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

Transient Chaotic Dimensionality Expansion by Recurrent Networks 递归网络的瞬态混沌维数展开

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-02-25 DOI: 10.1103/PhysRevX.11.021064

Christian Keup, Tobias Kühn, David Dahmen, M. Helias

{"title":"Transient Chaotic Dimensionality Expansion by Recurrent Networks","authors":"Christian Keup, Tobias Kühn, David Dahmen, M. Helias","doi":"10.1103/PhysRevX.11.021064","DOIUrl":"https://doi.org/10.1103/PhysRevX.11.021064","url":null,"abstract":"Cortical neurons communicate with spikes, which are discrete events in time. Even if the timings of the individual events are strongly chaotic (microscopic chaos), the rate of events might still be non-chaotic or at the edge of what is known as rate chaos. Such edge-of-chaos dynamics are beneficial to the computational power of neuronal networks. We analyze both types of chaotic dynamics in densely connected networks of asynchronous binary neurons, by developing and applying a model-independent field theory for neuronal networks. We find a strongly size-dependent transition to microscopic chaos. We then expose the conceptual difficulty at the heart of the definition of rate chaos, identify two reasonable definitions, and show that for neither of them the binary network dynamics crosses a transition to rate chaos. \u0000The analysis of diverging trajectories in chaotic networks also allows us to study classification of linearly non-separable classes of stimuli in a reservoir computing approach. We show that microscopic chaos rapidly expands the dimensionality of the representation while, crucially, the number of dimensions corrupted by noise lags behind. This translates to a transient peak in the networks' classification performance even deeply in the chaotic regime, challenging the view that computational performance is always optimal near the edge of chaos. This is a general effect in high dimensional chaotic systems, and not specific to binary networks: We also demonstrate it in a continuous 'rate' network, a spiking LIF network, and an LSTM network. For binary and LIF networks, classification performance peaks rapidly within one activation per participating neuron, demonstrating fast event-based computation that may be exploited by biological neural systems, for which we propose testable predictions.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80924372","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: 14

Anomalous low-energy properties in amorphous solids and the interplay of electric and elastic interactions of tunneling two-level systems 非晶固体的反常低能性质及隧穿两能级系统的电弹性相互作用

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-02-07 DOI: 10.1103/PHYSREVB.103.054202

A. Churkin, S. Matityahu, A. Maksymov, A. Burin, M. Schechter

引用次数: 3

Ground State Stability in Two Spin Glass Models 两种自旋玻璃模型的基态稳定性

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-01-17 DOI: 10.1007/978-3-030-60754-8_2

L. Arguin, C. Newman, D. Stein

引用次数: 1

Athermal Photoelectronic Effects in Non-Crystalline Chalcogenides: Current Status and Beyond 非晶硫属化合物的非热光电子效应:现状及展望

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-01-14 DOI: 10.1142/9789811215575_0009

S. Yannopoulos

引用次数: 3

Local integrals of motion for topologically ordered many-body localized systems 拓扑有序多体定域系统运动的局部积分

arXiv: Disordered Systems and Neural Networks Pub Date : 2020-01-09 DOI: 10.1103/PHYSREVRESEARCH.2.033099

T. Wahl, B. B'eri

引用次数: 4

Floquet dynamics of disordered bands with isolated critical energies 具有孤立临界能的无序带的Floquet动力学

arXiv: Disordered Systems and Neural Networks Pub Date : 2019-12-28 DOI: 10.1103/physrevb.102.134212

S. Ganeshan, Kartiek Agarwal, Kartiek Agarwal, R. Bhatt, R. Bhatt

{"title":"Floquet dynamics of disordered bands with isolated critical energies","authors":"S. Ganeshan, Kartiek Agarwal, Kartiek Agarwal, R. Bhatt, R. Bhatt","doi":"10.1103/physrevb.102.134212","DOIUrl":"https://doi.org/10.1103/physrevb.102.134212","url":null,"abstract":"We investigate the localization properties of driven models that exhibit a sub-extensive number of extended states in the static setting. We consider instances where the extended modes are or are not protected by topological considerations. To this end, we contrast the strongly driven disordered lowest Landau level, which we refer to as the random Landau model (RLM), with the random dimer model (RDM); the latter also has a sub-extensive set of delocalized modes in the middle of the spectrum whose origin is not topological. We map the driven models on to a higher dimensional effective model and numerically compute the localization length as a function of disorder strength, drive amplitude and frequency using the recursive Green's function method. Our numerical results indicate that in the presence of a strong drive (low frequency and/or large drive amplitude), the topologically protected RLM continues to exhibit a spectrum with both localized and delocalized (or critical) modes, but the spectral range of delocalized modes is enhanced by the driving. This occurs due to an admixture of the localized modes with extended modes arising due to the topologically protected critical energy in the middle of the spectrum. On the other hand, in the RDM, a weak drive immediately localizes the entire spectrum. This occurs in contrast to the naive expectation from perturbation theory that mixing between localized and delocalized modes generically enhances the delocalization of all modes. Our work highlights the importance of the origin of the delocalized modes in the localization properties of the corresponding Floquet model.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74433377","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

