Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

To overcome the above problem, we propose a novel technique called "Activity Regularization" (AR) that penalizes changes in the model's prediction on its learned information.

The review comment to be evaluated is:

The authors proposed a new regularizer for continual learning to tackle the catastrophic forgetting problem. The proposed method minimizes the KL-divergence between the prediction of previous models and current models on the stored samples of previous tasks. The idea is straightforward and sounds technical. Experiments show the effectiveness of the methods compared to state-of-the-art. Although the idea sounds interesting and the experiments look promising, the novelty of the paper seems to be limited. In addition, the experiments setting needs to be improved as well. In the following, you have detailed comments.

1. It seems to be an extension of Learning without Forgetting (LwF) Li & Hoiem 2017 with simply on the examples of previous tasks in the memory. LwF only regularizes on the current task. It is not clear what is the difference between the proposed method and LwF except this.
2. The authors fixed many critical hyper-parameters: temperature(5), learning rate(0.05), epochs(10). The author should report the results for all methods with these hyper-parameters chosen on the validation set.
3. The authors presented how they split the training and testing data. Please be clear how you split the validation set.
4. The authors argued that sample quality does not affect the proposed methods. Then the authors should show the variance from different random sampling.

The evidence to be evaluated is:To tackle the aforementioned problem, we propose to minimize the KL-divergence between the current model and the previous optimal models on the corresponding tasks.

In particular, for each task \(\mathcal{T}_{i}\), we store some of the samples \(\mathbf{x}_{i}\) and the prediction of the optimal model \(f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x}_{i})\) in a memory \(\mathcal{M}_{i}\); then the Activity Regularization (AR) objective for task \(\mathcal{T}_{t}\) is \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\] where \(\tau\) is the temperature used in softmax outputs. Our goal is to ensure that the new model \(\mathbf{\theta}\) behaves similarly with \(\mathbf{\theta}_{i}^{*}\) on the previous task \(\mathcal{T}_{t}\), thus we call this constraint as activity regularization.

We refer to this algorithm as "Deterministic Activity Regularization" (DAR) which imposes regularization constraints for all the previous tasks at every learning iteration.

Similar to approximated multi-task learning methods, DAR employs a regularization constraint on every of the past tasks when learning a new one, which requires calculating the KL-divergence resulting in an additional forward pass on the memory, and thus results in additional computational cost when training the models. Moreover, the number of regularizers for each task is equal to the number of previously observed tasks, which may considerably restrict the model's _plasticity_ to acquire new knowledge. That is, by enforcing too many constraints on the current model for reducing forgetting, we sacrifice its ability to learn new information.

7:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{D }}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{i<t}\sum_{\mathbf{x}\in\mathcal{M} _{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

```**Algorithm 1** Deterministic Activity Regularization (DAR) algorithm for Continual Learning. To address the weaknesses of DAR, we propose the Stochastic Activity Regularization (SAR), which randomly samples a past task and apply activity regularization on each gradient update when learning a new task. Algorithm 1 summarizes the proposed SAR algorithm for continual learning.

Then, when learning a new task, for each mini batch to update \(\mathbf{\theta}\), we apply AR on all of the previous memory. For SAR, we instead randomly sample an index i of the previous tasks and apply the AR only on that memory. As a result, SAR is much more robust as it improves the model's plasticity, alleviates catastrophic forgetting and has greater scalability. For DAR, we omit the sampling index i in step 7 and calculate the KL divergence on all the memory as in eqn. 7. The memory \(\mathcal{M}_{i}\) is used to store some training samples of the previous tasks which is used to regularize the current model when learning new tasks.

7: Sample an index i from \([0,\dots,t-1]\) 8:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{ D}}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{\mathbf{x}\in\mathcal{M}_{i}} \lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

Motivated from Hebbian learning (Hebbs, 1949), MAS (Aljundi et al., 2018a) proposes to penalize the \(\ell_{2}\) norm of the model's prediction. Selfless sequential learning (SNI) (Aljundi et al., 2018b) improves MAS by combining with it sparsity in each layer's activation.

To overcome this problem, we propose the deterministic activity regularization for continual learning, DAR, that enforces the new model's behaviour to be consistent with the optimal models on each of the previous tasks.

Input: Figure 2: Performance results on the split CIFAR-100 benchmark.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
Based on my review of the claim, evidence, and reviewer comments, here is my assessment:

The claim about proposing a "novel" Activity Regularization technique appears somewhat overstated. The evidence shows that AR is an extension of existing approaches, particularly Learning without Forgetting (LwF), as noted in the reviewer comments. While the method does show effectiveness in experiments (as demonstrated in Figure 2), the novelty is limited since it primarily applies KL-divergence regularization on stored samples, which is similar to existing techniques. The main innovation appears to be in the stochastic variant (SAR) rather than the core AR concept itself.

<score>4</score>

Justification:
1. Limited novelty - As pointed out by reviewer comment #1, the approach appears to be largely an extension of LwF with memory samples
2. The evidence shows the method is effective (Figure 2 results), but doesn't support claims of novelty
3. The technical approach (using KL-divergence for regularization) builds directly on established methods
4. The claim would be better stated by acknowledging its relationship to existing approaches rather than emphasizing novelty
5. The experimental validation has limitations noted by reviewers (fixed hyperparameters, validation split details missing)

The claim would be more accurate if presented as an extension or modification of existing regularization approaches rather than a novel technique.


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Then, when learning a new task, AR penalizes the KL-divergence between the current model's and the previous optimal model's predictions on the corresponding memory.

The evidence to be evaluated is:For example, Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes a form of distillation loss by minimizing the KL-divergence of past models and current model on the newly observed tasks.

To tackle the aforementioned problem, we propose to minimize the KL-divergence between the current model and the previous optimal models on the corresponding tasks. This can also be interpreted as distilling the knowledge from \(\mathbf{\theta}_{i}^{*}\) to \(\mathbf{\theta}\) on the corresponding data \(\mathcal{D}_{i}\). In particular, for each task \(\mathcal{T}_{i}\), we store some of the samples \(\mathbf{x}_{i}\) and the prediction of the optimal model \(f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x}_{i})\) in a memory \(\mathcal{M}_{i}\); then the Activity Regularization (AR) objective for task \(\mathcal{T}_{t}\) is \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\]

Our goal is to ensure that the new model \(\mathbf{\theta}\) behaves similarly with \(\mathbf{\theta}_{i}^{*}\) on the previous task \(\mathcal{T}_{t}\), thus we call this constraint as activity regularization.

Similar to approximated multi-task learning methods, DAR employs a regularization constraint on every of the past tasks when learning a new one, which requires calculating the KL-divergence resulting in an additional forward pass on the memory, and thus results in additional computational cost when training the models.

7:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{D }}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{i<t}\sum_{\mathbf{x}\in\mathcal{M} _{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

For DAR, we omit the sampling index i in step 7 and calculate the KL divergence on all the memory as in eqn. 7. The memory \(\mathcal{M}_{i}\) is used to store some training samples of the previous tasks which is used to regularize the current model when learning new tasks.

8:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{ D}}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{\mathbf{x}\in\mathcal{M}_{i}} \lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes to minimize the difference in KL-divergence of the current and previous models on the new tasks, which is a form of knowledge distillation penalty.

