arXiv - PHYS - Disordered Systems and Neural Networks最新文献_第4页

Scaling of Static and Dynamical Properties of Random Anisotropy Magnets 随机各向异性磁体的静态和动态特性缩放

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-31 DOI: arxiv-2407.21520

Dmitry A. Garanin, Eugene M. Chudnovsky

引用次数: 0

Hyperoptimized approximate contraction of tensor networks for rugged-energy-landscape spin glasses on periodic square and cubic lattices 周期性方形和立方晶格上崎岖能谱自旋玻璃张量网络的超优化近似收缩

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-31 DOI: arxiv-2407.21287

Adil A. Gangat, Johnnie Gray

{"title":"Hyperoptimized approximate contraction of tensor networks for rugged-energy-landscape spin glasses on periodic square and cubic lattices","authors":"Adil A. Gangat, Johnnie Gray","doi":"arxiv-2407.21287","DOIUrl":"https://doi.org/arxiv-2407.21287","url":null,"abstract":"Obtaining the low-energy configurations of spin glasses that have rugged\u0000energy landscapes is of direct relevance to combinatorial optimization and\u0000fundamental science. Search-based heuristics have difficulty with this task due\u0000to the existence of many local minima that are far from optimal. The work of\u0000[M. M. Rams et al., Phys. Rev. E 104, 025308 (2021)] demonstrates an\u0000alternative that can bypass this issue for spin glasses with planar or\u0000quasi-planar geometry: sampling the Boltzmann distribution via approximate\u0000contractions of tensor networks. The computational complexity of this approach\u0000is due only to the complexity of contracting the network, and is therefore\u0000independent of landscape ruggedness. Here we initiate an investigation of how\u0000to take this approach beyond (quasi-)planar geometry by utilizing\u0000hyperoptimized approximate contraction of tensor networks [J. Gray and G. K.-L.\u0000Chan, Phys. Rev. X 14, 011009 (2024)]. We perform tests on the periodic square-\u0000and cubic-lattice, planted-solution Ising spin glasses generated with tile\u0000planting [F. Hamze et al., Phys. Rev. E 97, 043303 (2018)] for up to 2304\u0000(square lattice) and 216 (cubic lattice) spins. For a fixed bond dimension, the\u0000time complexity is quadratic. With a bond dimension of only four, over the\u0000tested system sizes the average solution quality in the most rugged instance\u0000class remains at ~1% (square lattice) or ~10% (cubic lattice) of optimal. These\u0000results encourage further investigation of tensor network contraction for\u0000rugged-energy-landscape spin-glass problems, especially given that this\u0000approach is not limited to the Ising (i.e., binary) or two-body (i.e.,\u0000quadratic) settings.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exploring Loss Landscapes through the Lens of Spin Glass Theory 通过旋转玻璃理论探索损失景观

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-30 DOI: arxiv-2407.20724

Hao Liao, Wei Zhang, Zhanyi Huang, Zexiao Long, Mingyang Zhou, Xiaoqun Wu, Rui Mao, Chi Ho Yeung

{"title":"Exploring Loss Landscapes through the Lens of Spin Glass Theory","authors":"Hao Liao, Wei Zhang, Zhanyi Huang, Zexiao Long, Mingyang Zhou, Xiaoqun Wu, Rui Mao, Chi Ho Yeung","doi":"arxiv-2407.20724","DOIUrl":"https://doi.org/arxiv-2407.20724","url":null,"abstract":"In the past decade, significant strides in deep learning have led to numerous\u0000groundbreaking applications. Despite these advancements, the understanding of\u0000the high generalizability of deep learning, especially in such an\u0000over-parametrized space, remains limited. Successful applications are often\u0000considered as empirical rather than scientific achievements. For instance, deep\u0000neural networks' (DNNs) internal representations, decision-making mechanism,\u0000absence of overfitting in an over-parametrized space, high generalizability,\u0000etc., remain less understood. This paper delves into the loss landscape of DNNs\u0000through the lens of spin glass in statistical physics, i.e. a system\u0000characterized by a complex energy landscape with numerous metastable states, to\u0000better understand how DNNs work. We investigated a single hidden layer\u0000Rectified Linear Unit (ReLU) neural network model, and introduced several\u0000protocols to examine the analogy between DNNs (trained with datasets including\u0000MNIST and CIFAR10) and spin glass. Specifically, we used (1) random walk in the\u0000parameter space of DNNs to unravel the structures in their loss landscape; (2)\u0000a permutation-interpolation protocol to study the connection between copies of\u0000identical regions in the loss landscape due to the permutation symmetry in the\u0000hidden layers; (3) hierarchical clustering to reveal the hierarchy among\u0000trained solutions of DNNs, reminiscent of the so-called Replica Symmetry\u0000Breaking (RSB) phenomenon (i.e. the Parisi solution) in analogy to spin glass;\u0000(4) finally, we examine the relationship between the degree of the ruggedness\u0000of the loss landscape of the DNN and its generalizability, showing an\u0000improvement of flattened minima.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Coarse geometric approach to topological phases: Invariants from real-space representations 拓扑相位的粗几何方法：来自实空间表示的不变式