Interpreting machine learning of topological quantum phase transitions 解释拓扑量子相变的机器学习

arXiv: Disordered Systems and Neural Networks Pub Date : 2019-12-20 DOI: 10.1103/PHYSREVRESEARCH.2.023283

Yi Zhang, P. Ginsparg, Eun-Ah Kim

{"title":"Interpreting machine learning of topological quantum phase transitions","authors":"Yi Zhang, P. Ginsparg, Eun-Ah Kim","doi":"10.1103/PHYSREVRESEARCH.2.023283","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.2.023283","url":null,"abstract":"There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. \"Interpretability\" remains a concern: can we understand the basis for the ANN's decision-making criteria in order to inform our theoretical understanding? \"Interpretable\" machine learning in quantum matter has to date been restricted to linear models, such as support vector machines, due to the greater difficulty of interpreting non-linear ANNs. Here we consider topological quantum phase transitions in models of Chern insulator, $mathbb{Z}_2$ topological insulator, and $mathbb{Z}_2$ quantum spin liquid, each using a shallow fully connected feed-forward ANN. The use of quantum loop topography, a \"domain knowledge\"-guided approach to feature selection, facilitates the construction of faithful phase diagrams. Due to the relative simplicity of the ANN, its learning can be interpreted in each of the three cases. To identify the topological phases, the ANNs learn physically meaningful features, such as topological invariants and deconfinement of loops. The interpretability in these cases suggests hope for theoretical progress based on future uses of ANN-based machine learning on quantum many-body problems.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84135188","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: 26

Two-Dimensional Systems of Elongated Particles: From Diluted to Dense 二维细长粒子系统:从稀释到致密

arXiv: Disordered Systems and Neural Networks Pub Date : 2019-12-20 DOI: 10.1142/9789811216220_0004

N. Lebovka, Y. Tarasevich

引用次数: 7

Drive-induced many-body localization and coherent destruction of Stark many-body localization 驱动诱导多体定位与斯塔克多体定位的相干破坏

arXiv: Disordered Systems and Neural Networks Pub Date : 2019-12-19 DOI: 10.1103/PHYSREVB.102.024201

D. S. Bhakuni, Ritu Nehra, Auditya Sharma

{"title":"Drive-induced many-body localization and coherent destruction of Stark many-body localization","authors":"D. S. Bhakuni, Ritu Nehra, Auditya Sharma","doi":"10.1103/PHYSREVB.102.024201","DOIUrl":"https://doi.org/10.1103/PHYSREVB.102.024201","url":null,"abstract":"We study the phenomenon of many-body localization (MBL) in an interacting system subjected to a combined DC as well as a square wave AC electric field. First, the condition for the dynamical localization, coherent destruction of Wannier-Stark localization and super Bloch oscillations in the non-interacting limit, are obtained semi-classically. In the presence of interactions (and a confining/disordered potential), a static field alone leads to ``Stark many-body localization\", for sufficiently large field strengths. We find that in the presence of an additional high-frequency AC field, there are two ways of maintaining the MBL intact: either by resonant drive where the ratio of amplitude to the frequency of the drive ($A/omega$) is tuned at the dynamical localization point of the non-interacting limit or by off-resonant drive. Remarkably, resonant drive with $A/omega$ tuned away from the dynamical localization point leads to a emph{coherent destruction of Stark-MBL}. Moreover, a pure (high-frequency) AC field can also give rise to the MBL phase if $A/omega$ is tuned at the dynamical localization point of the zero dc field problem.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84072977","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: 11

EUCLIDEAN CORRELATIONS IN COMBINATORIAL OPTIMIZATION PROBLEMS: A STATISTICAL PHYSICS APPROACH 组合优化问题中的欧几里得相关性:统计物理方法

arXiv: Disordered Systems and Neural Networks Pub Date : 2019-12-17 DOI: 10.13130/DI-GIOACCHINO-ANDREA_PHD2019-12-17

Andrea Di Gioacchino

引用次数: 0