177 research outputs found

    NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems

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    We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural-network quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code

    NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems

    Get PDF
    We introduce version 3 of NetKet, the machine learning toolbox for many-body quantum physics. NetKet is built around neural-network quantum states and provides efficient algorithms for their evaluation and optimization. This new version is built on top of JAX, a differentiable programming and accelerated linear algebra framework for the Python programming language. The most significant new feature is the possibility to define arbitrary neural network ansätze in pure Python code using the concise notation of machine-learning frameworks, which allows for just-in-time compilation as well as the implicit generation of gradients thanks to automatic differentiation. NetKet 3 also comes with support for GPU and TPU accelerators, advanced support for discrete symmetry groups, chunking to scale up to thousands of degrees of freedom, drivers for quantum dynamics applications, and improved modularity, allowing users to use only parts of the toolbox as a foundation for their own code

    Tensor Network States: Optimizations and Applications in Quantum Many-Body Physics and Machine Learning

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    Tensor network states are ubiquitous in the investigation of quantum many-body (QMB) physics. Their advantage over other state representations is evident from their reduction in the computational complexity required to obtain various quantities of interest, namely observables. Additionally, they provide a natural platform for investigating entanglement properties within a system. In this dissertation, we develop various novel algorithms and optimizations to tensor networks for the investigation of QMB systems, including classical and quantum circuits. Specifically, we study optimizations for the two-dimensional Ising model in a transverse field, we create an algorithm for the kk-SAT problem, and we study the entanglement properties of random unitary circuits. In addition to these applications, we reinterpret renormalization group principles from QMB physics in the context of machine learning to develop a novel algorithm for the tasks of classification and regression, and then utilize machine learning architectures for the time evolution of operators in QMB systems

    Applied Harmonic Analysis and Data Science (hybrid meeting)

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    Data science has become a field of major importance for science and technology nowadays and poses a large variety of challenging mathematical questions. The area of applied harmonic analysis has a significant impact on such problems by providing methodologies both for theoretical questions and for a wide range of applications in signal and image processing and machine learning. Building on the success of three previous workshops on applied harmonic analysis in 2012, 2015 and 2018, this workshop focused on several exciting novel directions such as mathematical theory of deep learning, but also reported progress on long-standing open problems in the field

    Enhancing cardiac image segmentation through persistent homology regularization

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    Treballs Finals de Grau d'Enginyeria Informàtica, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Sergio Escalera Guerrero, Carles Casacuberta i Rubén Ballester Bautista[en] Cardiovascular diseases are a major cause of death and disability. Deep learning-based segmentation methods could help to reduce their severity by aiding in early diagnosing but high levels of accuracy are necessary. The vast majority of methods focus on correcting local errors and miss the global picture. To ad- dress this issue, researchers have developed techniques that incorporate global context and consider the relationships between pixels. Here, we apply persistent homology, a branch of topology that studies the topological structure of shapes, along with deep learning methods to improve the heart segmentation. We use multidimensional topological losses to avoid spurious components and holes and increase the total accuracy. We evaluate the performance of three different approaches: using the dice and pixel-wise losses with the sum of persistences of label diagrams as a regularizer, using the dice and pixel-wise losses with the bottleneck distance as a regularizer, and using both losses without any regularization. We find that, while more computationally demanding, the methods using topological regularizers outperform the other method in terms of accuracy

    Analog Photonics Computing for Information Processing, Inference and Optimisation

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    This review presents an overview of the current state-of-the-art in photonics computing, which leverages photons, photons coupled with matter, and optics-related technologies for effective and efficient computational purposes. It covers the history and development of photonics computing and modern analogue computing platforms and architectures, focusing on optimization tasks and neural network implementations. The authors examine special-purpose optimizers, mathematical descriptions of photonics optimizers, and their various interconnections. Disparate applications are discussed, including direct encoding, logistics, finance, phase retrieval, machine learning, neural networks, probabilistic graphical models, and image processing, among many others. The main directions of technological advancement and associated challenges in photonics computing are explored, along with an assessment of its efficiency. Finally, the paper discusses prospects and the field of optical quantum computing, providing insights into the potential applications of this technology.Comment: Invited submission by Journal of Advanced Quantum Technologies; accepted version 5/06/202

    High-Capacity Directional Graph Networks

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    Deep Neural Networks (DNN) have proven themselves to be a useful tool in many computer vision problems. One of the most popular forms of the DNN is the Convolutional Neural Network (CNN). The CNN effectively learns features on images by learning a weighted sum of local neighborhoods of pixels, creating filtered versions of the image. Point cloud analysis seems like it would benefit from this useful model. However, point clouds are much less structured than images. Many analogues to CNNs for point clouds have been proposed in the literature, but they are often much more constrained networks than the typical CNN. This is a matter of necessity: common point cloud benchmark datasets are fairly small and thus require strong regularization to mitigate overfitting. In this dissertation we propose two point cloud network models based on graph structures that achieve the high-capacity modeling capability of CNNs. In addition to showing their effectiveness on point cloud classification and segmentation in typical benchmark scenarios, we also propose two novel point cloud problems: ATLAS Detector segmentation and Computational Fluid Dynamics (CFD) surrogate modeling. We show that our networks are much more effective than others on these new problems because they benefit from deeper networks and extra capacity that other researchers have not pursued. These novel networks and datasets pave the way for future development of deeper, more sophisticated point cloud networks
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