning settings in order to control problems related to reusing the same replay samples. They show that this leads to increased performance across a variety of rehearsal based methods
strengths_and_weaknesses: *Strengths*

- The method performs well across a variety of datasets and methods. 



*Weakness*
- the motivation can be hard to follow at times, particularly the 3rd to last paragraph of the introduction is  vague and overly informal. Figure 1 should be more clearly explained as it takes sometime to understand what it is trying to show
- The authors do not consider the online setting where rehearsal methods are commonly applied
questions: - The method introduces additional hyperparameters alpha beta, how robust are these?
- What would happen if the incoming data, not the buffer data was used to compute  L_c-Lip? 
limitations: Yes
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper proposes inclusion of a smoothness regulariser in rehearsal training for alleviating the problem of catastrophic forgetting.  Authors present empirical evidence showing that adding the proposed regularise to existing rehearsal techniques reduces forgetting. 
strengths_and_weaknesses: This paper tackles two aspects of catastrophic forgetting: a new regularisation objective and the idea of combining regularisation (that alleviates catastrophic-forgetting) with rehearsal methods.  So I’ll tackle these two aspect separately.

As a new regulariser, I think the propose idea is not that fresh.  It seems like it’s just another facet of existing regularisation techniques that attempt to find flat minima for each of the tasks (Mirzadeh.etal 2020, Yin.etal 2021).   In fact, both those works already propose minimisation of the eigenvalue of the hessian matrix of the model - the only thing new here would be doing that on a per layer basis on weights…which may make the proposed method computational simpler.  Also, whereas Mirzadeh.etal2020 and Yin.etal2021 make  assumptions about Lipschitz smoothness of the learning model, in this work the objective is to maximise that smoothness.  I wonder if this work (just like Fisher-matrix based Elastic Weight Consolidation) is a special case of the Hessian-based regularisation proposed in Mirzadeh.etal2020 and Yin.etal2021?  If so, is the proposed estimator of smoothness better than the one introduced in Ritter.etal.2018?  Hard to tell at the moment, since the authors here don’t compare their regulariser against existing ones.

The second aspect, of combining rehearsal methods with regularisation methods for the purposes of reducing catastrophic forgetting is kind of interesting - perhaps a bit obvious, but nevertheless something that needs to be explored and evaluated.  However, in this case, I think there needs to be an empirical evaluation using other regularisers in addition to the proposed one.  Is the combination of rehearsal and the proposed regulariser better than a combination of rehearsal and the smart choices of training that flatten the minima proposed in Mirzadeh.etal2020?  Or is it better than combination of rehearsal than the regulariser of Ritter.etal.2018?  Is it slightly worse, but much faster?  And since these existing regularisers rely on Taylor series approximation of the Hessian of the loss function at minima of given tasks, could the fact that in rehersal we have access to some data from previous tasks be useful to improve that estimation?  Yin.etal2021 show the exact relationship of the error in the estimate of the Hessian to forgetting.



Mirzadeh.etal2020 - “Understanding hte role of training regimes in continual learning”
Yin.etal2021 - “Optimization and Generalization of Regularization-Based Continual Learning: a Loss Approximation Viewpoint”
Ritter.etal.2018 - “Online structured Laplace approximations for overcoming catastrophic forgetting”

questions: Why is the regularisation objective in equation 9 is so complicated?  In on term you try to make eigenvalue equal to c, in the other term you try to minimise c.  Why not just create an objective that minimises the eigenvalue?  Surely, if eigenvalue is less than c, that’s good...and so the first term is not always doing the right thing…and the combination of two is just a very complicated way of minimisation of the eigenvalue.
limitations: The limitation is that based on the lack of evaluation of the propose regularisation method against existing ones, it’s hard to tell if it is that good on its own.  As an investigation of the effectiveness of combining rehersal and regularisation, it’s not exhaustive enough, because it only takes into consideration a new regularistion method.  I think, as it is, the work is a good start to a possibly interesting investigation, that needs much more done in terms of critical evaluation of various combinations of rehearsal and other regularisation methods.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The authors focus on the Catastrophic Forgetting due to overfitting to the small dataset of memorised samples.  
They show the degradation of the decision boundary due to overfitting to a subset of data on the first tasks.  
They also show that the Lipchitz constant increases the smaller the memory buffer, which is tightly related to the decision boundary's deterioration.  
They introduce a regularisation scheme to minimise the Lipchitz constant over the samples in the memory.
strengths_and_weaknesses: ## Originality
### 1- Are the tasks or methods new? 

The method LiDER is new. However, the idea to constraint the Lipschitzness of the neural network and the way to do so is not new. 

### 2- Is the work a novel combination of well-known techniques? 

Yes, the work is an application of techniques to minimise the Lipschitzness of neural networks to Continual Learning.

### 3- Is it clear how this work differs from previous contributions? 

Yes, the main way this work differs from previous contributions are. :
- First application of the Lipschitzness minimisation to Continual Learning
- The design of the optimisation objective on the Lipschitz constant for continual learning.

### 4- Is related work adequately cited ?
To my knowledge, the related work is adequately cited

## Quality
### 1- Is the submission technically sound ? 

Yes, the submission is technically sound.

### 2- Are claims well supported (e.g., by theoretical analysis or experimental results) ?

Most claims were supported by experiments as evidence.

### 3- Are the methods used appropriate ?

The idea of focusing on the Lipschitzness seems relevant, given the improvements experimental results. 
Also, several works have pointed to the link between the flatness of the loss and Catastrophic Forgetting. 
Intuitively, a network with a smaller Lipschitzness constant would converge to a more stable optima.  

### 4- Is this a complete piece of work or work in progress ?

This is a complete piece of work.

