Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
review_content: summary: The paper suggests a new CIL (Class-incremental learning) algorithm. The proposed algorithm outperforms existing CIL algorithms in the sense that it is both reasonably accurate, and does not expose past examples to privacy breaches. Previous algorithms could have only achieved one of these desired properties.
strengths_and_weaknesses: Strengths:
1. The key contribution of an algorithm which is both accurate and private seems novel and significant. It is also well explained and motivated. 
2. A thorough literature review is conducted, assisting the reader to understand the paper's contribution.
3. The limitations of the algorithm (especially for small K values) are well explained.

Weaknesses:
1. It could have been interesting to analyze why for small K values ACIL does not outperform state-of-the-art, and perhaps even to conjecture whether there exists a private algorithm that outperforms the state-of-the-art for any value of K.
2. For the inexperienced reader, it is not obvious that the mild degradation mentioned in row 263 could really be explained by quantization errors, as he/she may not be familiar with the plausible rate of such kind of errors. Also, it might have been interesting to discuss what could happen when K is extremely large (in case that it is indeed an interesting scenario, and if it is not, it might be worth explaining why). As far as the (inexperienced) reader knows, the degradation might be catastrophically high in this case.
questions: Is the conjecture that the mild degradation mentioned in row 263 could be explained by quantization errors supported by the reference cited there? What is the reasonable damage that such errors usually cause?
limitations: Yes.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: In this paper, the authors propose a method to learn a perfect FC classifier for CIL without using exemplars. Instead, they need to store autocorrelation matrixes in the memory. They provide extensive experiments to show the effectiveness of the proposed method.
strengths_and_weaknesses: ### Strengths

- This paper is well-written and easy to follow.

- The proposed method achieves impressive results without using the exemplars.

- Extensive experiment results on multiple datasets are provided.

### Weaknesses

I have reviewed this paper as an ICML submission. During the review, I indicate the following weaknesses:

- In the abstract and introduction, the authors claimed they fully address the catastrophic forgetting problem. However, the results (e.g., in Table 1) of ACIL are still much lower than the joint training results. I think it is because CNN is fixed. Therefore, the authors should adjust their presentation and remove the claim of “fully addressing the catastrophic forgetting”.

- The proposed method needs to store autocorrelation matrixes in the memory. Thus, the author should also compare the memory usage between existing methods and the proposed method. The authors need to answer whether the proposed method requires more memory compared to saving exemplars.

- The proposed method uses a fixed CNN network after the first phase. So it is not possible to update the low-level image features with the new data in the following phases. If we observe some new classes that are very different from the first phase data, this method might not perform well. Maybe the authors should include some experiments to evaluate the above situation.

- There are some small typos in the paper. For example, the authors write “
Merits of ACL come with costs” in Line 014. However, the abbreviation “ACL” never appears before. I think it might be “CIL”. In Figure 1, the word “clasasifier” is incorrect.

- The authors should move the proof of Theorem 3.1 to the supplementary.

The above weaknesses have been addressed in the current version. Thus, I have no more questions and recommend acceptance. 
questions: See the "weaknesses" part. 
limitations: It would be better to add a section to discuss the potential negative societal impact.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper aims to tackle the problem of catastrophic forgetting without revisiting historical exemplars so that data privacy is preserved. To do this,  an analytic class-incremental learning (ACIL) algorithm is proposed with absolute memorization of past knowledge. Empirical results demonstrated competitive accuracy performance that does not degrade over increment of data classes during learning phases. . ACIL also outperformed the state-of-the-art methods for large-phase scenarios.
strengths_and_weaknesses: Strengths:
 - Section 3 clearly described the proposed algorithm. Even readers with no background in analytic learning and CIL can easily understand.
 - The idea of using analytic learning in CIL is novel and sound.
 - Has empirical evaluations demonstrating the power of ACIL.

Weaknesses:
 - Should explain the benchmarking algorithms in the empirical evaluations, e.g. what is LwF.
 - Should include more privacy-preserving baselines in the experiments. Currently, only LwF is used. How about the GAN-based methods mentioned in Section 2? Why not evaluate the GAN-based methods on these large datasets?
 - Should clarify how CNN was trained (separately for each phase or it is one CNN for every phase?)

 
questions: 1. Can you add descriptions of the benchmarking algorithms?
2. Why not evaluate the GAN-based methods on these large datasets?
3. Are the CNNs trained separately for each phase?
limitations: Not applicable.
review_title: null

Meta-review: metareview: The reviewers agree that this is a solid contribution. Please do revise the paper according to the reviewers comments and the discussion.
confidence: Certain
Decision: Accept