arXiv - PHYS - Disordered Systems and Neural Networks最新文献_第5页

Random Features Hopfield Networks generalize retrieval to previously unseen examples 随机特征霍普菲尔德网络将检索泛化到以前未见过的示例中

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-08 DOI: arxiv-2407.05658

Silvio Kalaj, Clarissa Lauditi, Gabriele Perugini, Carlo Lucibello, Enrico M. Malatesta, Matteo Negri

引用次数: 0

Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals 一维非互惠准晶体中 Lyapunov 指数的非对称传递矩阵分析

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-07-01 DOI: arxiv-2407.01372

Shan-Zhong Li, Enhong Cheng, Shi-Liang Zhu, Zhi Li

引用次数: 0

Anomalous random networks 反常随机网络

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-06-27 DOI: arxiv-2406.18882

Hong Zhang, Guohua Li

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Anomalous Random Neural Networks: a Special Renewal Process 反常随机神经网络：一种特殊的更新过程

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-06-27 DOI: arxiv-2406.18877

Hong Zhang, Guohua Li

引用次数: 0

Revisiting nonequilibrium characterization of glass: History dependence in solids 重新审视玻璃的非平衡特性：固体的历史依赖性

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-06-22 DOI: arxiv-2406.15726

Koun Shirai

{"title":"Revisiting nonequilibrium characterization of glass: History dependence in solids","authors":"Koun Shirai","doi":"arxiv-2406.15726","DOIUrl":"https://doi.org/arxiv-2406.15726","url":null,"abstract":"Glass has long been considered a nonequilibrium material. The primary reason\u0000is its history-dependent properties: the obtained properties are not uniquely\u0000determined by two state variables alone, namely, temperature and volume, but\u0000are affected by the process parameters, such as cooling rates. However, closer\u0000observations show that this history dependence is common in solid; in crystal\u0000growth, the properties of an obtained crystal are affected by the preparation\u0000conditions through defect structures and metallurgical structures. The problem\u0000with the previous reasoning of history dependence lies in the lack of\u0000appropriate specification of state variables. Without knowledge of the latter,\u0000describing thermodynamic states is impossible. The guiding principle to find\u0000state variables is provided by the first law of thermodynamics. The state\u0000variables of solids have been searched by requiring that the internal energy\u0000$U$ is a state function. Detailed information about the abovementioned\u0000microstructures is needed to describe the state function $U$. This can be\u0000accomplished by specifying the time-averaged positions R_{j} of all atoms\u0000comprising the solids. Therefore, R_{j} is a state variable for solids. Defect\u0000states, being metastable states, represent equilibrium states within a finite\u0000time (relaxation time). However, eternal equilibrium is nonexistent: the\u0000perfect crystal is thermodynamically unstable. Equilibrium states can only be\u0000considered at the local level. Glass is thus in equilibrium as long as its\u0000structure does not change. The relaxation time is controlled by the energy\u0000barriers by which a structure is sustained, and this time restriction is\u0000intimately related to the definition of state variables. The most important\u0000property of state variables is their invariance to time averaging. The\u0000time-averaged quantity R_{j} meets this invariance property.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505069","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

Reentrant localisation transitions and anomalous spectral properties in off-diagonal quasiperiodic systems 非对角准周期系统中的重入定位转换和反常谱特性

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-06-20 DOI: arxiv-2406.14193

Hugo Tabanelli, Claudio Castelnovo, Antonio Štrkalj

{"title":"Reentrant localisation transitions and anomalous spectral properties in off-diagonal quasiperiodic systems","authors":"Hugo Tabanelli, Claudio Castelnovo, Antonio Štrkalj","doi":"arxiv-2406.14193","DOIUrl":"https://doi.org/arxiv-2406.14193","url":null,"abstract":"We investigate the localisation properties of quasiperiodic tight-binding\u0000chains with hopping terms modulated by the interpolating\u0000Aubry-Andr'e-Fibonacci (IAAF) function. This off-diagonal IAAF model allows\u0000for a smooth and controllable interpolation between two paradigmatic\u0000quasiperiodic models: the Aubry-Andr'e and the Fibonacci model. Our analysis\u0000shows that the spectrum of this model can be divided into three principal\u0000bands, namely, two molecular bands at the edge of the spectrum and one atomic\u0000band in the middle, for all values of the interpolating parameter. We reveal\u0000that the states in the molecular bands undergo multiple re-entrant localisation\u0000transitions, a behaviour previously reported in the diagonal IAAF model. We\u0000link the emergence of these reentrant phenomena to symmetry points of the\u0000quasiperiodic modulation and, with that, explain the main ground state\u0000properties of the system. The atomic states in the middle band show no traces\u0000of localised phases and remain either extended or critical for any value of the\u0000interpolating parameter. Using a renormalisation group approach, adapted from\u0000the Fibonacci model, we explain the extended nature of the middle band. These\u0000findings expand our knowledge of phase transitions within quasiperiodic systems\u0000and highlight the interplay between extended, critical, and localised states.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505073","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

The effect of hyperuniform disorder on band gaps 超均匀无序对带隙的影响

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-06-17 DOI: arxiv-2406.11710

Jonas F. Karcher, Sarang Gopalakrishnan, Mikael C. Rechtsman

引用次数: 0

Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings 具有指数跳跃的非赫米提准晶体的精确复迁移率边缘和鞭毛虫光谱

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-06-16 DOI: arxiv-2406.10769

Li Wang, Jiaqi Liu, Zhenbo Wang, Shu Chen

引用次数: 0

Spectral and Entanglement Properties of the Random Exchange Heisenberg Chain 随机交换海森堡链的谱和纠缠特性

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-06-14 DOI: arxiv-2406.09985

Yilun Gao, Rudolf A. Römer

引用次数: 0

Dynamical Mean-Field Theory of Self-Attention Neural Networks 自注意神经网络的动态平均场理论

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-06-11 DOI: arxiv-2406.07247

Ángel Poc-López, Miguel Aguilera

{"title":"Dynamical Mean-Field Theory of Self-Attention Neural Networks","authors":"Ángel Poc-López, Miguel Aguilera","doi":"arxiv-2406.07247","DOIUrl":"https://doi.org/arxiv-2406.07247","url":null,"abstract":"Transformer-based models have demonstrated exceptional performance across\u0000diverse domains, becoming the state-of-the-art solution for addressing\u0000sequential machine learning problems. Even though we have a general\u0000understanding of the fundamental components in the transformer architecture,\u0000little is known about how they operate or what are their expected dynamics.\u0000Recently, there has been an increasing interest in exploring the relationship\u0000between attention mechanisms and Hopfield networks, promising to shed light on\u0000the statistical physics of transformer networks. However, to date, the\u0000dynamical regimes of transformer-like models have not been studied in depth. In\u0000this paper, we address this gap by using methods for the study of asymmetric\u0000Hopfield networks in nonequilibrium regimes --namely path integral methods over\u0000generating functionals, yielding dynamics governed by concurrent mean-field\u0000variables. Assuming 1-bit tokens and weights, we derive analytical\u0000approximations for the behavior of large self-attention neural networks coupled\u0000to a softmax output, which become exact in the large limit size. Our findings\u0000reveal nontrivial dynamical phenomena, including nonequilibrium phase\u0000transitions associated with chaotic bifurcations, even for very simple\u0000configurations with a few encoded features and a very short context window.\u0000Finally, we discuss the potential of our analytic approach to improve our\u0000understanding of the inner workings of transformer models, potentially reducing\u0000computational training costs and enhancing model interpretability.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505074","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