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:

We further develop a stochastic version of AR that randomly samples a task and apply AR in each mini-batch update.

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: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 \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\]

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. For SAR, we instead randomly sample an index i of the previous tasks and apply the AR only on that memory.

Although more sophisticated methods such as the greedy \(K\)-center algorithm can be used to select data points that spread through out the input space (Nguyen et al., 2018), in this work, even random sampling works well with our methods and can achieve state-of-the-art results.

6: Sample \(\mathcal{D}=\{\mathbf{x}^{(n)},y^{(n)}\}_{n=1}^{N}\) a batch from training data \(\mathcal{D}_{t}\) 7: Sample an index i from \([0,\dots,t-1]\)

We further improve DAR with a stochastic sampling regularizer (SAR), which balances the model's stability and plasticity, allowing the model to acquire new knowledge, alleviate forgetting and has greater scalability. Through extensive experiments on popular continual learning benchmarks, we show that DAR and SAR consistently outperforms state-of-the-art methods.

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

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 "We further develop a stochastic version of AR that randomly samples a task and apply AR in each mini-batch update."

Summary: The evidence strongly supports this claim through:
1. Clear mathematical formulation showing how SAR randomly samples a past task index i
2. Explicit algorithm steps showing task sampling (Step 7)
3. Detailed explanation of how SAR differs from DAR in applying AR only on sampled memory
4. Figure 1 demonstrates SAR's implementation across different memory sizes
5. The reviewer comments don't dispute this specific technical claim about the stochastic sampling approach

The claim is well-stated as it precisely describes what the method does without exaggerating its novelty or capabilities. It simply states the technical modification made to the AR approach through stochastic sampling, which is fully supported by the mathematical and algorithmic evidence provided.

<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:

Stochastic AR allows the network to be more flexible when acquiring new knowledge while still alleviating catastrophic forgetting.

The evidence to be evaluated is: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 \(\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_{t})\).

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

Finally, the type of losses \(\mathcal{L}_{k<t}\) can be flexibly changed to other loss rather than the negative log-likelihood.

By changing the losses \(\mathcal{L}_{k<t}\), we can recover different solutions for continual learning in the literature.

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 \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\] where \(\tau\) is the temperature used in softmax outputs.

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.

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.

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.

4:\(\mathcal{M}_{t}\leftarrow\) add random samples from \(\mathcal{D}_{t}\) to the memory.

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

Both DAR and SAR outperforms the baselines by large margins, achieving accuracy of 94.9% and 94.8% respectively.

Both DAR and SAR are consistently better than GEM at all memory size.

At 2500 samples, both DAR and SAR achieves over 96% accuracy, showing great scalability.

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.

Except the first task where all models are the same, SAR achieves slightly higher accuracy than DAR on 6 out of 9 remaining tasks. Overall SAR performs better than DAR by a small margin, showing that it can achieve similar results compare to DAR and has more scalability. 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.

We further improve DAR with a stochastic sampling regularizer (SAR), which balances the model's stability and plasticity, allowing the model to acquire new knowledge, alleviate forgetting and has greater scalability.

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 "Stochastic AR allows the network to be more flexible when acquiring new knowledge while still alleviating catastrophic forgetting" appears to be well-supported by the evidence but slightly overstated. The evidence shows SAR performs marginally better than DAR in 6 out of 9 tasks and demonstrates good performance in preventing catastrophic forgetting. However, while the flexibility benefit is mentioned theoretically, the empirical evidence shows only modest improvements over DAR. The graphs show both methods perform similarly, with SAR showing slight advantages in some scenarios but not dramatically better flexibility.

<score>2</score>

Justification:
1. The empirical results support SAR's effectiveness:
- Figure 1 shows SAR maintains high accuracy across tasks
- Figure 2(b) shows SAR slightly outperforms DAR in most tasks
- Both achieve similar final accuracies (94.8% vs 94.9%)

2. The claim's limitations:
- The flexibility advantage is theoretically explained but not strongly demonstrated empirically
- The performance difference between SAR and DAR is modest
- The evidence doesn't conclusively prove increased flexibility is the key factor in performance

3. The evidence demonstrates that SAR works well but doesn't fully validate the stronger implications about flexibility in the claim. The more measured conclusion would be that SAR provides comparable performance to DAR with potential benefits for scalability.


