A study on hardware design for high performance artificial neural network by using FPGA and NoC

制度:新 ; 報告番号:甲3421号 ; 学位の種類:博士(工学) ; 授与年月日:2011/9/15 ; 早大学位記番号:新574

Determination of the Semion Code Threshold using Neural Decoders

We compute the error threshold for the semion code, the companion of the Kitaev toric code with the same gauge symmetry group $\mathbb{Z}_2$. The application of statistical mechanical mapping methods is highly discouraged for the semion code, since the code is non-Pauli and non-CSS. Thus, we use machine learning methods, taking advantage of the near-optimal performance of some neural network decoders: multilayer perceptrons and convolutional neural networks (CNNs). We find the values $p_{\text {eff}}=9.5\%$ for uncorrelated bit-flip and phase-flip noise, and $p_{\text {eff}}=10.5\%$ for depolarizing noise. We contrast these values with a similar analysis of the Kitaev toric code on a hexagonal lattice with the same methods. For convolutional neural networks, we use the ResNet architecture, which allows us to implement very deep networks and results in better performance and scalability than the multilayer perceptron approach. We analyze and compare in detail both approaches and provide a clear argument favoring the CNN as the best suited numerical method for the semion code.Comment: Minor correction

Graphics processor unit hardware acceleration of Levenberg-Marquardt artificial neural network training

This paper makes two principal contributions. The first is that there appears to be no previous a description in the research literature of an artificial neural network implementation on a graphics processor unit (GPU) that uses the Levenberg-Marquardt (LM) training method. The second is an initial attempt at determining when it is computationally beneficial to exploit a GPU’s parallel nature in preference to the traditional implementation on a central processing unit (CPU). The paper describes the approach taken to successfully implement the LM method, discusses the advantages of this approach for GPU implementation and presents results that compare GPU and CPU performance on two test data sets

Fourier Neural Operator for Parametric Partial Differential Equations

The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and the Navier-Stokes equation (including the turbulent regime). Our Fourier neural operator shows state-of-the-art performance compared to existing neural network methodologies and it is up to three orders of magnitude faster compared to traditional PDE solvers

Isometric Representations in Neural Networks Improve Robustness

Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a layer forms a representation reflecting the transformation that the layer implements on its inputs. In order to utilize the structure in the data in a truthful manner, such representations should reflect the input distances and thus be continuous and isometric. Supporting this statement, recent findings in neuroscience propose that generalization and robustness are tied to neural representations being continuously differentiable. In machine learning, most algorithms lack robustness and are generally thought to rely on aspects of the data that differ from those that humans use, as is commonly seen in adversarial attacks. During cross-entropy classification, the metric and structural properties of network representations are usually broken both between and within classes. This side effect from training can lead to instabilities under perturbations near locations where such structure is not preserved. One of the standard solutions to obtain robustness is to add ad hoc regularization terms, but to our knowledge, forcing representations to preserve the metric structure of the input data as a stabilising mechanism has not yet been studied. In this work, we train neural networks to perform classification while simultaneously maintaining within-class metric structure, leading to isometric within-class representations. Such network representations turn out to be beneficial for accurate and robust inference. By stacking layers with this property we create a network architecture that facilitates hierarchical manipulation of internal neural representations. Finally, we verify that isometric regularization improves the robustness to adversarial attacks on MNIST.Comment: 14 pages, 4 figure

Anyon models in quantum codes and topological superconductors

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Teórica, leída el 27-11-2020En esta tesis estudiamos dos temas relacionados con la información cuántica y la topología: los superconductores topológicos y la corrección cuántica topológica de errores. Los superconductores topológicos han sido ampliamente estudiados, hecho parcialmente motivado por la búsqueda de fermiones de Majorana en sistemas de materia condensada. Estas cuasipartículas son anyones no abelianos y se pueden utilizar para el procesamiento de información cuántica. Recientemente se han presentado varias propuestas y experimentos en los que se obtienen superconductores topológicos mediante la construcción de heteroestructuras. Dichas heteroestructuras generalmente consisten en un superconductor de onda s acoplado a un semiconductor. En la publicación [P1] exploramos la posibilidad de diseñar un superconductor topológico utilizando un superconductor padre de onda d acoplado a un gas de electrones bidimensional con interacción de espín-órbita y un campo Zeeman. Hallamos una expresión analítica de los estados de Majorana y comparamos estos resultados con los obtenidos cuando se usa un superconductor de ondas convencional.In this thesis we study two main topics related to the interplay between quantum information and topology: topological superconductors and topological quantum error correction. Topological superconductors have been extensively studied, partly motivated by the search of a condensed-matter realization of Majorana fermions. These quasiparticles are non-Abelian anyons and can be used for quantum information processing. There have been several proposals and experiments where topological superconductors are realized by building heterostructures. These heterostructures usually consist of an s-wave superconductor proximity-coupled to a semiconductor. In publication [P1] we explore the possibility of engineering a topological superconductor using a d-wave parent superconductor coupled to a two-dimensional electron gas with spin-orbit coupling and a Zeeman field. We determine an analytical expression of the Majorana states and compare these results to the ones obtained using a conventional s-wave superconductor...Fac. de Ciencias FísicasTRUEunpu

Representative Datasets: The Perceptron Case

One of the main drawbacks of the practical use of neural networks is the long time needed in the training process. Such training process consists in an iterative change of parameters trying to minimize a loss function. These changes are driven by a dataset, which can be seen as a set of labeled points in an n-dimensional space. In this paper, we explore the concept of representative dataset which is smaller than the original dataset and satisfies a nearness condition independent of isometric transformations. The representativeness is measured using persistence diagrams due to its computational efficiency. We also prove that the accuracy of the learning process of a neural network on a representative dataset is comparable with the accuracy on the original dataset when the neural network architecture is a perceptron and the loss function is the mean squared error. These theoretical results accompanied with experimentation open a door to the size reduction of the dataset in order to gain time in the training process of any neural network