To overcome this problem, we propose the deterministic activity regularization for continual learning, DAR, that enforces the new model's behaviour to be consistent with the optimal models on each of the previous tasks. As the result, DAR is much more resistant to noise in the memory since its goal is to maintain the previously optimized decision boundary.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
Let me assess the claim against the provided evidence:

1. Review & Summary:
The claim states that "AR penalizes the KL-divergence between the current model's and the previous optimal model's predictions on the corresponding memory." This is well-supported by multiple pieces of evidence:

- Equation 7 explicitly shows the KL-divergence term between f_θ (current model) and f_θ*_i (previous optimal model) on memory M_i
- The implementation details in steps 7 and 8 demonstrate the practical application of this KL-divergence penalty
- The text directly states "we propose to minimize the KL-divergence between the current model and the previous optimal models on the corresponding tasks"

The claim is precise and accurately reflects what is shown in the mathematical formulations and descriptive text without any exaggeration.

<score>1</score>

Justification:
1. Direct Mathematical Support: Equation 7 and the gradient updates in steps 7-8 provide explicit mathematical verification of the claim.
2. Accurate Terminology: The use of "penalizes" and "KL-divergence" in the claim matches exactly with how the method is implemented.
3. Precise Scope: The claim specifically mentions "corresponding memory" which aligns with the evidence showing the method operates on stored memory M_i.
4. No Overstatement: The claim makes no exaggerated claims about performance or capabilities beyond what is mathematically demonstrated.


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Then, when learning a new task, AR penalizes the KL-divergence between the current model's and the previous optimal model's predictions on the corresponding memory.

The review comment to be evaluated is:

This paper proposes an approach to mitigate catastrophic forgetting in supervised learning by regularizing activations. The paper views previous techniques (EWC, SI, and GEM) under a multi-task learning lens, and then proposes an additional loss term to minimise the KL between activations from previous and current models, on previous tasks - this is based on a memory which stores some previous samples and their corresponding activations.

I think it is a simple and intuitive approach and a well-written paper. Unfortunately I have a number of concerns that I think preclude publication in the current state.

First, in terms of related work, I believe this is very similar to Learning without forgetting (LwF), with the difference that the KL-divergence is computed on samples kept from the previous tasks. This is briefly mentioned in the paper, but I think it needs to be made more explicit, and LwF should be a baseline in the experiments to clearly indicate the benefit of keeping this data. There is also a relationship to EWC: given the connection between the Fisher information and KL, it can be viewed as minimising the KL divergence in parameter space, rather than in activation space (which is the case here). Also note that EWC uses the true Fisher rather than the empirical, contrary to the derivation in equation (2).
There are also a number of papers that haven’t been cited in the related work [1][2][3][4].

Second, I think the motivation in Section 3.1 could be more convincing. Most importantly, it’s not clear to me that the decision boundary *shouldn’t* change for previously misclassified examples, as this could be an opportunity for backwards transfer.
Further, I don’t think the point in the last paragraph about having a small data portion is relevant, since they are from the same data distribution, and we would expect misclassified samples to be in the same (low) frequency in Fisher estimation as overall. I think the point of this paragraph is just that it is important to consider the entire predictive distribution of previous tasks rather than the probability of the correct class, so this should be stated more clearly and then justified.

Finally, I think the experimental justification could be improved as well. Beyond permuted MNIST (which it has been argued is not as useful as other baselines [4]), only the final performance on split notMNIST / CIFAR-100 is reported. Some comments and questions:
- The accuracies of EWC (and possibly SI) in the table are worse than reported in previous work (eg. [1]), so I think this needs to be examined.
- What is the fine-tuning baseline (I don't believe it is actually clearly defined)? How can it be so low in figure 2a but better in 2b?
- I think plots over time (performance on all tasks) would be much more useful than the final performance in Table 2 and Fig 2.
- Errors and error bars would be beneficial for all results.
- Table 1 should also include the references provided.

Some other comments and questions:
- Compared to eqn (2), eqn (6) is missing the ½ constant.
- Typos in section 5.3: "SI performs better than SI", and VAR instead of SAR.
- Section 2, unclear of meaning of "coined with the likelihood" (should this be “coincide”?)
- The first line should be “Humans have the ability to learn...” In general, I think the introduction could use another proofread for grammar and readability as I saw a few minor things.

[1] Nguyen, Cuong V., et al. "Variational Continual Learning." ICLR, 2018.
[2] Schwarz, Jonathan, et al. "Progress & Compress: A scalable framework for continual learning." ICML, 2018.
[3] Shin, Hanul, et al. "Continual learning with deep generative replay." NIPS, 2017.
[4] Farquhar, Sebastian, and Yarin Gal. "Towards Robust Evaluations of Continual Learning." arXiv, 2018.

The evidence to be evaluated is:For example, Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes a form of distillation loss by minimizing the KL-divergence of past models and current model on the newly observed tasks.

To tackle the aforementioned problem, we propose to minimize the KL-divergence between the current model and the previous optimal models on the corresponding tasks. This can also be interpreted as distilling the knowledge from \(\mathbf{\theta}_{i}^{*}\) to \(\mathbf{\theta}\) on the corresponding data \(\mathcal{D}_{i}\). In particular, for each task \(\mathcal{T}_{i}\), we store some of the samples \(\mathbf{x}_{i}\) and the prediction of the optimal model \(f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x}_{i})\) in a memory \(\mathcal{M}_{i}\); then the Activity Regularization (AR) objective for task \(\mathcal{T}_{t}\) is \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\]

Our goal is to ensure that the new model \(\mathbf{\theta}\) behaves similarly with \(\mathbf{\theta}_{i}^{*}\) on the previous task \(\mathcal{T}_{t}\), thus we call this constraint as activity regularization.

Similar to approximated multi-task learning methods, DAR employs a regularization constraint on every of the past tasks when learning a new one, which requires calculating the KL-divergence resulting in an additional forward pass on the memory, and thus results in additional computational cost when training the models.

7:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{D }}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{i<t}\sum_{\mathbf{x}\in\mathcal{M} _{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

For DAR, we omit the sampling index i in step 7 and calculate the KL divergence on all the memory as in eqn. 7. The memory \(\mathcal{M}_{i}\) is used to store some training samples of the previous tasks which is used to regularize the current model when learning new tasks.

8:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{ D}}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{\mathbf{x}\in\mathcal{M}_{i}} \lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes to minimize the difference in KL-divergence of the current and previous models on the new tasks, which is a form of knowledge distillation penalty.

To overcome this problem, we propose the deterministic activity regularization for continual learning, DAR, that enforces the new model's behaviour to be consistent with the optimal models on each of the previous tasks. As the result, DAR is much more resistant to noise in the memory since its goal is to maintain the previously optimized decision boundary.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
Let me assess the claim: "Then, when learning a new task, AR penalizes the KL-divergence between the current model's and the previous optimal model's predictions on the corresponding memory."

This claim appears to be well-stated based on the evidence provided. The evidence directly supports this through:
1. Equation 7 explicitly shows the KL-divergence penalty term between current model θ and previous optimal model θ_i* on memory M_i
2. The algorithmic steps (7 and 8) demonstrate this regularization implementation
3. The evidence clearly states this is done to "ensure that the new model θ behaves similarly with θ_i* on the previous task"

The reviewer's comments actually reinforce this by acknowledging the KL-divergence approach, though noting its similarity to Learning without Forgetting (LwF). The claim simply describes the technical mechanism without overstating its novelty or effectiveness.

<score>1</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Then, when learning a new task, AR penalizes the KL-divergence between the current model's and the previous optimal model's predictions on the corresponding memory.

The review comment to be evaluated is:

The paper addresses the problem of continual learning from a sequence of supervised tasks. The main contribution of the paper are the following. The work:
* puts the problem in uniform general framework in which many of the state-of-the-art methods fit
* identifies some drawbacks of some the state of the art methods (namely EWC- Kirkpatrick et al., 2017 and GEM-Lopez-Paz et al., 2017) .