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:

Stochastic AR allows the network to be more flexible when acquiring new knowledge while still alleviating 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: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 \(\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_{t})\).

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

Finally, the type of losses \(\mathcal{L}_{k<t}\) can be flexibly changed to other loss rather than the negative log-likelihood.

By changing the losses \(\mathcal{L}_{k<t}\), we can recover different solutions for continual learning in the literature.

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 \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\] where \(\tau\) is the temperature used in softmax outputs.

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.

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.

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.

4:\(\mathcal{M}_{t}\leftarrow\) add random samples from \(\mathcal{D}_{t}\) to the memory.

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

Both DAR and SAR outperforms the baselines by large margins, achieving accuracy of 94.9% and 94.8% respectively.

Both DAR and SAR are consistently better than GEM at all memory size.

At 2500 samples, both DAR and SAR achieves over 96% accuracy, showing great scalability.

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.

Except the first task where all models are the same, SAR achieves slightly higher accuracy than DAR on 6 out of 9 remaining tasks. Overall SAR performs better than DAR by a small margin, showing that it can achieve similar results compare to DAR and has more scalability. 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.

We further improve DAR with a stochastic sampling regularizer (SAR), which balances the model's stability and plasticity, allowing the model to acquire new knowledge, alleviate forgetting and has greater scalability.

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 "Stochastic AR allows the network to be more flexible when acquiring new knowledge while still alleviating catastrophic forgetting" appears somewhat overstated. While the evidence shows SAR performs slightly better than DAR on 6 out of 9 tasks and demonstrates good performance in preventing catastrophic forgetting, the improvements are modest. The reviewer points out that experimental justification could be improved, with missing error bars and limited benchmarks. The evidence doesn't conclusively demonstrate increased "flexibility" in acquiring new knowledge, though it shows comparable performance with potentially better scalability.

<score>3</score>

Justification:
1. The performance improvements shown in Figures 1 and 2 demonstrate SAR's effectiveness but not dramatically superior flexibility
2. The reviewer notes limitations in experimental validation and missing comparisons to relevant baselines like LwF
3. While SAR shows good performance in preventing forgetting, the evidence for improved flexibility in acquiring new knowledge is limited
4. The claim would be better stated with more measured language about the modest improvements and specific contexts where benefits were observed
5. Direct evidence from the paper shows SAR performs "slightly higher" than DAR and achieves results "similar" to DAR, suggesting more modest benefits than the claim implies


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:

Stochastic AR allows the network to be more flexible when acquiring new knowledge while still alleviating 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: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 \(\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_{t})\).

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

Finally, the type of losses \(\mathcal{L}_{k<t}\) can be flexibly changed to other loss rather than the negative log-likelihood.

By changing the losses \(\mathcal{L}_{k<t}\), we can recover different solutions for continual learning in the literature.

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 \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\] where \(\tau\) is the temperature used in softmax outputs.

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.

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.

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.

4:\(\mathcal{M}_{t}\leftarrow\) add random samples from \(\mathcal{D}_{t}\) to the memory.

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

Both DAR and SAR outperforms the baselines by large margins, achieving accuracy of 94.9% and 94.8% respectively.

Both DAR and SAR are consistently better than GEM at all memory size.

At 2500 samples, both DAR and SAR achieves over 96% accuracy, showing great scalability.

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.

Except the first task where all models are the same, SAR achieves slightly higher accuracy than DAR on 6 out of 9 remaining tasks. Overall SAR performs better than DAR by a small margin, showing that it can achieve similar results compare to DAR and has more scalability. 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.

We further improve DAR with a stochastic sampling regularizer (SAR), which balances the model's stability and plasticity, allowing the model to acquire new knowledge, alleviate forgetting and has greater scalability.

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 "Stochastic AR allows the network to be more flexible when acquiring new knowledge while still alleviating catastrophic forgetting" appears somewhat overstated relative to the supporting data.

