Learning Efficient Tensor Representations with Ring Structure Networks
emph{Tensor train (TT) decomposition} is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. In this paper, we propose a more generalized tensor decomposition with ring structure network by employing circular multilinear products over a sequence of lower-order core tensors, which is termed as TR representation. Several learning algorithms including blockwise ALS with adaptive tensor ranks and SGD with high scalability are presented. Furthermore, the mathematical properties are investigated, which enables us to perform basic algebra operations in a computationally efficiently way by using TR representations. Experimental results on synthetic signals and real-world datasets demonstrate the effectiveness of TR model and the learning algorithms. In particular, we show that the structure information and high-order correlations within a 2D image can be captured efficiently by employing tensorization and TR representation.
 This paper proposes a tensor train decomposition with a ring structure for function approximation and data compression. Most of the techniques used are well-known in the tensor community (outside of machine learning). The main contribution of the paper is the introduce such techniques to the ML community and presents experimental results for support. The paper is rather preliminary in its examination. For example, it is claimed that the proposed decomposition provides "enhanced representation ability", but this is not justified rigorously either via more comprehensive experimentation or via a theoretical justification. Furthermore, the paper lacks in novelty aspect, as it is uses mostly well-known techniques.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Learning Efficient Tensor Representations with Ring Structure Networks
emph{Tensor train (TT) decomposition} is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. In this paper, we propose a more generalized tensor decomposition with ring structure network by employing circular multilinear products over a sequence of lower-order core tensors, which is termed as TR representation. Several learning algorithms including blockwise ALS with adaptive tensor ranks and SGD with high scalability are presented. Furthermore, the mathematical properties are investigated, which enables us to perform basic algebra operations in a computationally efficiently way by using TR representations. Experimental results on synthetic signals and real-world datasets demonstrate the effectiveness of TR model and the learning algorithms. In particular, we show that the structure information and high-order correlations within a 2D image can be captured efficiently by employing tensorization and TR representation.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 This paper proposes a tensor train decomposition with a ring structure for function approximation and data compression. Most of the techniques used are well-known in the tensor community (outside of machine learning). The main contribution of the paper is the introduce such techniques to the ML community and presents experimental results for support. The paper is rather preliminary in its examination. For example, it is claimed that the proposed decomposition provides "enhanced representation ability", but this is not justified rigorously either via more comprehensive experimentation or via a theoretical justification. Furthermore, the paper lacks in novelty aspect, as it is uses mostly well-known techniques.
assistant
 This paper proposes a tensor train decomposition with a ring structure for function approximation and data compression. Most of the techniques used are well-known in the tensor community (outside of machine learning). The main contribution of the paper is the introduce such techniques to the ML community and presents experimental results for support. The paper is rather preliminary in its examination. For example, it is claimed that the proposed decomposition provides "enhanced representation ability", but this is not justified rigorously either via more comprehensive experimentation or via a theoretical justification. Furthermore, the paper lacks in novelty aspect, as it is uses mostly well-known techniques.