Kati8/ICLR_2023_2025 huggingface dataset:
authors: Xiao Chuanfu
authors: Cuiyu Liu
authors: Qianchao Zhu
authors: Min Li
authors: Chao Yang
reviews: 
Comments: This paper presents a algorithm for locating the largest and smallest elements in a tensor with low-rank format. The algorithm combines an alternating iterative method and a maximum block increasing approach, along with a newly-designed block-search strategy. The proposed algorithm achieves improvements in accuracy and efficiency compared to existing methods, as demonstrated through numerical experiments. It also discusses the use of the algorithm in various low-rank representations and highlights its advantage of obtaining both the largest/smallest elements and their location simultaneously.
Strengths: *1. Quality:*  The paper presents an algorithm that significantly improves upon existing methods by achieving remarkable advances in both accuracy and efficiency. The comparisons with existing methods underscore the superior performance of the proposed approach in terms of both accuracy and computational efficiency. Moreover, the paper discusses the algorithm's applicability to various low-rank representations, including CP, Tucker, and TT formats.

*2. Clarity:*  The authors employ precise mathematical notations consistently, facilitating the understanding of the proposed algorithm, theoretical analysis, and numerical experiments.
Weaknesses: 1. *Limited Novelty:* The paper draws inspiration from prior work and utilizes established techniques. It doesn't clearly differentiate how the proposed algorithms significantly advance beyond existing methods, both conceptually and theoretically. A more thorough exploration of the novelty would strengthen the paper's contribution.

2. *Limited Impact:* The paper's contribution is niche, addressing a specific task related to low-rank tensors. It lacks the potential to significantly impact or disrupt the broader machine learning community. A broader discussion of potential applications or extensions could enhance its relevance.

3. *Lack of Code Availability:* The absence of publicly available code for replicating the proposed algorithm limits reproducibility and practical usability for the research community. Providing code would improve transparency and facilitate further research.

4. *Inadequate Discussion of Limitations:* The paper does not thoroughly discuss potential limitations or challenges associated with applying the proposed algorithm in practical scenarios. A comprehensive examination of limitations is essential for practical decision-making.
Recommendation: 5: marginally below the acceptance threshold
Reviewer confidence: 3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Soundness/correctness: 2 fair
Clarity: 3 good
reviews: 
Comments: The paper presents an approach for computing the largest elements of a factorized tensor by means of alternating optimization.
Strengths: + The results regarding convergence of the method would make the approach valuable for a reasonably formulated problem.
Weaknesses: - The paper seems to obfuscate at least two major technical oversights:
    - The symmetric tensor eigenvalue formulation of the problem is used, by different factor matrices are optimized by alternating optimization. In the symmetric tensor eigenvalue problem, each component of the rank-1 factorization is typically set to be the same. Symmetry is mentioned in the problem definition in Section II, but never thereafter.
    - The proof of theorem 1 does not appear complete or correct to me. Convergence is considered based only the objective function, which is convergent for any method that has a nondecreasing and bounded objective. Hence, the contrast to convergence of standard alternating least squares does not make sense. See, Uschmajew, A. (2012). Local convergence of the alternating least squares algorithm for canonical tensor approximation. SIAM Journal on Matrix Analysis and Applications, 33(2), 639-652.

I believe the paper should not be published due to technical errors that are obfuscated by the writing.
Recommendation: 1: strong reject
Reviewer confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness/correctness: 1 poor
Clarity: 1 poor
reviews: 
Comments: In this paper, the authors develop algorithms aimed at identifying the largest and smallest elements in a factorized tensor. They propose an alternating iterative algorithm, which is enhanced with a maximum block increasing approach and a novel block-search strategy. The validation of their method is provided through both theoretical analysis and experimental evaluations.
Strengths: This paper presents a novel approach to a problem arising from tensor analysis - locating the largest/smallest elements in a tensor in the low-rank format. The strengths of the paper can be highlighted as follows:

1. The authors propose a continuous optimization model that is different from the existing methods. This model could be applied to various low-rank representations such as CP, Tucker, and TT formats.

2. The proposed method demonstrates significant improvements in both accuracy and efficiency over existing works in numerical experiments. This suggests that the method may be practically useful in real-world applications.
Weaknesses: While the paper presents a novel approach to locating the largest/smallest elements in a tensor in a low-rank format, some weaknesses mainly related to the theoretical results can be identified:

1. Theorem 1 formulates an equivalent optimization problem for finding the largest element in a tensor, which is a crucial step in the authors' method. However, the paper does not provide an in-depth analysis of this equivalent problem. For example, it would be beneficial to understand the number of minimizers that this problem may have. Such analysis could provide insights into the complexity and potential pitfalls of the optimization problem, and could be critical for the algorithm's performance.

2. Theorem 2 shows that the proposed algorithm's subsequence converges to a stationary point of the optimization problem. However, it's unclear whether the entire sequence converges, and more importantly, whether it converges to the optimal solution. The absence of these guarantees may limit the algorithm's reliability and effectiveness in practice.

3. While Theorem 3 establishes a linear convergence rate to the optimal solution, it does so under the assumption that the initial point is sufficiently close to the optimal solution. Regrettably, the paper falls short in providing a discussion on how to obtain such an initial point. Furthermore, the paper does not explore the potential existence of multiple optimal solutions, a factor that could significantly affect the algorithm's convergence behavior.
Recommendation: 3: reject, not good enough
Reviewer confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness/correctness: 3 good
Clarity: 3 good