* proposes two versions of an approach to address these drawbacks
The main identified problem in EWC and GEM is that both methods result in a zero penalty when both the previous and current models misclassify a sample, even if they make different mistakes.
To solve this problem, the authors propose to keep a memory of randomly sampled data from the previous task, and distil the knowledge from the optima of the previous tasks to the current one using a KL penalty. The first version considers computing this penalty from the whole sequence of tasks, while the second randomly selects one task at each iteration and uses it to compute the penalty, paying some overall accuracy for plasticity.

While the paper is clear and well written, I have some concerns about it's quality, originality and significance.

Originality: The work seems to me to be very related to LwF. The main difference is that while LwF uses only the new data for the KL penalty, this paper keeps a memory of previously seen data to compute this loss.

Significance: While the way the authors approached the problem seems well structured and motivated, and is based on a sound observation, the authors limited themselves to experiments where the task data have similar structure. I am not sure how significant the improvement of the method would be in the more challenging and realistic setting where the data comes from different domains.  I am more specifically skeptical about the stochastic version of the algorithm in that case.

Quality:
* The proposed algorithm stores some data from previous tasks along with the outputs of the corresponding optimal model. While knowledge distillation as proposed would result in a non zero penalty when the new model makes different prediction, it still doesn't take advantage of the new information to probably correct the previous models prediction when it is wrong. Why not keeping the ground truth labels instead? This won't increase the memory requirement, and may give better results. It would be interesting to compare against such a method.
* I think selecting the samples to keep in memory randomly could to be suboptimal.  Other selection methods can be considered. A previous work:  iCaRL: Incremental Classifier and Representation Learning, Rebuffi et al. 2017, gives way to select representative samples. It would be interesting to see the effect of such a selection on the results.

Overall, while the paper doesn't present any significant flaw, it doesn't add much to the continual learning literature either, which explains my rating.

The evidence to be evaluated is:For example, Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes a form of distillation loss by minimizing the KL-divergence of past models and current model on the newly observed tasks.

To tackle the aforementioned problem, we propose to minimize the KL-divergence between the current model and the previous optimal models on the corresponding tasks. This can also be interpreted as distilling the knowledge from \(\mathbf{\theta}_{i}^{*}\) to \(\mathbf{\theta}\) on the corresponding data \(\mathcal{D}_{i}\). In particular, for each task \(\mathcal{T}_{i}\), we store some of the samples \(\mathbf{x}_{i}\) and the prediction of the optimal model \(f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x}_{i})\) in a memory \(\mathcal{M}_{i}\); then the Activity Regularization (AR) objective for task \(\mathcal{T}_{t}\) is \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\]

Our goal is to ensure that the new model \(\mathbf{\theta}\) behaves similarly with \(\mathbf{\theta}_{i}^{*}\) on the previous task \(\mathcal{T}_{t}\), thus we call this constraint as activity regularization.

Similar to approximated multi-task learning methods, DAR employs a regularization constraint on every of the past tasks when learning a new one, which requires calculating the KL-divergence resulting in an additional forward pass on the memory, and thus results in additional computational cost when training the models.

7:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{D }}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{i<t}\sum_{\mathbf{x}\in\mathcal{M} _{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

For DAR, we omit the sampling index i in step 7 and calculate the KL divergence on all the memory as in eqn. 7. The memory \(\mathcal{M}_{i}\) is used to store some training samples of the previous tasks which is used to regularize the current model when learning new tasks.

8:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{ D}}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{\mathbf{x}\in\mathcal{M}_{i}} \lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes to minimize the difference in KL-divergence of the current and previous models on the new tasks, which is a form of knowledge distillation penalty.

To overcome this problem, we propose the deterministic activity regularization for continual learning, DAR, that enforces the new model's behaviour to be consistent with the optimal models on each of the previous tasks. As the result, DAR is much more resistant to noise in the memory since its goal is to maintain the previously optimized decision boundary.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
Let me evaluate the claim based on the evidence provided:

The claim states that "AR penalizes the KL-divergence between the current model's and the previous optimal model's predictions on the corresponding memory."

Based on my review:
- The evidence clearly shows this through equation (7) which explicitly shows the KL divergence penalty term between f_θ (current model) and f_θ*_i (previous optimal model) on memory M_i
- The reviewer acknowledges this mechanism but points out its similarity to LwF, with the main difference being that AR uses stored memory data while LwF uses new data
- The evidence demonstrates that this is implemented in both DAR and SAR variants through equations 7 and 8
- The claim is a straightforward technical description that matches the mathematical formulation shown in the evidence without exaggeration

The claim appears to be well-stated as it accurately reflects the mathematical formulation and implementation described in the evidence without overstating the novelty or capabilities.

<score>1</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Then, when learning a new task, AR penalizes the KL-divergence between the current model's and the previous optimal model's predictions on the corresponding memory.

The review comment to be evaluated is:

The authors proposed a new regularizer for continual learning to tackle the catastrophic forgetting problem. The proposed method minimizes the KL-divergence between the prediction of previous models and current models on the stored samples of previous tasks. The idea is straightforward and sounds technical. Experiments show the effectiveness of the methods compared to state-of-the-art. Although the idea sounds interesting and the experiments look promising, the novelty of the paper seems to be limited. In addition, the experiments setting needs to be improved as well. In the following, you have detailed comments.

1. It seems to be an extension of Learning without Forgetting (LwF) Li & Hoiem 2017 with simply on the examples of previous tasks in the memory. LwF only regularizes on the current task. It is not clear what is the difference between the proposed method and LwF except this.
2. The authors fixed many critical hyper-parameters: temperature(5), learning rate(0.05), epochs(10). The author should report the results for all methods with these hyper-parameters chosen on the validation set.
3. The authors presented how they split the training and testing data. Please be clear how you split the validation set.
4. The authors argued that sample quality does not affect the proposed methods. Then the authors should show the variance from different random sampling.

The evidence to be evaluated is:For example, Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes a form of distillation loss by minimizing the KL-divergence of past models and current model on the newly observed tasks.

To tackle the aforementioned problem, we propose to minimize the KL-divergence between the current model and the previous optimal models on the corresponding tasks. This can also be interpreted as distilling the knowledge from \(\mathbf{\theta}_{i}^{*}\) to \(\mathbf{\theta}\) on the corresponding data \(\mathcal{D}_{i}\). In particular, for each task \(\mathcal{T}_{i}\), we store some of the samples \(\mathbf{x}_{i}\) and the prediction of the optimal model \(f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x}_{i})\) in a memory \(\mathcal{M}_{i}\); then the Activity Regularization (AR) objective for task \(\mathcal{T}_{t}\) is \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\]

Our goal is to ensure that the new model \(\mathbf{\theta}\) behaves similarly with \(\mathbf{\theta}_{i}^{*}\) on the previous task \(\mathcal{T}_{t}\), thus we call this constraint as activity regularization.

Similar to approximated multi-task learning methods, DAR employs a regularization constraint on every of the past tasks when learning a new one, which requires calculating the KL-divergence resulting in an additional forward pass on the memory, and thus results in additional computational cost when training the models.

7:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{D }}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{i<t}\sum_{\mathbf{x}\in\mathcal{M} _{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

For DAR, we omit the sampling index i in step 7 and calculate the KL divergence on all the memory as in eqn. 7. The memory \(\mathcal{M}_{i}\) is used to store some training samples of the previous tasks which is used to regularize the current model when learning new tasks.

8:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{ D}}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{\mathbf{x}\in\mathcal{M}_{i}} \lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes to minimize the difference in KL-divergence of the current and previous models on the new tasks, which is a form of knowledge distillation penalty.

To overcome this problem, we propose the deterministic activity regularization for continual learning, DAR, that enforces the new model's behaviour to be consistent with the optimal models on each of the previous tasks. As the result, DAR is much more resistant to noise in the memory since its goal is to maintain the previously optimized decision boundary.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
I'll evaluate the claim: "Then, when learning a new task, AR penalizes the KL-divergence between the current model's and the previous optimal model's predictions on the corresponding memory."

Analysis:
The claim appears to be well-stated based on the evidence provided. The evidence directly supports this through:

1. The mathematical formulation in equation (7) explicitly shows the KL-divergence penalty between current model θ and previous optimal models θ_i* on memory M_i
2. The implementation details in steps 7 and 8 confirm this mechanism
3. The difference from LwF is clarified - LwF uses KL-divergence on new tasks while AR uses it on stored memory samples

The reviewer's comments about similarity to LwF are acknowledged, but the key technical distinction is clearly documented in the evidence. The claim accurately describes the method without exaggeration.

<score>1</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

This objective is to ensure that the new model will be consistent with the previous optimal ones on the old tasks, thus avoiding catastrophic forgetting.

The evidence to be evaluated is:Consider the continual learning problem where the learner \(\mathbf{\theta}\) receives a sequence of T tasks \(\mathcal{T}=\{\mathcal{T}_{1},\mathcal{T}_{2},\ldots,\mathcal{T}_{T}\}\), each of which consists of a training data \(\mathcal{D}_{t}\). At any given time \(t\), only task \(\mathcal{T}_{t}\) are presented to the learner \(\mathbf{\theta}\) and it has to learn to solve the current task without access to the training data of any previous tasks. The goal of continual learning is to train the learner such that it can solve the not only current task \(\mathcal{T}_{t}\) but also all the previous tasks \(\mathcal{T}_{k<t}\). To avoid forgetting previous knowledge, when learning task \(\mathcal{T}_{t}\), the learner \(\mathbf{\theta}\) minimize the multi-task learning objective as \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_ {t})+\lambda_{t-1}\mathcal{L}_{t-1}(\mathbf{\theta},\mathcal{D}_{t-1})+\ldots+ \lambda_{1}\mathcal{L}_{1}(\mathbf{\theta},\mathcal{D}_{1}), \tag{1}\] where the loss \(\mathcal{L}_{i}(\mathbf{\theta},\mathcal{D}_{i})\) is usually the negative log-likelihood \(-\sum_{\mathbf{x},y\in\mathcal{D}_{i}}\log p(y|\mathbf{x};\mathbf{\theta})\) of the corresponding training data and \(\lambda_{i}\) regulates the importance of task \(\mathcal{T}_{i}\) to all the tasks observed so far. In continual learning, at time \(t\), we do not have access to the data \(\mathcal{D}_{k<t}\) to evaluate the loss \(\mathcal{L}_{k<t}\), thus, we need to approximate the past losses \(\mathcal{L}_{k<t}(\mathbf{\theta},\mathcal{D}_{k})\) when minimizing \(\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_{t})\).

\[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_ {t})+\sum_{i<t}\lambda_{k}(\mathbf{\theta}-\mathbf{\theta}_{i}^{*})^{T}\mathbf{F}_{i}(\bm {\theta}-\mathbf{\theta}_{i}^{*}), \tag{3}\]

According to eqn. 3, we can minimize the negative log-likelihood of \(\mathbf{\theta}\) on the previous tasks without explicitly storing the training samples because the data distribution are already captured in the Fisher information.

Another approach to achieve the approximated multi-task learning objective in eqn. 1 is based on the observation that at the beginning of task \(\mathcal{T}_{t}\), we initialize \(\mathbf{\theta}=\mathbf{\theta}_{t-1}^{*}\), whose value already minimized the lost \(\tilde{\mathcal{L}}_{t-1}\). From this, if we can consider eqn. 1 as minimizing the loss \(\mathcal{L}_{t}(\mathbf{\theta})\) with the constraints that previous losses are not allowed to increase after every mini-batch update, which is the GEM objective. In particular, GEM optimize the following problem \[\begin{array}{ll}\text{Minimize}_{\mathbf{\theta},\mathcal{D}_{t}}&\mathcal{L}_ {t}(\mathbf{\theta})\\ \text{subject to}&\mathcal{L}_{k}(\mathbf{\theta},\mathcal{M}_{k})\leq\mathcal{L}_ {k}(\mathbf{\theta}_{t-1}^{*},\mathcal{M}_{k}),\forall k<t,\end{array} \tag{5}\]where the loss \(\mathcal{L}_{k}\) is evaluated at the memory \(\mathcal{M}_{k}\) that stores some of the training samples from task \(\mathcal{T}_{k}\). GEM further converts the constraints in eqn. 5 into the gradient constraints of the losses and solve them using quadratic programming.

For example, Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes a form of distillation loss by minimizing the KL-divergence of past models and current model on the newly observed tasks. By changing the losses \(\mathcal{L}_{k<t}\), we can recover different solutions for continual learning in the literature.

In general, if we have too many misclassified samples or label noise, the decision boundary on the previous task might be altered despite minimizing the EWC or GEM objective. This phenomenon happens based on an assumption that we usually do not train the model to have 0 error on the training set to avoid overfitting and we only use a relatively small data portion to estimate the Fisher or store as memory. Therefore, EWC and GEM might not correctly penalize the current model from changing the past tasks' optimized decision boundaries. To tackle the aforementioned problem, we propose to minimize the KL-divergence between the current model and the previous optimal models on the corresponding tasks. This can also be interpreted as distilling the knowledge from \(\mathbf{\theta}_{i}^{*}\) to \(\mathbf{\theta}\) on the corresponding data \(\mathcal{D}_{i}\). In particular, for each task \(\mathcal{T}_{i}\), we store some of the samples \(\mathbf{x}_{i}\) and the prediction of the optimal model \(f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x}_{i})\) in a memory \(\mathcal{M}_{i}\); then the Activity Regularization (AR) objective for task \(\mathcal{T}_{t}\) is \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\]

Our goal is to ensure that the new model \(\mathbf{\theta}\) behaves similarly with \(\mathbf{\theta}_{i}^{*}\) on the previous task \(\mathcal{T}_{t}\), thus we call this constraint as activity regularization.

We refer to this algorithm as "Deterministic Activity Regularization" (DAR) which imposes regularization constraints for all the previous tasks at every learning iteration.

7:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{D }}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{i<t}\sum_{\mathbf{x}\in\mathcal{M} _{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

To address the weaknesses of DAR, we propose the Stochastic Activity Regularization (SAR), which randomly samples a past task and apply activity regularization on each gradient update when learning a new task.

Then, when learning a new task, for each mini batch to update \(\mathbf{\theta}\), we apply AR on all of the previous memory.

As a result, SAR is much more robust as it improves the model's plasticity, alleviates catastrophic forgetting and has greater scalability.

The memory \(\mathcal{M}_{i}\) is used to store some training samples of the previous tasks which is used to regularize the current model when learning new tasks.

8:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{ D}}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{\mathbf{x}\in\mathcal{M}_{i}} \lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

The goal of continual learning is to build a learner that can continuously learn from a stream of tasks while still maintain its previously acquired knowledge.