While the figures show SAR performs similarly or slightly better than DAR in some cases, the evidence doesn't definitively demonstrate increased "flexibility" in knowledge acquisition. The graphs mainly show comparable performance between DAR and SAR, with modest improvements in some scenarios. The reviewer also raises valid concerns about the method's effectiveness in more challenging settings with data from different domains.

The claim would be better stated with more measured language acknowledging the incremental nature of the improvements and potential limitations.

<score>3</score>

Justification:
1. The evidence shows SAR achieves "slightly higher accuracy than DAR on 6 out of 9 remaining tasks" and performs "better than DAR by a small margin" - suggesting modest rather than dramatic improvements
2. The reviewer notes skepticism about "how significant the improvement of the method would be in the more challenging and realistic setting"
3. While Figure 1 shows good performance for SAR, it's comparable to DAR rather than demonstrating clearly superior flexibility
4. The random sampling approach is questioned by the reviewer as potentially "suboptimal" compared to other selection methods
5. The claim overstates the degree of demonstrated improvement in flexibility/plasticity without acknowledging limitations


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:

Stochastic AR allows the network to be more flexible when acquiring new knowledge while still alleviating catastrophic forgetting.

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 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 \(\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_{t})\).

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

Finally, the type of losses \(\mathcal{L}_{k<t}\) can be flexibly changed to other loss rather than the negative log-likelihood.

By changing the losses \(\mathcal{L}_{k<t}\), we can recover different solutions for continual learning in the literature.

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 \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\] where \(\tau\) is the temperature used in softmax outputs.

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.

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.

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.

4:\(\mathcal{M}_{t}\leftarrow\) add random samples from \(\mathcal{D}_{t}\) to the memory.

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

Both DAR and SAR outperforms the baselines by large margins, achieving accuracy of 94.9% and 94.8% respectively.

Both DAR and SAR are consistently better than GEM at all memory size.

At 2500 samples, both DAR and SAR achieves over 96% accuracy, showing great scalability.

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.

Except the first task where all models are the same, SAR achieves slightly higher accuracy than DAR on 6 out of 9 remaining tasks. Overall SAR performs better than DAR by a small margin, showing that it can achieve similar results compare to DAR and has more scalability. 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.

We further improve DAR with a stochastic sampling regularizer (SAR), which balances the model's stability and plasticity, allowing the model to acquire new knowledge, alleviate forgetting and has greater scalability.

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:
Based on my evaluation of the claim "Stochastic AR allows the network to be more flexible when acquiring new knowledge while still alleviating catastrophic forgetting," I find this to be moderately overstated relative to the evidence provided.

The evidence shows SAR performs slightly better than DAR in 6 out of 9 tasks and achieves comparable overall results. While Fig. 1 demonstrates both SAR and DAR outperform baselines in preventing catastrophic forgetting, and Fig. 2 shows consistent performance, the claim of increased "flexibility" in acquiring new knowledge isn't strongly substantiated. The review comment also points out limited novelty compared to LwF and lack of validation for hyperparameter choices.

<score>3</score>

Justification:
1. The claim's strength is partially supported by:
- Empirical results showing SAR matches or slightly exceeds DAR's performance
- Evidence of forgetting prevention in benchmark tests
- Demonstrated scalability with different memory sizes

2. However, the claim is somewhat overstated because:
- Limited experimental validation of the "flexibility" claim
- Reviewer notes insufficient hyperparameter testing
- No direct evidence comparing knowledge acquisition capabilities
- The improvements over DAR appear incremental rather than transformative

The claim would be better stated if it focused on the demonstrated empirical performance improvements rather than making broader assertions about flexibility and knowledge acquisition.


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:

We then analyze the weakness of existing approaches, and propose a novel regularization method named "Activity Regularization" (AR), which alleviates forgetting meanwhile keeping model's plasticity to acquire new knowledge.

The evidence to be evaluated is: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 \(\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_{t})\).

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

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. While EWC and GEM are two popular methods for continual learning, we argue that they are sensitive to misclassified samples selected in the memory or used to estimate the Fisher information.

