Detecting ergodic bubbles at the crossover to many-body localization using neural networks

Szołdra, Tomasz; Sierant, Piotr; Kottmann, Korbinian; Lewenstein, Maciej; Zakrzewski, Jakub

doi:10.1103/physrevb.104.l140202

Cited by 11 publications

(5 citation statements)

References 83 publications

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“…In particular, we find that the optimal predictions of SL, LBC, and PBM, are not explicitly based on learning order parameters, i.e., recognizing prevalent patterns or orderings. We anticipate that similar analyses will be useful to gain an understanding of other methods for identifying phase transitions from data based on NNs [19,25,29,78] and related classification tasks in condensed matter physics [79][80][81][82][83][84]. For example, in Refs.…”

Section: Discussionmentioning

confidence: 99%

Replacing neural networks by optimal analytical predictors for the detection of phase transitions

Arnold¹,

Schäfer²

2022

Preprint

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Identifying phase transitions and classifying phases of matter is central to understanding the properties and behavior of a broad range of material systems. In recent years, machine-learning (ML) techniques have been successfully applied to perform such tasks in a data-driven manner. However, the success of this approach notwithstanding, we still lack a clear understanding of ML methods for detecting phase transitions, particularly of those that utilize neural networks (NNs). In this work, we derive analytical expressions for the optimal output of three widely used NNbased methods for detecting phase transitions. These optimal predictions correspond to the output obtained in the limit of perfectly trained and sufficiently large NNs. The inner workings of the considered methods are revealed through the explicit dependence of the optimal output on the input data. By evaluating the analytical expressions, we can identify phase transitions from data without training NNs. Our theoretical results are supported by extensive numerical simulations covering, e.g., topological, quantum, and many-body localization phase transitions. We expect similar analyses to provide a deeper understanding of other classification tasks in condensed matter physics.

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Section: Discussionmentioning

confidence: 99%

Replacing neural networks by optimal analytical predictors for the detection of phase transitions

Arnold¹,

Schäfer²

2022

Preprint

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“…Challenges to explanation by predictive models accrue from multiple sources. For instance, when locomotion begins, the neural events associated with footfalls are neither independent nor predictable [29], implying broken ergodicity [30][31][32][33][34][35][36]. Moreover, stride-to-stride variations are also not awGn but are more consistent with fractional Gaussian noise (fGn; awGn is a special case of fGn which lacks any temporal correlations) [37][38][39].…”

Section: Plos Onementioning

confidence: 99%

Temporal organization of stride-to-stride variations contradicts predictive models for sensorimotor control of footfalls during walking

Mangalam,

Kelty-Stephen,

Sommerfeld

et al. 2023

PLoS ONE

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Walking exhibits stride-to-stride variations. Given ongoing perturbations, these variations critically support continuous adaptations between the goal-directed organism and its surroundings. Here, we report that stride-to-stride variations during self-paced overground walking show cascade-like intermittency—stride intervals become uneven because stride intervals of different sizes interact and do not simply balance each other. Moreover, even when synchronizing footfalls with visual cues with variable timing of presentation, asynchrony in the timings of the cue and footfall shows cascade-like intermittency. This evidence conflicts with theories about the sensorimotor control of walking, according to which internal predictive models correct asynchrony in the timings of the cue and footfall from one stride to the next on crossing thresholds leading to the risk of falling. Hence, models of the sensorimotor control of walking must account for stride-to-stride variations beyond the constraints of threshold-dependent predictive internal models.

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“…Other applicationspecic integrated circuits (ASICs) like the tensor processing unit (TPU) are developed specically for deep learning by Google. 6 Chapter 1. Motivation various dierent systems and automatically points out new properties, eects or phases.…”

Section: Motivationmentioning

confidence: 99%

“…Furthermore, the algorithm proposed by McCulloch [56] has advantages in terms of convergence and stability in comparison to alternative formulations. For clarity and analogy to the original paper [56], we assume a two-site unit cell and note 6 The name transfer matrix is of historical origin and may be confusing since the object is clearly not a matrix (rank 2 tensor). that this can be extended to arbitrary unit cell sizes L ∞ ≥ 2 7 .…”

Section: Other Algorithms Innite Dmrg (Idmrg)mentioning

confidence: 99%

“…In this chapter, we are going to introduce the concept of deep anomaly detection, which will be the foundation of the works described in the following chapters. This method has been successfully employed in our works in [1,3,4,5,6] and was already adapted by others in [112,113,114]. Anomaly detection with and without deep neural networks is an active eld of research in computer science.…”

Section: Deep Anomaly Detection For Unsupervised Phase Discoverymentioning

confidence: 99%

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Investigating quantum many-body systems with tensor networks, machine learning and quantum computers

Kottmann

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(English) We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical simulations are done with state-of-the-art tensor network methods in one and two spatial dimensions. For one dimensional systems, we utilize matrix product states (MPS) that have many practical advantages and can be optimized using the efficient density matrix renormalization group (DMRG) algorithm. The data for two dimensional systems is obtained from entangled projected pair states (PEPS) optimized via imaginary time evolution. Data in form of observables, entanglement spectra, or parts of the state vectors from these simulations, is then fed into a deep learning (DL) pipeline where we perform anomaly detection to map out the phase diagram. We extend this notion to quantum computers and introduce quantum variational anomaly detection. Here, we first simulate the ground state and then process it in a quantum machine learning (QML) manner. Both simulation and QML routines are performed on the same device, which we demonstrate both in classical simulation and on a physical quantum computer hosted by IBM. (Español) En esta tesis, realizamos simulaciónes cuánticas en ordenadores clásicos y cuánticos y diseñamos un marco de aprendizaje automático en el que podemos construir diagramas de fase de sistemas cuánticos de muchas partículas de manera no supervisada. Las simulaciones clásicas se realizan con métodos de red de tensores de última generación en una y dos dimensiones espaciales. Para sistemas unidimensionales, utilizamos estados de productos de matrices (MPS) que tienen muchas ventajas prácticas y pueden optimizarse utilizando el eficiente algoritmo del grupo de renormalización de matrices de densidad (DMRG). Los datos para sistemas bidimensionales se obtienen mediante los denominados estados de pares entrelazados proyectados (PEPS) optimizados a través de la evolución en tiempo imaginario. Los datos, en forma de observables, espectros de entrelazamiento o partes de los vectores de estado de estas simulaciones, se introducen luego en un algoritmo de aprendizaje profundo (DL) donde realizamos la detección de anomalías para construir el diagrama de fase. Extendemos esta noción a los ordenadores cuánticos e introducimos la detección de anomalías cuánticas variacionales. Aquí, primero simulamos el estado fundamental y luego lo procesamos utilizando el aprendizaje automático cuántico (QML). Tanto las rutinas de simulación como el QML se realizan en el mismo dispositivo, lo que demostramos tanto en una simulación clásica como en un ordenador cuántico real de IBM.

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Detecting ergodic bubbles at the crossover to many-body localization using neural networks

Cited by 11 publications

References 83 publications

Replacing neural networks by optimal analytical predictors for the detection of phase transitions

Replacing neural networks by optimal analytical predictors for the detection of phase transitions

Temporal organization of stride-to-stride variations contradicts predictive models for sensorimotor control of footfalls during walking

Investigating quantum many-body systems with tensor networks, machine learning and quantum computers

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