**Structural regularization** approaches employ penalties on the network's parameters, encourage the important parameters of previous tasks to not change when learning the new task. The parameter importance can be estimated by calculating the Fisher information as in EWC (Kirkpatrick et al., 2017) or directly measure how changes in each parameter will affect the change in the loss function as proposed in SI (Zenke et al., 2017).

Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes to minimize the difference in KL-divergence of the current and previous models on the new tasks, which is a form of knowledge distillation penalty. Similarly, Less-forgetting learning (LF) (Jung et al., 2019) proposes to minimize the \(\ell_{2}\) norm of the two prediction in stead of KL-divergence as LwF. Motivated from Hebbian learning (Hebbs, 1949), MAS (Aljundi et al., 2018a) proposes to penalize the \(\ell_{2}\) norm of the model's prediction.

Our approaches, DAR and SAR, distills past models on their correctly trained data, thus maintaining the past knowledge for new models.

Finally, **ensemble learning** techniques addresses catastrophic forgetting by having a dedicated sub-network for each task.

After training a task, the corresponding sub-network is frozen and will not allowed to change, thus completely immune to catastrophic forgetting.

Catastrophic forgetting is avoided by using a form of structural regularizer. Ensemble learning approaches are usually resistant to catastrophic forgetting as the cost of either unbounded growth of model's size or cannot be applied to different network architectures.

For EWC, at the end of training, we randomly sample \(N=200\) samples to estimate the diagonal Fisher matrix and store the optimal model \(\mathbf{\theta}_{i}^{*}\) for each task.

SI performs better than EWC thanks to its Fisher approximation strategy on the whole data. GEM attains 91.8% accuracy, higher than both EWC, SI and VCL due the its strong constraints.

Both DAR and SAR are consistently better than GEM at all memory size. Only at 2500 samples, GEM performs better than our methods at 200 samples. At 2500 samples, both DAR and SAR achieves over 96% accuracy, showing great scalability. Across all methods, performance consistently improves when the memory size increases. When only a small amount of samples are available in the memory, e.g. 200 and 500, GEM may overfit to these samples, leading to the performance degrade on the whole past data sets.

In both cases, our methods show advantage over GEM, maintaining performance on previous task by enforcing model's consistency.

noisy memory can easily cause catastrophic forgetting in EWC and GEM while SI is more resistant to noise since it approximates the Fisher on all observed samples of past tasks.

We report the averaged accuracy after 10 tasks in fig. 1(a), where EWC and SI are not as effective as alleviating forgetting as in previous experiments because this benchmark is more challenging.

We propose an approximated multi-task learning framework that can alleviate catastrophic forgetting, an important challenge in continual learning and show that several previous solutions in the literature are special cases of this framework.

To overcome this problem, we propose the deterministic activity regularization for continual learning, DAR, that enforces the new model's behaviour to be consistent with the optimal models on each of the previous tasks. As the result, DAR is much more resistant to noise in the memory since its goal is to maintain the previously optimized decision boundary.

Finally, we show that DAR and SAR can be applied on both MLP and CNN, effectively alleviate catastrophic forgetting.

Input: Figure 1: Comparison of different memory size on the permuted MNIST experiments.

Input: Figure 2: Performance results on the split CIFAR-100 benchmark.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After careful review of the claim "This objective is to ensure that the new model will be consistent with the previous optimal ones on the old tasks, thus avoiding catastrophic forgetting," I find this to be a well-stated claim supported by substantial evidence.

The evidence demonstrates:
- Mathematical formulation showing how consistency with previous tasks is maintained through regularization
- Empirical results in Figures 1 and 2 showing improved performance in avoiding catastrophic forgetting
- Detailed explanation of both DAR and SAR approaches that implement this objective
- Comparative analysis showing how the proposed methods outperform baselines
- Clear demonstration that maintaining consistency with previous optimal models helps prevent forgetting

The claim accurately reflects the technical approach and results without exaggeration or overstatement.

<score>1</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

This objective is to ensure that the new model will be consistent with the previous optimal ones on the old tasks, thus avoiding catastrophic forgetting.

The review comment to be evaluated is:

This paper proposes an approach to mitigate catastrophic forgetting in supervised learning by regularizing activations. The paper views previous techniques (EWC, SI, and GEM) under a multi-task learning lens, and then proposes an additional loss term to minimise the KL between activations from previous and current models, on previous tasks - this is based on a memory which stores some previous samples and their corresponding activations.

I think it is a simple and intuitive approach and a well-written paper. Unfortunately I have a number of concerns that I think preclude publication in the current state.

First, in terms of related work, I believe this is very similar to Learning without forgetting (LwF), with the difference that the KL-divergence is computed on samples kept from the previous tasks. This is briefly mentioned in the paper, but I think it needs to be made more explicit, and LwF should be a baseline in the experiments to clearly indicate the benefit of keeping this data. There is also a relationship to EWC: given the connection between the Fisher information and KL, it can be viewed as minimising the KL divergence in parameter space, rather than in activation space (which is the case here). Also note that EWC uses the true Fisher rather than the empirical, contrary to the derivation in equation (2).
There are also a number of papers that haven’t been cited in the related work [1][2][3][4].

Second, I think the motivation in Section 3.1 could be more convincing. Most importantly, it’s not clear to me that the decision boundary *shouldn’t* change for previously misclassified examples, as this could be an opportunity for backwards transfer.
Further, I don’t think the point in the last paragraph about having a small data portion is relevant, since they are from the same data distribution, and we would expect misclassified samples to be in the same (low) frequency in Fisher estimation as overall. I think the point of this paragraph is just that it is important to consider the entire predictive distribution of previous tasks rather than the probability of the correct class, so this should be stated more clearly and then justified.

Finally, I think the experimental justification could be improved as well. Beyond permuted MNIST (which it has been argued is not as useful as other baselines [4]), only the final performance on split notMNIST / CIFAR-100 is reported. Some comments and questions:
- The accuracies of EWC (and possibly SI) in the table are worse than reported in previous work (eg. [1]), so I think this needs to be examined.
- What is the fine-tuning baseline (I don't believe it is actually clearly defined)? How can it be so low in figure 2a but better in 2b?
- I think plots over time (performance on all tasks) would be much more useful than the final performance in Table 2 and Fig 2.
- Errors and error bars would be beneficial for all results.
- Table 1 should also include the references provided.

Some other comments and questions:
- Compared to eqn (2), eqn (6) is missing the ½ constant.
- Typos in section 5.3: "SI performs better than SI", and VAR instead of SAR.
- Section 2, unclear of meaning of "coined with the likelihood" (should this be “coincide”?)
- The first line should be “Humans have the ability to learn...” In general, I think the introduction could use another proofread for grammar and readability as I saw a few minor things.

[1] Nguyen, Cuong V., et al. "Variational Continual Learning." ICLR, 2018.
[2] Schwarz, Jonathan, et al. "Progress & Compress: A scalable framework for continual learning." ICML, 2018.
[3] Shin, Hanul, et al. "Continual learning with deep generative replay." NIPS, 2017.
[4] Farquhar, Sebastian, and Yarin Gal. "Towards Robust Evaluations of Continual Learning." arXiv, 2018.