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-23 DOI: arxiv-2407.16494

Christoph S. Setescak, Caio Lewenkopf, Matthias Ludewig

引用次数: 0

Some new results for the GHWS model GHWS 模型的一些新成果

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-19 DOI: arxiv-2407.14318

Leonardo Reyes

引用次数: 0

Phase induced localization transition 相位诱导定位转换

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-14 DOI: arxiv-2407.10043

Tong Liu, Xingbo Wei, Youguo Wang

引用次数: 0

Statistical Localization of Electromagnetic Signals in Disordered Time-Varying Cavity 无序时变腔体内电磁信号的统计定位

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-12 DOI: arxiv-2407.21023

Bo Zhou, Xingsong Feng, Xianmin Guo, Fei Gao, Hongsheng Chen, Zuojia Wang

{"title":"Statistical Localization of Electromagnetic Signals in Disordered Time-Varying Cavity","authors":"Bo Zhou, Xingsong Feng, Xianmin Guo, Fei Gao, Hongsheng Chen, Zuojia Wang","doi":"arxiv-2407.21023","DOIUrl":"https://doi.org/arxiv-2407.21023","url":null,"abstract":"In this letter, we investigate the statistical properties of electromagnetic\u0000signals after different times of duration within one-dimensional\u0000local-disordered time-varying cavities, where both spatial and temporal\u0000disorders are added. Our findings reveal that, in the vast majority of cases,\u0000adequate temporal disorder in local space can make the electromagnetic field\u0000statistically localized, obeying a normal distribution at a specific point in\u0000time of arbitrary location within the cavity. We employ the concept of\u0000disordered space-time crystals and leverage Lindeberg's and Lyapunov's theorems\u0000to theoretically prove the normal distribution of the field values.\u0000Furthermore, we find that with the increase of energy provided by time\u0000variation, the probability of extreme fields will significantly increase and\u0000the field intensity eventually is de-normalized, that is, deviating from the\u0000normal distribution. This study not only sheds light on the statistical\u0000properties of transient signals in local-disordered time-varying systems but\u0000also paves the way for further exploration in wave dynamics of analogous\u0000systems.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Encoding arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines 在空间光子伊辛机上编码任意伊辛哈密顿子

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-12 DOI: arxiv-2407.09161

Jason Sakellariou, Alexis Askitopoulos, Georgios Pastras, Symeon I. Tsintzos

{"title":"Encoding arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines","authors":"Jason Sakellariou, Alexis Askitopoulos, Georgios Pastras, Symeon I. Tsintzos","doi":"arxiv-2407.09161","DOIUrl":"https://doi.org/arxiv-2407.09161","url":null,"abstract":"Photonic Ising Machines constitute an emergent new paradigm of computation,\u0000geared towards tackling combinatorial optimization problems that can be reduced\u0000to the problem of finding the ground state of an Ising model. Spatial Photonic\u0000Ising Machines have proven to be advantageous for simulating fully connected\u0000large-scale spin systems. However, fine control of a general interaction matrix\u0000$J$ has so far only been accomplished through eigenvalue decomposition methods\u0000that either limit the scalability or increase the execution time of the\u0000optimization process. We introduce and experimentally validate a SPIM instance\u0000that enables direct control over the full interaction matrix, enabling the\u0000encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We\u0000demonstrate the conformity of the experimentally measured Ising energy with the\u0000theoretically expected values and then proceed to solve both the unweighted and\u0000weighted graph partitioning problems, showcasing a systematic convergence to an\u0000optimal solution via simulated annealing. Our approach greatly expands the\u0000applicability of SPIMs for real-world applications without sacrificing any of\u0000the inherent advantages of the system, and paves the way to encoding the full\u0000range of NP problems that are known to be equivalent to Ising models, on SPIM\u0000devices.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141720400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Very Effective and Simple Diffusion Reconstruction for the Diluted Ising Model 针对稀释伊辛模型的非常有效而简单的扩散重构

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-09 DOI: arxiv-2407.07266

Stefano Bae, Enzo Marinari, Federico Ricci-Tersenghi

引用次数: 0

About the AT line in Replica Symmetry Breaking assumption for spin glasses 关于自旋玻璃的复制对称性破缺假设中的 AT 线

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-09 DOI: arxiv-2407.06701

Linda Albanese

引用次数: 0