Knowledge Management System of Institute of Theoretical Physics, CAS
Li, Sujie1; Pan, Feng1; Zhou, Pengfei1; Zhang, Pan2,3
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| Boltzmann machines as two-dimensional tensor networks | |
| Source Publication | PHYSICAL REVIEW B
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| Language | 英语 |
| Abstract | Restricted Boltzmann machines (RBMs) and deep Boltzmann machines (DBMs) are important models in machine learning, and recently found numerous applications in quantum many-body physics. We show that there are fundamental connections between them and tensor networks. In particular, we demonstrate that any RBM and DBM can be exactly represented as a two-dimensional tensor network. This representation gives characterizations of the expressive power of RBMs and DBMs using entanglement structures of the tensor networks, and also provides an efficient tensor network contraction algorithm for the computing partition function of RBMs and DBMs. Using numerical experiments, we show that the proposed algorithm is more accurate than the state-of-the-art machine learning methods in estimating the partition function of RBMs and DBMs, and have potential applications in training DBMs for general machine learning tasks. |
| 2021 | |
| ISSN | 2469-9950 |
| Volume | 104Issue:7Pages:75154 |
| Cooperation Status | 国内 |
| Subject Area | Materials Science ; Physics |
| MOST Discipline Catalogue | Materials Science, Multidisciplinary ; Physics, Applied ; Physics, Condensed Matter |
| DOI | 10.1103/PhysRevB.104.075154 |
| Indexed By | SCIE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.itp.ac.cn/handle/311006/27278 |
| Collection | SCI期刊论文 |
| Affiliation | 1.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Phys Sci, Beijing 100049, Peoples R China 3.UCAS, Hangzhou Inst Adv Study, Sch Fundamental Phys & Math Sci, Hangzhou 310024, Peoples R China 4.Int Ctr Theoret Phys Asia Pacific, Beijing, Peoples R China |
| Recommended Citation GB/T 7714 | Li, Sujie,Pan, Feng,Zhou, Pengfei,et al. Boltzmann machines as two-dimensional tensor networks[J]. PHYSICAL REVIEW B,2021,104(7):75154. |
| APA | Li, Sujie,Pan, Feng,Zhou, Pengfei,&Zhang, Pan.(2021).Boltzmann machines as two-dimensional tensor networks.PHYSICAL REVIEW B,104(7),75154. |
| MLA | Li, Sujie,et al."Boltzmann machines as two-dimensional tensor networks".PHYSICAL REVIEW B 104.7(2021):75154. |
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