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mainzer k artificial intelligence neuromorphic systems 2024

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Textbook in PDF format This book argues for neuromorphic systems as a technology of the future, which are oriented towards the energy efficiency of natural brains. Energy efficiency is a dramatic claim in times of environmental and climate challenges which should consider the sustainability goals of the United Nations (UN). Mathematically, neuromorphic computing is connected to analogue ('real') computing, which theoretically overcomes the limits of digital Turing computability. Therefore, the book also considers material sciences and engineering sciences which start to realize neuromorphic computing in hardware. Other mathematical formalisms such as quantum mechanics also open up new solutions (e.g., quantum computing) beyond the limits of digital Turing computability. These research fields are no longer merely of theoretical interest, they promise increasing innovation power of market interest. Nevertheless, neuromorphic computing is connected with deep logical, mathematical, and epistemic questions. Does it open new avenues to Artificial General Intelligence (AGI)? All these tendencies of research and innovation demonstrate that we need more integrated research in the foundations of logic, mathematics, physics, engineering sciences, cognitive science, and philosophy. The book is a plea for this kind of research. This chapter explains the mathematical principles of Machine Learning. The basis is a statistical learning theory in which Bayesian probability theory is used. Learning algorithms of neural networks are formulated using Bayesian methods. The limits of their performance (e.g., pattern recognition) depend on the assumed linear or nonlinear mathematical methods. Some examples of applications in life sciences are discussed. The astounding performance of today’s statistical learning theory is based on the enormous technical and practical computing and storage capacities. These technical standards also explain the success of chatbots with large language models (LLMs) and very large neural networks. The question arises as to whether and to what extent Artificial Intelligence (AI) systems can also recognize causal relationships and not just statistical correlations. In the end, it is shown that very large neural networks can be mathematically formalized and classified as complex dynamic systems. Their explainability and computability therefore again depend on the mathematical formalism assumed. The extent to which the possibilities and limits of computability depend on the assumed mathematical formalism is particularly evident in Quantum Computing. Here, methods, algorithms, and basic concepts of classical digital computing must be translated into the mathematical formalism of quantum mechanics and new concepts of quantum formalism must be utilized in order to overcome the classical limits of computability. In the sense of Church’s thesis, a classical digital computer can also be understood as a circuit of Boolean gates that process bits. In quantum computing, they are replaced by quantum gates that represent the unitary operators of quantum mechanics and process quantum bits. The enormous computing advantages are due to the special features of quantum mechanical states such as superposition and entanglement. The calculation results of a quantum computer are explained by the quantum mechanical measurement process. Classical calculation methods such as fast Fourier transformations are translated into quantum formalism and thus enable the solution of di?cult calculation problems in polynomial time (e.g., factorization with the Shor algorithm). However, in this case, it cannot be ruled out that there is also a classical digital solution in polynomial time. This distinguishes the result from the fundamental impossibility of a digital solution, which was shown for real computing in Chapter 7. Classical pattern recognition and classi?cation of Machine Learning (ML) with neural networks can also be translated into quantum formalism and lead to a considerable increase in performance with superposition and entanglement. In quantum complexity theory, previous NP problems can be traced back to P problems. In quantum computing too, the theoretical possibilities and limits depend on the mathematical formalism assumed. The technical-physical realization of a quantum computer, on the contrary, is again an empirical question. Preface Chapter 1 Introduction Chapter 2 Foundations of Digital Computability Chapter 3 Complexity Degrees of Digital Computability Chapter 4 Foundations of Real Computability Chapter 5 Complexity Degrees of Real Computability Chapter 6 Real Computability of Neural Networks Chapter 7 Digital Limits of Real Computing Chapter 8 Real Solvability of Real Computing Chapter 9 Limits and Solvability of Machine Learning Chapter 10 Limits and Solvability of Quantum Computing Chapter 11 Limits and Solvability of Relativistic Computing Chapter 12 Neurobiological and Cognitive Foundations of Neuromorphic Systems Chapter 13 Technological Prospects of Electronic Neuromorphic Systems Chapter 14 Technological Prospects of Photonic Neuromorphic Systems Chapter 15 Strategic Prospects of Neuromorphic Systems with Sustainable and Responsible AI

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mainzer k artificial intelligence neuromorphic systems 2024

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