Beyond holography: the entropic quantum gravity foundations of image processing

Abstract

Recently, thanks to the development of artificial intelligence (AI) there is increasing scientific attention in establishing the connections between theoretical physics and AI. Traditionally, these connections have been focusing mostly on the relation between string theory and image processing and involve important theoretical paradigms such as holography. Recently G. Bianconi has formulated the Gravity from Entropy (GfE) approach to quantum gravity in which gravity is derived from the geometric quantum relative entropy (GQRE) between two metrics associated with the Lorentzian spacetime. Here it is demonstrated that the famous Perona-Malik algorithm for image processing is the gradient flow that maximizes the GfE action in its simple warm-up scenario. Specifically, this algorithm is the outcome of the maximization of the GfE action calculated between two Euclidean metrics: the one of the support of the image and the one induced by the image. As the Perona-Malik algorithm is known to preserve sharp contours, this implies that the GfE action, does not in general lead to uniform images upon iteration of the gradient flow dynamics as it would be intuitively expected from entropic actions maximising classical entropies. Rather, the outcome of the maximization of the GfE action is compatible with the preservation of complex structures. These results provide the geometrical and information theory foundations for the Perona-Malik algorithm and might contribute to establish deeper connections between GfE, machine learning and brain research.

arXiv comment(7 pages, 1 figure)

References in corpus (19)

• The Large N Limit of Superconformal Field Theories and Supergravity
• The World as a Hologram
• Geometric deep learning: going beyond Euclidean data
• Machine learning and the physical sciences
• Machine learning phases of matter
• The Role of Relative Entropy in Quantum Information Theory
• The physics of higher-order interactions in complex systems
• Layer aggregation and reducibility of multilayer interconnected networks
• Notes on Some Entanglement Properties of Quantum Field Theory
• Entropy measures for complex networks: Toward an information theory of complex topologies
• A survey on Semi-, Self- and Unsupervised Learning for Image Classification
• Spectral entropies as information-theoretic tools for complex network comparison
• The Shannon and the Von Neumann entropy of random networks with heterogeneous expected degree
• Machine Learning in the String Landscape
• Unveiling the higher-order organization of multivariate time series
• Fibration symmetries uncover the building blocks of biological networks
• Gravity from entropy
• Wave function network description and Kolmogorov complexity of quantum many-body systems
• The quantum relative entropy of the Schwarzschild black-hole and the area law