Supervised learning with projected entangled pair states
文献类型：期刊论文
| 作者 | Cheng, Song1; Wang, Lei1,2; Zhang, Pan3,4,5
|
| 刊名 | PHYSICAL REVIEW B
 |
| 出版日期 | 2021 |
| 卷号 | 103期号:12页码:125117 |
| 关键词 | MATRIX PRODUCT STATES |
| ISSN号 | 2469-9950 |
| DOI | 10.1103/PhysRevB.103.125117 |
| 英文摘要 | Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only treelike tensor networks such as the matrix product states and tree tensor networks have been considered, even for modeling two-dimensional data such as images. In this work, we construct supervised learning models for images using the projected entangled pair states (PEPS), a two-dimensional tensor network having a similar structure prior to natural images. Our approach first performs a feature map, which transforms the image data to a product state on a grid, then contracts the product state to a PEPS with trainable parameters to predict image labels. The tensor elements of PEPS are trained by minimizing differences between training labels and predicted labels. The proposed model is evaluated on image classifications using the Modified National Institute of Standards and Technology database (MNIST) and the Fashion-MNIST datasets. We show that our model is significantly superior to existing models using treelike tensor networks. Moreover, using the same input features, our method performs as well as the multilayer perceptron classifier, but with much fewer parameters and is more stable. Our results shed light on potential applications of two-dimensional tensor network models in machine learning. |
| 学科主题 | Materials Science ; Physics |
| 语种 | 英语 |
| 源URL | [http://ir.itp.ac.cn/handle/311006/27495]  |
| 专题 | 理论物理研究所_理论物理所1978-2010年知识产出 |
| 作者单位 | 1.Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101407, Peoples R China 2.Chinese Acad Sci, Inst Phys, Beijing 100190, Peoples R China 3.Songshan Lake Mat Lab, Dongguan 523808, Guangdong, Peoples R China 4.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China 5.UCAS, Hangzhou Inst Adv Study, Sch Fundamental Phys & Math Sci, Hangzhou 310024, Peoples R China 6.Int Ctr Theoret Phys Asia Pacific, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Cheng, Song,Wang, Lei,Zhang, Pan. Supervised learning with projected entangled pair states[J]. PHYSICAL REVIEW B,2021,103(12):125117. |
| APA | Cheng, Song,Wang, Lei,&Zhang, Pan.(2021).Supervised learning with projected entangled pair states.PHYSICAL REVIEW B,103(12),125117. |
| MLA | Cheng, Song,et al."Supervised learning with projected entangled pair states".PHYSICAL REVIEW B 103.12(2021):125117. |
入库方式： OAI收割
来源：理论物理研究所
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。