### 5- Are the authors careful and honest about evaluating both the strengths and weaknesses of their work ?

The authors discussed the limitations of their work in terms of : 
- computational requirements.
- the non applicability of the method to attention based architectures.

## Clarity:
### 1- Is the submission clearly written?
- The paper is well written and easy to follow.
- The experimental setup is presented in detail
- The background is clearly presented and helped me ramp-up on the Lipschitzness of neural networks.

### 2- Is it well organised? (If not, please make constructive suggestions for improving its clarity.)

Overall the paper is well organised and was easy to follow.

### 3- Does it adequately inform the reader? (Note that a superbly written paper provides enough information for an expert reader to reproduce its results.)

The hyperparameters to reproduce the experiments are provided in the appendix. Also, the code was provided in supplementary materials.

## Significance:
### 1- Are the results important? 

Strengths : 
- The method is easy to implement and applicable as an addition to a large number of algorithms. 
- The method achieves improvements on the order of 5 to 8% gains in FAA for split-ImageNet and Split CUB-200, for  DER++, and up to 10% in AF.

Weaknesses :
- The gains LiDER bring are most significant, mostly in split miniImageNet and Split CUB-200 and for a subset of the algorithms.

### 2- Are others (researchers or practitioners) likely to use the ideas or build on them?
- Given that the method is easy to implement, practitioners are likely to benchmark the idea against other methods for applications.
- However, it's unclear to which extend the computational overhead of the power iteration method makes LiDER applicable to large scale real world applications.

### 3- Does the submission address a difficult task in a better way than previous work? 

The method is designed to be plugged on top of other methods. In the experiments, this leads to an improvement or the same performance in most cases.

### 4- Does it advance the state of the art in a demonstrable way? 
- The method achieves improvements on the order of 5 to 8% gains in FAA for split-ImageNet and Split CUB-200, for  DER++, and up to 10% in AF.
- The gains LiDER bring are most significant, mostly in split miniImageNet and Split CUB-200 and for a subset of the algorithms.
questions: - In 5.4, could you please explain the selection process of the fixed target ?
- Could you clarify which performance is reported in Table 4 ?

Tiny recommendations for clarity (don't impact the score) :
- In the appendix, presenting the hyper-parameters in a table format may make them more readable :)  
- I think it would be more clear to add the standard errors in the same table as the means. Maybe split the tables into two tables : FAA and FF.
limitations: The authors have adequately addressed the limitations and potential negative impact of the work.
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: In this work authors propose LIDER - an extension to the existing continual learning methods with buffer replay, through additional regularisation based on Lipschitz constant that reduces overfitting to examples stored in the buffer, by improving the generalisation of the classifier. In experimental studies LIDER improves the performance of recent state-of-the-art methods.
strengths_and_weaknesses: Strengths:
- Interesting initial insights and convincing motivation of the work
- Well prepared experimentation section wit setups that provide better understanding of what is the main impact of the proposed solution. Good performance evaluation with well selected baseline methods that tackle the problem of buffer based continual learning in different ways
- Experiments indicate that solution improves recent state-of-the-art approaches, for some setups by a large margin

Weaknesses:
- Comparison to related works is very limited, a few crucial state-of-the-art methods are missing in both related works and experiments. Most importantly similar work - "Gradient-based Editing of Memory Examples for Online Task-free Continual Learning" where buffer examples are adjusted in order to similarly to this method improve the performance of several baseline buffer based continual learning methods.
- In Eq. 5  an observation is introduced that ReLU can be understood as matrix multiplication by a diagonal matrix with either zeros or ones. On top of this an upper bound of Lipschitz constant for ReLU activation is proposed that can be interpreted as switching ReLU to identity function. This is a very significant simplification that basically reduces calculation of proposed Lipschitz based regularisation for all complex architectures as if they were linear models.
- For many experiments (iCARL - splitCUB, GDumb (smaller buffer), ER-ACE(pre-trained CIFAR100), Hessian Eigenvalues),  gain observed with proposed solution is marginal. Without confidence interval it is hard to evaluate if LIDER improves results over the random factor. 


Small details:
- [116] also known
- [247] Why Unexpectedly? I guess it is rather expected that performance decreases when probability of switching labels in buffer poisoning increases.
questions: - In this submission a second - additional regularisation term is introduced that forces Lipschitz constants of individual layers to be as close to 0 as possible. As stated in the work, employment of this regularisation should lead to lower sensitivity to changes in the input. I miss the direct link, why this should prevent continually trained model from overfitting to limited examples in the buffer?
- Can authors provide any explanation why Lipschitz constant is higher in a continual-learning setup with buffered examples? I intuitively understand why is it so, but how does it relate theoretically?

- Not really a question, but an idea. It would be interesting for the future work to see if proposed solution might be used as a regularisation for generative rehearsal approaches in order to reduce overfitting to part of the data distribution that is better covered by a generative model.

limitations: Yes
review_title: null

Meta-review: metareview: In order to solve the inherent problem of rehearsal-based continual learning methods (a problem in which a small pool of data from the previous tasks is repeatedly used for learning and hence we have a tight and unstable decision boundary), this paper proposes a method to provide smoothness of the backbone network by placing constraints on the Lipschitz constant of each layer. All reviewers unanimously recognized the strengths of this paper - sufficient performance improvement  in the designed experiments and convincing insight/motivation etc. However, some reviewers were concerned that the baselines or experimental settings are somehow weak, and the authors partially resolved this through additional experiments during discussion phase. Nevertheless, more diverse experimental results need to be added in the final version. Especially, this ac thinks that if the experimental results for more various buffer sizes are included in the final version, the experimental quality will be improved and the insight of the authors can be better supported.
 
confidence: Certain
Decision: Accept