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 \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\] 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.

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.

```**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.

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.

7: Sample an index i from \([0,\dots,t-1]\) 8:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{ D}}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{\mathbf{x}\in\mathcal{M}_{i}} \lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\) 9:\(\mathbf{\theta}\leftarrow\mathbf{\theta}-\alpha\cdot\text{SGD}(\mathbf{\theta},g_{\mathbf{ \theta}})\) 10:return\(\mathbf{\theta}\) ```**Algorithm 2** Stochastic Activity Regularization (SAR) algorithm for Continual Learning.

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. Prior works can be broadly categorized into 4 main approaches: (1) structural regularization, (2) functional regularization, (3) Bayesian learning and (4) ensemble learning. **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).

**Functional regularization** methods employ the regularizer on the model's output rather than its parameters. Different from structural regularization, functional regularization aims to preserve the learned input-output mapping function of the network. 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. Selfless sequential learning (SNI) (Aljundi et al., 2018b) improves MAS by combining with it sparsity in each layer's activation. Different from LwF that distills previous models on the current data, which contradicts the goal of knowledge distillation since past models are not trained on the new data, they provide noise to the current model. 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. The learning of sub-networks can either be explicit or implicit. In explicit ensemble learning, each sub-network is either newly initialized whenever a new tasks arrives as in Progressive Neural Network (Rusu et al., 2016) or searched from a big network as proposed in Pathner (Fernando et al., 2017). After training a task, the corresponding sub-network is frozen and will not allowed to change, thus completely immune to catastrophic forgetting. In contrast, implicit ensemble learning can be considered as a hybrid method of explicit ensemble with other types of regularization. Dynamically expandable networks (Yoon et al., 2018) proposes to learn sub-networks in a pre-initialized network through sparsity, adding new neurons whenever needed. 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. In this work, we propose an approximated multi-task learning framework to unify both structural and functional regularization, in which our proposed activity regularization is a special case.

From the results, EWC perform the worst although requiring the most "memory unit". 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 outperforms the baselines by large margins, achieving accuracy of 94.9% and 94.8% respectively. We also investigate the scalability of our methods when more samples are available in the memory.

Both DAR and SAR are consistently better than GEM at all memory size.

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. As more samples are stored, the memory can better represent the past tasks, results in performance improvement.

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.

Finally, both DAR and VAR consistently perform better than the baselines, achieving 97.6% and 97.7% accuracy respectively.

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. We further analyze the weakness of two popular methods: EWC and GEM, showing that they are sensitive to mistakes and noise in the Fisher or memory. 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.

We further improve DAR with a stochastic sampling regularizer (SAR), which balances the model's stability and plasticity, allowing the model to acquire new knowledge, alleviate forgetting and has greater scalability.

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

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, I find that the claim about analyzing weaknesses of existing approaches and proposing a novel "Activity Regularization" method is moderately well-stated, with some elements of overstatement. The evidence shows:

- Clear analysis of weaknesses in existing methods (EWC and GEM's sensitivity to misclassified samples)
- Detailed mathematical formulation and experimental validation of the AR approach
- Performance improvements demonstrated through empirical results (Figure 2)
- However, the claim's strength is somewhat tempered by:
  - Limited benchmarking scenarios
  - The improvements, while consistent, are incremental rather than transformative (e.g., 94.8-94.9% vs 91.8% for GEM)

The evidence generally supports the claim, but the language could be more measured regarding the degree of improvement.

<score>2</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:

We then analyze the weakness of existing approaches, and propose a novel regularization method named "Activity Regularization" (AR), which alleviates forgetting meanwhile keeping model's plasticity to acquire new knowledge.

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: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 \(\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_{t})\).

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

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. While EWC and GEM are two popular methods for continual learning, we argue that they are sensitive to misclassified samples selected in the memory or used to estimate the Fisher information.

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 \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\] 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.

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.

```**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.

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.

