Anyonic statistics and large horizon diffeomorphisms for Loop Quantum Gravity Black Holes

We investigate the role played by large diffeomorphisms of quantum Isolated Horizons for the statistics of LQG Black Holes by means of their relation to the braid group. To this aim the symmetries of Chern-Simons theory are recapitulated with particular regard to the aforementioned type of diffeomorphisms. For the punctured spherical horizon, these are elements of the mapping class group of $S^2$, which is almost isomorphic to a corresponding braid group on this particular manifold. The mutual exchange of quantum entities in two dimensions is achieved by the braid group, rendering the statistics anyonic. With this we argue that the quantum Isolated Horizon model of LQG based on $SU(2)_k$-Chern-Simons theory explicitly exhibits non-abelian anyonic statistics. In this way a connection to the theory behind the fractional quantum Hall effect and that of topological quantum computation is established, where non-abelian anyons play a significant role.Comment: 20 pages, 8 figures, closest to published versio

Dopant Network Processing Units: Towards Efficient Neural-network Emulators with High-capacity Nanoelectronic Nodes

The rapidly growing computational demands of deep neural networks require novel hardware designs. Recently, tunable nanoelectronic devices were developed based on hopping electrons through a network of dopant atoms in silicon. These "Dopant Network Processing Units" (DNPUs) are highly energy-efficient and have potentially very high throughput. By adapting the control voltages applied to its terminals, a single DNPU can solve a variety of linearly non-separable classification problems. However, using a single device has limitations due to the implicit single-node architecture. This paper presents a promising novel approach to neural information processing by introducing DNPUs as high-capacity neurons and moving from a single to a multi-neuron framework. By implementing and testing a small multi-DNPU classifier in hardware, we show that feed-forward DNPU networks improve the performance of a single DNPU from 77% to 94% test accuracy on a binary classification task with concentric classes on a plane. Furthermore, motivated by the integration of DNPUs with memristor arrays, we study the potential of using DNPUs in combination with linear layers. We show by simulation that a single-layer MNIST classifier with only 10 DNPUs achieves over 96% test accuracy. Our results pave the road towards hardware neural-network emulators that offer atomic-scale information processing with low latency and energy consumption

Gradient Descent in Materio

Deep learning, a multi-layered neural network approach inspired by the brain, has revolutionized machine learning. One of its key enablers has been backpropagation, an algorithm that computes the gradient of a loss function with respect to the weights in the neural network model, in combination with its use in gradient descent. However, the implementation of deep learning in digital computers is intrinsically wasteful, with energy consumption becoming prohibitively high for many applications. This has stimulated the development of specialized hardware, ranging from neuromorphic CMOS integrated circuits and integrated photonic tensor cores to unconventional, material-based computing systems. The learning process in these material systems, taking place, e.g., by artificial evolution or surrogate neural network modelling, is still a complicated and time-consuming process. Here, we demonstrate an efficient and accurate homodyne gradient extraction method for performing gradient descent on the loss function directly in the material system. We demonstrate the method in our recently developed dopant network processing units, where we readily realize all Boolean gates. This shows that gradient descent can in principle be fully implemented in materio using simple electronics, opening up the way to autonomously learning material systems

brains-py, A framework to support research on energy-efficient unconventional hardware for machine learning

Projections about the limitations of digital computers for deep learning models are leading to a shift towards domain-specific hardware, where novel analogue components are sought after, due to their potential advantages in power consumption. This paper introduces brains-py, a generic framework to facilitate research on different sorts of disordered nano-material networks for natural and energy-efficient analogue computing. Mainly, it has been applied to the concept of dopant network processing units (DNPUs), a novel and promising CMOS-compatible nano-scale tunable system based on doped silicon with potentially very low-power consumption at the inference stage. The framework focuses on two material-learning-based approaches, for training DNPUs to compute supervised learning tasks: evolution-in-matter and surrogate models.While evolution-in-matter focuses on providing a quick exploration of newly manufactured single DNPUs, the surrogate model approach is used for the design and simulation of the interconnection between multiple DNPUs, enabling the exploration of their scalability. All simulation results can be seamlessly validated on hardware, saving time and costs associated with their reproduction. The framework is generic and can be reused for research on various materials with different design aspects, providing support for the most common tasks requiredfor doing experiments with these novel materials.<br/

Omecamtiv mecarbil in chronic heart failure with reduced ejection fraction, GALACTIC‐HF: baseline characteristics and comparison with contemporary clinical trials

Aims: The safety and efficacy of the novel selective cardiac myosin activator, omecamtiv mecarbil, in patients with heart failure with reduced ejection fraction (HFrEF) is tested in the Global Approach to Lowering Adverse Cardiac outcomes Through Improving Contractility in Heart Failure (GALACTIC‐HF) trial. Here we describe the baseline characteristics of participants in GALACTIC‐HF and how these compare with other contemporary trials. Methods and Results: Adults with established HFrEF, New York Heart Association functional class (NYHA) ≥ II, EF ≤35%, elevated natriuretic peptides and either current hospitalization for HF or history of hospitalization/ emergency department visit for HF within a year were randomized to either placebo or omecamtiv mecarbil (pharmacokinetic‐guided dosing: 25, 37.5 or 50 mg bid). 8256 patients [male (79%), non‐white (22%), mean age 65 years] were enrolled with a mean EF 27%, ischemic etiology in 54%, NYHA II 53% and III/IV 47%, and median NT‐proBNP 1971 pg/mL. HF therapies at baseline were among the most effectively employed in contemporary HF trials. GALACTIC‐HF randomized patients representative of recent HF registries and trials with substantial numbers of patients also having characteristics understudied in previous trials including more from North America (n = 1386), enrolled as inpatients (n = 2084), systolic blood pressure &lt; 100 mmHg (n = 1127), estimated glomerular filtration rate &lt; 30 mL/min/1.73 m2 (n = 528), and treated with sacubitril‐valsartan at baseline (n = 1594). Conclusions: GALACTIC‐HF enrolled a well‐treated, high‐risk population from both inpatient and outpatient settings, which will provide a definitive evaluation of the efficacy and safety of this novel therapy, as well as informing its potential future implementation

