Adaptive Mixture of Low-Rank Factorizations for Compact Neural Modeling
Modern deep neural networks have a large amount of weights, which make them difficult to deploy on computation constrained devices such as mobile phones. One common approach to reduce the model size and computational cost is to use low-rank factorization to approximate a weight matrix. However, performing standard low-rank factorization with a small rank can hurt the model expressiveness and significantly decrease the performance. In this work, we propose to use a mixture of multiple low-rank factorizations to model a large weight matrix, and the mixture coefficients are computed dynamically depending on its input. We demonstrate the effectiveness of the proposed approach on both language modeling and image classification tasks. Experiments show that our method not only improves the computation efficiency but also maintains (sometimes outperforms) its accuracy compared with the full-rank counterparts.
 In this paper, the authors propose a compression technique to reduce the number of parameters to learn in a neural network without losing expressiveness. The paper nicely introduces the problem of lack in espressiveness with low-rank factorizations, a well-known technique to reduce the number of parameters in a network. The authors propose to use a linear combination of low-rank factorizations with coefficients adaptively computed on data input. Through a nice toy example based on XNOR data, they provide a good proof of concept showing that the accuracy of the proposed technique outperforms the classical low-rank approach. I enjoyed reading the paper, which gives an intuitive line of reasoning providing also extensive experimental results on multilayer perceptron, convolutional neural networks and recurrent neural networks as well. The proposal is based on an intuitive line of reasoning with no strong theoretical founding. However, they provide a quick theoretical result in the appendix (Proposition 1) but, I couldn’t understand very well its implications on the expressiveness of proposed method against classical low-rank approach.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Adaptive Mixture of Low-Rank Factorizations for Compact Neural Modeling
Modern deep neural networks have a large amount of weights, which make them difficult to deploy on computation constrained devices such as mobile phones. One common approach to reduce the model size and computational cost is to use low-rank factorization to approximate a weight matrix. However, performing standard low-rank factorization with a small rank can hurt the model expressiveness and significantly decrease the performance. In this work, we propose to use a mixture of multiple low-rank factorizations to model a large weight matrix, and the mixture coefficients are computed dynamically depending on its input. We demonstrate the effectiveness of the proposed approach on both language modeling and image classification tasks. Experiments show that our method not only improves the computation efficiency but also maintains (sometimes outperforms) its accuracy compared with the full-rank counterparts.
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>



 In this paper, the authors propose a compression technique to reduce the number of parameters to learn in a neural network without losing expressiveness. The paper nicely introduces the problem of lack in espressiveness with low-rank factorizations, a well-known technique to reduce the number of parameters in a network. The authors propose to use a linear combination of low-rank factorizations with coefficients adaptively computed on data input. Through a nice toy example based on XNOR data, they provide a good proof of concept showing that the accuracy of the proposed technique outperforms the classical low-rank approach. I enjoyed reading the paper, which gives an intuitive line of reasoning providing also extensive experimental results on multilayer perceptron, convolutional neural networks and recurrent neural networks as well. The proposal is based on an intuitive line of reasoning with no strong theoretical founding. However, they provide a quick theoretical result in the appendix (Proposition 1) but, I couldn’t understand very well its implications on the expressiveness of proposed method against classical low-rank approach.
assistant
 In this paper, the authors propose a compression technique to reduce the number of parameters to learn in a neural network without losing expressiveness. The paper nicely introduces the problem of lack in espressiveness with low-rank factorizations, a well-known technique to reduce the number of parameters in a network. The authors propose to use a linear combination of low-rank factorizations with coefficients adaptively computed on data input. Through a nice toy example based on XNOR data, they provide a good proof of concept showing that the accuracy of the proposed technique outperforms the classical low-rank approach. I enjoyed reading the paper, which gives an intuitive line of reasoning providing also extensive experimental results on multilayer perceptron, convolutional neural networks and recurrent neural networks as well. The proposal is based on an intuitive line of reasoning with no strong theoretical founding. However, they provide a quick theoretical result in the appendix (Proposition 1) but, I couldn’t understand very well its implications on the expressiveness of proposed method against classical low-rank approach.