7: Sample an index i from \([0,\dots,t-1]\) 8:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{ D}}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{\mathbf{x}\in\mathcal{M}_{i}} \lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\) 9:\(\mathbf{\theta}\leftarrow\mathbf{\theta}-\alpha\cdot\text{SGD}(\mathbf{\theta},g_{\mathbf{ \theta}})\) 10:return\(\mathbf{\theta}\) ```**Algorithm 2** Stochastic Activity Regularization (SAR) algorithm for Continual Learning.

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. Prior works can be broadly categorized into 4 main approaches: (1) structural regularization, (2) functional regularization, (3) Bayesian learning and (4) ensemble learning. **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).

**Functional regularization** methods employ the regularizer on the model's output rather than its parameters. Different from structural regularization, functional regularization aims to preserve the learned input-output mapping function of the network. 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. Selfless sequential learning (SNI) (Aljundi et al., 2018b) improves MAS by combining with it sparsity in each layer's activation. Different from LwF that distills previous models on the current data, which contradicts the goal of knowledge distillation since past models are not trained on the new data, they provide noise to the current model. 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. The learning of sub-networks can either be explicit or implicit. In explicit ensemble learning, each sub-network is either newly initialized whenever a new tasks arrives as in Progressive Neural Network (Rusu et al., 2016) or searched from a big network as proposed in Pathner (Fernando et al., 2017). After training a task, the corresponding sub-network is frozen and will not allowed to change, thus completely immune to catastrophic forgetting. In contrast, implicit ensemble learning can be considered as a hybrid method of explicit ensemble with other types of regularization. Dynamically expandable networks (Yoon et al., 2018) proposes to learn sub-networks in a pre-initialized network through sparsity, adding new neurons whenever needed. 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. In this work, we propose an approximated multi-task learning framework to unify both structural and functional regularization, in which our proposed activity regularization is a special case.

From the results, EWC perform the worst although requiring the most "memory unit". 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 outperforms the baselines by large margins, achieving accuracy of 94.9% and 94.8% respectively. We also investigate the scalability of our methods when more samples are available in the memory.

Both DAR and SAR are consistently better than GEM at all memory size.

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. As more samples are stored, the memory can better represent the past tasks, results in performance improvement.

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.

Finally, both DAR and VAR consistently perform better than the baselines, achieving 97.6% and 97.7% accuracy respectively.

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. We further analyze the weakness of two popular methods: EWC and GEM, showing that they are sensitive to mistakes and noise in the Fisher or memory. 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.

We further improve DAR with a stochastic sampling regularizer (SAR), which balances the model's stability and plasticity, allowing the model to acquire new knowledge, alleviate forgetting and has greater scalability.

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

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 review comments, I find the claim to be moderately overstated. Here's why:

The claim states that AR "alleviates forgetting meanwhile keeping model's plasticity," but the evidence shows mixed results. While DAR/SAR do show improvements over baselines in some experiments, the reviewer points out several key limitations:

1. The approach is very similar to existing work (LwF) which isn't adequately acknowledged
2. The experimental validation could be stronger (limited benchmarks, missing error bars, unclear baselines)
3. The plasticity claim isn't fully substantiated with comprehensive evidence
4. Some reported baseline results are worse than in previous work

While the method does show promise in addressing catastrophic forgetting, the certainty and breadth of the claim exceeds what is demonstrated by the evidence.

<score>4</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:

We then analyze the weakness of existing approaches, and propose a novel regularization method named "Activity Regularization" (AR), which alleviates forgetting meanwhile keeping model's plasticity to acquire new knowledge.

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: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 \(\mathcal{L}_{t}(\mathbf{\theta},\mathcal{D}_{t})\).

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

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. While EWC and GEM are two popular methods for continual learning, we argue that they are sensitive to misclassified samples selected in the memory or used to estimate the Fisher information.

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 \[\tilde{\mathcal{L}}_{t}(\mathbf{\theta})=\mathcal{L}_{t}(\mathbf{\theta})+\sum_{i<t} \sum_{\mathbf{x}\in\mathcal{M}_{i}}\lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{ \theta}_{i}^{*}}(\mathbf{x})\bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}, \tag{7}\] 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.

