Artificial Neural Networks
During the last years much effort was expended to combine (quantum) physics with machine learning methods. This has led to many useful and interesting results. One of those was an ansatz to parametrize quantum spin-1/2 systems with a generative artificial
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Artificial Neural Networks
During the last years much effort was expended to combine (quantum) physics with machine learning methods. This has led to many useful and interesting results. One of those was an ansatz to parametrize quantum spin-1/2 systems with a generative artificial neural network, specifically the restricted Boltzmann machine. We further analyze this ansatz within this thesis. In this chapter we therefore introduce the basic rudiments of machine learning techniques based on artificial neural networks. This provides the foundation to introduce the parametrization ansatz of spin-1/2 systems. Albeit not all the concepts discussed here are employed further within this thesis, we give a detailed overview. The concepts of feed-forward neural networks are discussed in Sect. 3.1 based on [1–3], which provide an introduction to artificial neural networks. Section 3.2 discusses the restricted Boltzmann machine in detail and is based on [1–4], while in Sect. 3.3.1 we introduce supervised learning according to [1–3, 5]. The basics of unsupervised learning are discussed in Sect. 3.3.2 based on [1–4, 6] and we consider reinforcement learning in Sect. 3.3.3 according to [2, 7]. Besides the introduction of the basic methods, we give a review of applications of machine learning methods in (quantum) physics in Sect. 3.4, which is based on two detailed reviews given in [3, 7]. We end the chapter with discussing the neuromorphic hardware present in the BrainScaleS group at Heidelberg University, which emulates an artificial neural network on an analog hardware with hardwired spiking neurons. We are interested in combining this hardware with the quantum state parametrization based on artificial neural networks.
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 S. Czischek, Neural-Network Simulation of Strongly Correlated Quantum Systems, Springer Theses, https://doi.org/10.1007/978-3-030-52715-0_3
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3 Artificial Neural Networks
3.1 Discriminative Models: Feed-Forward Neural Networks Nowadays, machine learning has become a famous approach in many regimes of technology and has found a wide range of applications, where it has shown significant improvements. To name a few examples, machine learning led to impressive progress in the fields of autonomous driving, text or speech recognition, and playing computer games. A famous application is also Google’s AlphaGo, a machine which bet the European champion Fan Hui [8], as well as world champion Lee Sedol in the game “Go”. All these applications are based on the task to recognize patterns in huge amounts of data [7]. While many approaches and methods of machine learning exist, which perform differently depending on the tasks considered, methods based on artificial neural networks (ANN) show remarkable results. This is especially true since people started to compose deep networks showing more internal structure. An illustrating example for the power of these models is image recognition, where the network
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