The evidence to be evaluated is:Consider the continual learning problem where the learner \(\mathbf{\theta}\) receives a sequence of T tasks \(\mathcal{T}=\{\mathcal{T}_{1},\mathcal{T}_{2},\ldots,\mathcal{T}_{T}\}\), each of which consists of a training data \(\mathcal{D}_{t}\). At any given time \(t\), only task \(\mathcal{T}_{t}\) are presented to the learner \(\mathbf{\theta}\) and it has to learn to solve the current task without access to the training data of any previous tasks. The goal of continual learning is to train the learner such that it can solve the not only current task \(\mathcal{T}_{t}\) but also all the previous tasks \(\mathcal{T}_{k<t}\). To avoid forgetting previous knowledge, when learning task \(\mathcal{T}_{t}\), the learner \(\mathbf{\theta}\) minimize the multi-task learning objective as \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_ {t})+\lambda_{t-1}\mathcal{L}_{t-1}(\mathbf{\theta},\mathcal{D}_{t-1})+\ldots+ \lambda_{1}\mathcal{L}_{1}(\mathbf{\theta},\mathcal{D}_{1}), \tag{1}\] where the loss \(\mathcal{L}_{i}(\mathbf{\theta},\mathcal{D}_{i})\) is usually the negative log-likelihood \(-\sum_{\mathbf{x},y\in\mathcal{D}_{i}}\log p(y|\mathbf{x};\mathbf{\theta})\) of the corresponding training data and \(\lambda_{i}\) regulates the importance of task \(\mathcal{T}_{i}\) to all the tasks observed so far. In continual learning, at time \(t\), we do not have access to the data \(\mathcal{D}_{k<t}\) to evaluate the loss \(\mathcal{L}_{k<t}\), thus, we need to approximate the past losses \(\mathcal{L}_{k<t}(\mathbf{\theta},\mathcal{D}_{k})\) when minimizing \(\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_{t})\).

\[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_ {t})+\sum_{i<t}\lambda_{k}(\mathbf{\theta}-\mathbf{\theta}_{i}^{*})^{T}\mathbf{F}_{i}(\bm {\theta}-\mathbf{\theta}_{i}^{*}), \tag{3}\]

According to eqn. 3, we can minimize the negative log-likelihood of \(\mathbf{\theta}\) on the previous tasks without explicitly storing the training samples because the data distribution are already captured in the Fisher information.

Another approach to achieve the approximated multi-task learning objective in eqn. 1 is based on the observation that at the beginning of task \(\mathcal{T}_{t}\), we initialize \(\mathbf{\theta}=\mathbf{\theta}_{t-1}^{*}\), whose value already minimized the lost \(\tilde{\mathcal{L}}_{t-1}\). From this, if we can consider eqn. 1 as minimizing the loss \(\mathcal{L}_{t}(\mathbf{\theta})\) with the constraints that previous losses are not allowed to increase after every mini-batch update, which is the GEM objective. In particular, GEM optimize the following problem \[\begin{array}{ll}\text{Minimize}_{\mathbf{\theta},\mathcal{D}_{t}}&\mathcal{L}_ {t}(\mathbf{\theta})\\ \text{subject to}&\mathcal{L}_{k}(\mathbf{\theta},\mathcal{M}_{k})\leq\mathcal{L}_ {k}(\mathbf{\theta}_{t-1}^{*},\mathcal{M}_{k}),\forall k<t,\end{array} \tag{5}\]where the loss \(\mathcal{L}_{k}\) is evaluated at the memory \(\mathcal{M}_{k}\) that stores some of the training samples from task \(\mathcal{T}_{k}\). GEM further converts the constraints in eqn. 5 into the gradient constraints of the losses and solve them using quadratic programming.

For example, Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes a form of distillation loss by minimizing the KL-divergence of past models and current model on the newly observed tasks. By changing the losses \(\mathcal{L}_{k<t}\), we can recover different solutions for continual learning in the literature.

In general, if we have too many misclassified samples or label noise, the decision boundary on the previous task might be altered despite minimizing the EWC or GEM objective. This phenomenon happens based on an assumption that we usually do not train the model to have 0 error on the training set to avoid overfitting and we only use a relatively small data portion to estimate the Fisher or store as memory. Therefore, EWC and GEM might not correctly penalize the current model from changing the past tasks' optimized decision boundaries. To tackle the aforementioned problem, we propose to minimize the KL-divergence between the current model and the previous optimal models on the corresponding tasks. This can also be interpreted as distilling the knowledge from \(\mathbf{\theta}_{i}^{*}\) to \(\mathbf{\theta}\) on the corresponding data \(\mathcal{D}_{i}\). In particular, for each task \(\mathcal{T}_{i}\), we store some of the samples \(\mathbf{x}_{i}\) and the prediction of the optimal model \(f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x}_{i})\) in a memory \(\mathcal{M}_{i}\); then the Activity Regularization (AR) objective for task \(\mathcal{T}_{t}\) is \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\]

Our goal is to ensure that the new model \(\mathbf{\theta}\) behaves similarly with \(\mathbf{\theta}_{i}^{*}\) on the previous task \(\mathcal{T}_{t}\), thus we call this constraint as activity regularization.

We refer to this algorithm as "Deterministic Activity Regularization" (DAR) which imposes regularization constraints for all the previous tasks at every learning iteration.

7:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{D }}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{i<t}\sum_{\mathbf{x}\in\mathcal{M} _{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

To address the weaknesses of DAR, we propose the Stochastic Activity Regularization (SAR), which randomly samples a past task and apply activity regularization on each gradient update when learning a new task.

Then, when learning a new task, for each mini batch to update \(\mathbf{\theta}\), we apply AR on all of the previous memory.

As a result, SAR is much more robust as it improves the model's plasticity, alleviates catastrophic forgetting and has greater scalability.

The memory \(\mathcal{M}_{i}\) is used to store some training samples of the previous tasks which is used to regularize the current model when learning new tasks.

8:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{ D}}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{\mathbf{x}\in\mathcal{M}_{i}} \lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

The goal of continual learning is to build a learner that can continuously learn from a stream of tasks while still maintain its previously acquired knowledge.

**Structural regularization** approaches employ penalties on the network's parameters, encourage the important parameters of previous tasks to not change when learning the new task. The parameter importance can be estimated by calculating the Fisher information as in EWC (Kirkpatrick et al., 2017) or directly measure how changes in each parameter will affect the change in the loss function as proposed in SI (Zenke et al., 2017).

Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes to minimize the difference in KL-divergence of the current and previous models on the new tasks, which is a form of knowledge distillation penalty. Similarly, Less-forgetting learning (LF) (Jung et al., 2019) proposes to minimize the \(\ell_{2}\) norm of the two prediction in stead of KL-divergence as LwF. Motivated from Hebbian learning (Hebbs, 1949), MAS (Aljundi et al., 2018a) proposes to penalize the \(\ell_{2}\) norm of the model's prediction.

Our approaches, DAR and SAR, distills past models on their correctly trained data, thus maintaining the past knowledge for new models.

Finally, **ensemble learning** techniques addresses catastrophic forgetting by having a dedicated sub-network for each task.

After training a task, the corresponding sub-network is frozen and will not allowed to change, thus completely immune to catastrophic forgetting.

Catastrophic forgetting is avoided by using a form of structural regularizer. Ensemble learning approaches are usually resistant to catastrophic forgetting as the cost of either unbounded growth of model's size or cannot be applied to different network architectures.

For EWC, at the end of training, we randomly sample \(N=200\) samples to estimate the diagonal Fisher matrix and store the optimal model \(\mathbf{\theta}_{i}^{*}\) for each task.

SI performs better than EWC thanks to its Fisher approximation strategy on the whole data. GEM attains 91.8% accuracy, higher than both EWC, SI and VCL due the its strong constraints.

Both DAR and SAR are consistently better than GEM at all memory size. Only at 2500 samples, GEM performs better than our methods at 200 samples. At 2500 samples, both DAR and SAR achieves over 96% accuracy, showing great scalability. Across all methods, performance consistently improves when the memory size increases. When only a small amount of samples are available in the memory, e.g. 200 and 500, GEM may overfit to these samples, leading to the performance degrade on the whole past data sets.