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.

```**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.

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.

7: Sample an index i from \([0,\dots,t-1]\) 8:\(g_{\mathbf{\theta}}\leftarrow\nabla_{\mathbf{\theta}}\left[\sum_{\mathbf{x},y\in\mathcal{ D}}\mathcal{L}_{t}(\mathbf{\theta},(\mathbf{x},y))+\sum_{\mathbf{x}\in\mathcal{M}_{i}} \lambda_{i}KL\bigg{(}\frac{1}{\tau}f_{\mathbf{\theta}_{i}^{*}}(\mathbf{x})\ \bigg{\|}\ \frac{1}{\tau}f_{\mathbf{\theta}}(\mathbf{x})\bigg{)}\right]\) 9:\(\mathbf{\theta}\leftarrow\mathbf{\theta}-\alpha\cdot\text{SGD}(\mathbf{\theta},g_{\mathbf{ \theta}})\) 10:return\(\mathbf{\theta}\) ```**Algorithm 2** Stochastic Activity Regularization (SAR) algorithm for Continual Learning.

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. Prior works can be broadly categorized into 4 main approaches: (1) structural regularization, (2) functional regularization, (3) Bayesian learning and (4) ensemble learning. **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).

**Functional regularization** methods employ the regularizer on the model's output rather than its parameters. Different from structural regularization, functional regularization aims to preserve the learned input-output mapping function of the network. 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. Selfless sequential learning (SNI) (Aljundi et al., 2018b) improves MAS by combining with it sparsity in each layer's activation. Different from LwF that distills previous models on the current data, which contradicts the goal of knowledge distillation since past models are not trained on the new data, they provide noise to the current model. 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. The learning of sub-networks can either be explicit or implicit. In explicit ensemble learning, each sub-network is either newly initialized whenever a new tasks arrives as in Progressive Neural Network (Rusu et al., 2016) or searched from a big network as proposed in Pathner (Fernando et al., 2017). After training a task, the corresponding sub-network is frozen and will not allowed to change, thus completely immune to catastrophic forgetting. In contrast, implicit ensemble learning can be considered as a hybrid method of explicit ensemble with other types of regularization. Dynamically expandable networks (Yoon et al., 2018) proposes to learn sub-networks in a pre-initialized network through sparsity, adding new neurons whenever needed. 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. In this work, we propose an approximated multi-task learning framework to unify both structural and functional regularization, in which our proposed activity regularization is a special case.

From the results, EWC perform the worst although requiring the most "memory unit". 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 outperforms the baselines by large margins, achieving accuracy of 94.9% and 94.8% respectively. We also investigate the scalability of our methods when more samples are available in the memory.

Both DAR and SAR are consistently better than GEM at all memory size.

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. As more samples are stored, the memory can better represent the past tasks, results in performance improvement.

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.

Finally, both DAR and VAR consistently perform better than the baselines, achieving 97.6% and 97.7% accuracy respectively.

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. We further analyze the weakness of two popular methods: EWC and GEM, showing that they are sensitive to mistakes and noise in the Fisher or memory. 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.

We further improve DAR with a stochastic sampling regularizer (SAR), which balances the model's stability and plasticity, allowing the model to acquire new knowledge, alleviate forgetting and has greater scalability.

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

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 about analyzing weaknesses and proposing AR appears partly supported but somewhat overstated. While the paper does identify specific weaknesses in EWC and GEM (sensitivity to misclassified samples), and proposes AR as a solution, the reviewer raises valid concerns about originality (similarity to LwF) and significance (limited experimental scope). The evidence shows AR achieving better accuracy than baselines, but the improvements are incremental rather than transformative. The claim could be more measured in describing AR as an incremental improvement rather than a truly "novel" method that definitively solves the stated problems.

<score>3</score>

Justification:
1. The review comments highlight limited originality, noting strong similarity to existing LwF method
2. The experimental results show improvements over baselines (94.9% vs 91.8% for GEM), but not dramatically novel performance gains
3. Evidence supports identification of specific weaknesses in existing approaches
4. Limited experimental scope (similar data structure) raises questions about broader applicability
5. The use of "novel" appears overstated given the incremental nature of the improvements and similarity to existing work