Loop Quantum Gravity meets Topological Phases of Matter at the Black Hole horizon

In this work we investigate the role played by large diffeomorphisms of quantum isolated horizons for the statistics of Loop Quantum Gravity black holes by means of their relation to the braid group. The mutual exchange of quantum entities in two dimensions is achieved by the braid group, rendering the statistics anyonic. With this we argue that the quantum isolated horizon model of LQG based on SU(2)_k-Chern-Simons theory explicitly exhibits non-abelian anyonic statistics, since the quantum gravitational degrees of freedom of the horizon can be seen as flux-charge composites. In this way a connection to the theory behind the fractional quantum Hall effect and that of topological quantum computation is established, where non-abelian anyons play a significant role.</jats:p

A deep-learning approach to realizing functionality in nanoelectronic devices

Many nanoscale devices require precise optimization to function. Tuning them to the desired operation regime becomes increasingly difficult and time-consuming when the number of terminals and couplings grows. Imperfections and device-to-device variations hinder optimization that uses physics-based models. Deep neural networks (DNNs) can model various complex physical phenomena but, so far, are mainly used as predictive tools. Here, we propose a generic deep-learning approach to efficiently optimize complex, multi-terminal nanoelectronic devices for desired functionality. We demonstrate our approach for realizing functionality in a disordered network of dopant atoms in silicon. We model the input–output characteristics of the device with a DNN, and subsequently optimize control parameters in the DNN model through gradient descent to realize various classification tasks. When the corresponding control settings are applied to the physical device, the resulting functionality is as predicted by the DNN model. We expect our approach to contribute to fast, in situ optimization of complex (quantum) nanoelectronic devices

Classification with a disordered dopant-atom network in silicon

Classification is an important task at which both biological and artificial neural networks excel1,2. In machine learning, nonlinear projection into a high-dimensional feature space can make data linearly separable3,4, simplifying the classification of complex features. Such nonlinear projections are computationally expensive in conventional computers. A promising approach is to exploit physical materials systems that perform this nonlinear projection intrinsically, because of their high computational density5, inherent parallelism and energy efficiency6,7. However, existing approaches either rely on the systems’ time dynamics, which requires sequential data processing and therefore hinders parallel computation5,6,8, or employ large materials systems that are difficult to scale up7. Here we use a parallel, nanoscale approach inspired by filters in the brain1 and artificial neural networks2 to perform nonlinear classification and feature extraction. We exploit the nonlinearity of hopping conduction9,10,11 through an electrically tunable network of boron dopant atoms in silicon, reconfiguring the network through artificial evolution to realize different computational functions. We first solve the canonical two-input binary classification problem, realizing all Boolean logic gates12 up to room temperature, demonstrating nonlinear classification with the nanomaterial system. We then evolve our dopant network to realize feature filters2 that can perform four-input binary classification on the Modified National Institute of Standards and Technology handwritten digit database. Implementation of our material-based filters substantially improves the classification accuracy over that of a linear classifier directly applied to the original data13. Our results establish a paradigm of silicon-based electronics for small-footprint and energy-efficient computation14

Classification with a disordered dopant-atom network in silicon

\u3cp\u3eClassification is an important task at which both biological and artificial neural networks excel\u3csup\u3e1,2\u3c/sup\u3e. In machine learning, nonlinear projection into a high-dimensional feature space can make data linearly separable\u3csup\u3e3,4\u3c/sup\u3e, simplifying the classification of complex features. Such nonlinear projections are computationally expensive in conventional computers. A promising approach is to exploit physical materials systems that perform this nonlinear projection intrinsically, because of their high computational density\u3csup\u3e5\u3c/sup\u3e, inherent parallelism and energy efficiency\u3csup\u3e6,7\u3c/sup\u3e. However, existing approaches either rely on the systems’ time dynamics, which requires sequential data processing and therefore hinders parallel computation\u3csup\u3e5,6,8\u3c/sup\u3e, or employ large materials systems that are difficult to scale up\u3csup\u3e7\u3c/sup\u3e. Here we use a parallel, nanoscale approach inspired by filters in the brain\u3csup\u3e1\u3c/sup\u3e and artificial neural networks\u3csup\u3e2\u3c/sup\u3e to perform nonlinear classification and feature extraction. We exploit the nonlinearity of hopping conduction\u3csup\u3e9–11\u3c/sup\u3e through an electrically tunable network of boron dopant atoms in silicon, reconfiguring the network through artificial evolution to realize different computational functions. We first solve the canonical two-input binary classification problem, realizing all Boolean logic gates\u3csup\u3e12\u3c/sup\u3e up to room temperature, demonstrating nonlinear classification with the nanomaterial system. We then evolve our dopant network to realize feature filters\u3csup\u3e2\u3c/sup\u3e that can perform four-input binary classification on the Modified National Institute of Standards and Technology handwritten digit database. Implementation of our material-based filters substantially improves the classification accuracy over that of a linear classifier directly applied to the original data\u3csup\u3e13\u3c/sup\u3e. Our results establish a paradigm of silicon-based electronics for small-footprint and energy-efficient computation\u3csup\u3e14\u3c/sup\u3e.\u3c/p\u3