In both cases, our methods show advantage over GEM, maintaining performance on previous task by enforcing model's consistency.

noisy memory can easily cause catastrophic forgetting in EWC and GEM while SI is more resistant to noise since it approximates the Fisher on all observed samples of past tasks.

We report the averaged accuracy after 10 tasks in fig. 1(a), where EWC and SI are not as effective as alleviating forgetting as in previous experiments because this benchmark is more challenging.

We propose an approximated multi-task learning framework that can alleviate catastrophic forgetting, an important challenge in continual learning and show that several previous solutions in the literature are special cases of this framework.

To overcome this problem, we propose the deterministic activity regularization for continual learning, DAR, that enforces the new model's behaviour to be consistent with the optimal models on each of the previous tasks. As the result, DAR is much more resistant to noise in the memory since its goal is to maintain the previously optimized decision boundary.

Finally, we show that DAR and SAR can be applied on both MLP and CNN, effectively alleviate catastrophic forgetting.

Input: Figure 1: Comparison of different memory size on the permuted MNIST experiments.

Input: Figure 2: Performance results on the split CIFAR-100 benchmark.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence, the claim "This objective is to ensure that the new model will be consistent with the previous optimal ones on the old tasks, thus avoiding catastrophic forgetting" appears partially overstated. While the evidence shows that DAR/SAR methods aim to maintain consistency with previous models through activity regularization, the results demonstrate they reduce but don't completely "ensure" or avoid forgetting. Figure 1 shows gradual performance decline across tasks, even with larger memory sizes. The review also points out limitations in experimental validation and similarity to existing approaches like LwF. The claim would be better stated as "aims to reduce" rather than "ensure."

<score>3</score>

Justification:
- The empirical results show declining performance over tasks (Fig 1), indicating consistency is improved but not ensured
- The reviewer notes similarity to existing approaches like LwF, suggesting the claim overstates uniqueness
- Key limitations in experimental validation are highlighted by the reviewer
- The paper's own results acknowledge that memory size impacts effectiveness, showing the approach doesn't guarantee consistency
- More measured language about "reducing" rather than "ensuring" would better match the evidence


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

This objective is to ensure that the new model will be consistent with the previous optimal ones on the old tasks, thus avoiding catastrophic forgetting.

The review comment to be evaluated is:

The paper addresses the problem of continual learning from a sequence of supervised tasks. The main contribution of the paper are the following. The work:
* puts the problem in uniform general framework in which many of the state-of-the-art methods fit
* identifies some drawbacks of some the state of the art methods (namely EWC- Kirkpatrick et al., 2017 and GEM-Lopez-Paz et al., 2017) .
* proposes two versions of an approach to address these drawbacks
The main identified problem in EWC and GEM is that both methods result in a zero penalty when both the previous and current models misclassify a sample, even if they make different mistakes.
To solve this problem, the authors propose to keep a memory of randomly sampled data from the previous task, and distil the knowledge from the optima of the previous tasks to the current one using a KL penalty. The first version considers computing this penalty from the whole sequence of tasks, while the second randomly selects one task at each iteration and uses it to compute the penalty, paying some overall accuracy for plasticity.

While the paper is clear and well written, I have some concerns about it's quality, originality and significance.

Originality: The work seems to me to be very related to LwF. The main difference is that while LwF uses only the new data for the KL penalty, this paper keeps a memory of previously seen data to compute this loss.

Significance: While the way the authors approached the problem seems well structured and motivated, and is based on a sound observation, the authors limited themselves to experiments where the task data have similar structure. I am not sure how significant the improvement of the method would be in the more challenging and realistic setting where the data comes from different domains.  I am more specifically skeptical about the stochastic version of the algorithm in that case.

Quality:
* The proposed algorithm stores some data from previous tasks along with the outputs of the corresponding optimal model. While knowledge distillation as proposed would result in a non zero penalty when the new model makes different prediction, it still doesn't take advantage of the new information to probably correct the previous models prediction when it is wrong. Why not keeping the ground truth labels instead? This won't increase the memory requirement, and may give better results. It would be interesting to compare against such a method.
* I think selecting the samples to keep in memory randomly could to be suboptimal.  Other selection methods can be considered. A previous work:  iCaRL: Incremental Classifier and Representation Learning, Rebuffi et al. 2017, gives way to select representative samples. It would be interesting to see the effect of such a selection on the results.

Overall, while the paper doesn't present any significant flaw, it doesn't add much to the continual learning literature either, which explains my rating.

The evidence to be evaluated is:Consider the continual learning problem where the learner \(\mathbf{\theta}\) receives a sequence of T tasks \(\mathcal{T}=\{\mathcal{T}_{1},\mathcal{T}_{2},\ldots,\mathcal{T}_{T}\}\), each of which consists of a training data \(\mathcal{D}_{t}\). At any given time \(t\), only task \(\mathcal{T}_{t}\) are presented to the learner \(\mathbf{\theta}\) and it has to learn to solve the current task without access to the training data of any previous tasks. The goal of continual learning is to train the learner such that it can solve the not only current task \(\mathcal{T}_{t}\) but also all the previous tasks \(\mathcal{T}_{k<t}\). To avoid forgetting previous knowledge, when learning task \(\mathcal{T}_{t}\), the learner \(\mathbf{\theta}\) minimize the multi-task learning objective as \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_ {t})+\lambda_{t-1}\mathcal{L}_{t-1}(\mathbf{\theta},\mathcal{D}_{t-1})+\ldots+ \lambda_{1}\mathcal{L}_{1}(\mathbf{\theta},\mathcal{D}_{1}), \tag{1}\] where the loss \(\mathcal{L}_{i}(\mathbf{\theta},\mathcal{D}_{i})\) is usually the negative log-likelihood \(-\sum_{\mathbf{x},y\in\mathcal{D}_{i}}\log p(y|\mathbf{x};\mathbf{\theta})\) of the corresponding training data and \(\lambda_{i}\) regulates the importance of task \(\mathcal{T}_{i}\) to all the tasks observed so far. In continual learning, at time \(t\), we do not have access to the data \(\mathcal{D}_{k<t}\) to evaluate the loss \(\mathcal{L}_{k<t}\), thus, we need to approximate the past losses \(\mathcal{L}_{k<t}(\mathbf{\theta},\mathcal{D}_{k})\) when minimizing \(\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_{t})\).

\[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_ {t})+\sum_{i<t}\lambda_{k}(\mathbf{\theta}-\mathbf{\theta}_{i}^{*})^{T}\mathbf{F}_{i}(\bm {\theta}-\mathbf{\theta}_{i}^{*}), \tag{3}\]

According to eqn. 3, we can minimize the negative log-likelihood of \(\mathbf{\theta}\) on the previous tasks without explicitly storing the training samples because the data distribution are already captured in the Fisher information.

Another approach to achieve the approximated multi-task learning objective in eqn. 1 is based on the observation that at the beginning of task \(\mathcal{T}_{t}\), we initialize \(\mathbf{\theta}=\mathbf{\theta}_{t-1}^{*}\), whose value already minimized the lost \(\tilde{\mathcal{L}}_{t-1}\). From this, if we can consider eqn. 1 as minimizing the loss \(\mathcal{L}_{t}(\mathbf{\theta})\) with the constraints that previous losses are not allowed to increase after every mini-batch update, which is the GEM objective. In particular, GEM optimize the following problem \[\begin{array}{ll}\text{Minimize}_{\mathbf{\theta},\mathcal{D}_{t}}&\mathcal{L}_ {t}(\mathbf{\theta})\\ \text{subject to}&\mathcal{L}_{k}(\mathbf{\theta},\mathcal{M}_{k})\leq\mathcal{L}_ {k}(\mathbf{\theta}_{t-1}^{*},\mathcal{M}_{k}),\forall k<t,\end{array} \tag{5}\]where the loss \(\mathcal{L}_{k}\) is evaluated at the memory \(\mathcal{M}_{k}\) that stores some of the training samples from task \(\mathcal{T}_{k}\). GEM further converts the constraints in eqn. 5 into the gradient constraints of the losses and solve them using quadratic programming.

For example, Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes a form of distillation loss by minimizing the KL-divergence of past models and current model on the newly observed tasks. By changing the losses \(\mathcal{L}_{k<t}\), we can recover different solutions for continual learning in the literature.

In general, if we have too many misclassified samples or label noise, the decision boundary on the previous task might be altered despite minimizing the EWC or GEM objective. This phenomenon happens based on an assumption that we usually do not train the model to have 0 error on the training set to avoid overfitting and we only use a relatively small data portion to estimate the Fisher or store as memory. Therefore, EWC and GEM might not correctly penalize the current model from changing the past tasks' optimized decision boundaries. To tackle the aforementioned problem, we propose to minimize the KL-divergence between the current model and the previous optimal models on the corresponding tasks. This can also be interpreted as distilling the knowledge from \(\mathbf{\theta}_{i}^{*}\) to \(\mathbf{\theta}\) on the corresponding data \(\mathcal{D}_{i}\). In particular, for each task \(\mathcal{T}_{i}\), we store some of the samples \(\mathbf{x}_{i}\) and the prediction of the optimal model \(f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x}_{i})\) in a memory \(\mathcal{M}_{i}\); then the Activity Regularization (AR) objective for task \(\mathcal{T}_{t}\) is \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\]

Our goal is to ensure that the new model \(\mathbf{\theta}\) behaves similarly with \(\mathbf{\theta}_{i}^{*}\) on the previous task \(\mathcal{T}_{t}\), thus we call this constraint as activity regularization.

We refer to this algorithm as "Deterministic Activity Regularization" (DAR) which imposes regularization constraints for all the previous tasks at every learning iteration.

7:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{D }}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{i<t}\sum_{\mathbf{x}\in\mathcal{M} _{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

To address the weaknesses of DAR, we propose the Stochastic Activity Regularization (SAR), which randomly samples a past task and apply activity regularization on each gradient update when learning a new task.

Then, when learning a new task, for each mini batch to update \(\mathbf{\theta}\), we apply AR on all of the previous memory.

As a result, SAR is much more robust as it improves the model's plasticity, alleviates catastrophic forgetting and has greater scalability.

The memory \(\mathcal{M}_{i}\) is used to store some training samples of the previous tasks which is used to regularize the current model when learning new tasks.

8:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{ D}}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{\mathbf{x}\in\mathcal{M}_{i}} \lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\)

The goal of continual learning is to build a learner that can continuously learn from a stream of tasks while still maintain its previously acquired knowledge.

**Structural regularization** approaches employ penalties on the network's parameters, encourage the important parameters of previous tasks to not change when learning the new task. The parameter importance can be estimated by calculating the Fisher information as in EWC (Kirkpatrick et al., 2017) or directly measure how changes in each parameter will affect the change in the loss function as proposed in SI (Zenke et al., 2017).

Learning without Forgetting (LwF) (Li & Hoiem, 2017) proposes to minimize the difference in KL-divergence of the current and previous models on the new tasks, which is a form of knowledge distillation penalty. Similarly, Less-forgetting learning (LF) (Jung et al., 2019) proposes to minimize the \(\ell_{2}\) norm of the two prediction in stead of KL-divergence as LwF. Motivated from Hebbian learning (Hebbs, 1949), MAS (Aljundi et al., 2018a) proposes to penalize the \(\ell_{2}\) norm of the model's prediction.

Our approaches, DAR and SAR, distills past models on their correctly trained data, thus maintaining the past knowledge for new models.

Finally, **ensemble learning** techniques addresses catastrophic forgetting by having a dedicated sub-network for each task.

After training a task, the corresponding sub-network is frozen and will not allowed to change, thus completely immune to catastrophic forgetting.

Catastrophic forgetting is avoided by using a form of structural regularizer. Ensemble learning approaches are usually resistant to catastrophic forgetting as the cost of either unbounded growth of model's size or cannot be applied to different network architectures.

For EWC, at the end of training, we randomly sample \(N=200\) samples to estimate the diagonal Fisher matrix and store the optimal model \(\mathbf{\theta}_{i}^{*}\) for each task.

SI performs better than EWC thanks to its Fisher approximation strategy on the whole data. GEM attains 91.8% accuracy, higher than both EWC, SI and VCL due the its strong constraints.

Both DAR and SAR are consistently better than GEM at all memory size. Only at 2500 samples, GEM performs better than our methods at 200 samples. At 2500 samples, both DAR and SAR achieves over 96% accuracy, showing great scalability. Across all methods, performance consistently improves when the memory size increases. When only a small amount of samples are available in the memory, e.g. 200 and 500, GEM may overfit to these samples, leading to the performance degrade on the whole past data sets.

In both cases, our methods show advantage over GEM, maintaining performance on previous task by enforcing model's consistency.

noisy memory can easily cause catastrophic forgetting in EWC and GEM while SI is more resistant to noise since it approximates the Fisher on all observed samples of past tasks.

We report the averaged accuracy after 10 tasks in fig. 1(a), where EWC and SI are not as effective as alleviating forgetting as in previous experiments because this benchmark is more challenging.

We propose an approximated multi-task learning framework that can alleviate catastrophic forgetting, an important challenge in continual learning and show that several previous solutions in the literature are special cases of this framework.

To overcome this problem, we propose the deterministic activity regularization for continual learning, DAR, that enforces the new model's behaviour to be consistent with the optimal models on each of the previous tasks. As the result, DAR is much more resistant to noise in the memory since its goal is to maintain the previously optimized decision boundary.

Finally, we show that DAR and SAR can be applied on both MLP and CNN, effectively alleviate catastrophic forgetting.

Input: Figure 1: Comparison of different memory size on the permuted MNIST experiments.

Input: Figure 2: Performance results on the split CIFAR-100 benchmark.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence and claim "This objective is to ensure that the new model will be consistent with the previous optimal ones on the old tasks, thus avoiding catastrophic forgetting", I find this to be a moderately overstated claim.

While the evidence shows DAR/SAR methods do help maintain consistency with previous models and reduce catastrophic forgetting (as shown in Figures 1-2), the effectiveness varies based on memory size and experimental conditions. The review comments highlight limitations not acknowledged in the claim - particularly regarding performance across different domains and suboptimal random sampling. The claim presents the objective as definitively ensuring consistency, when the evidence suggests it helps but doesn't guarantee it.

<score>3</score>

Justification:
1. The evidence shows positive but variable results:
- "Both DAR and SAR are consistently better than GEM at all memory size"
- But performance depends on memory size: "Across all methods, performance consistently improves when the memory size increases"

2. Review raises valid concerns not addressed in claim:
- "I am not sure how significant the improvement of the method would be in the more challenging and realistic setting where the data comes from different domains"
- "selecting the samples to keep in memory randomly could to be suboptimal"

3. The claim uses absolute language ("ensure") when the evidence shows the method helps reduce but doesn't completely eliminate catastrophic forgetting.