Information Field Theory and Artificial Intelligence

Abstract

Information field theory (IFT), the information theory for fields, is a mathematical framework for signal reconstruction and non-parametric inverse problems. Artificial intelligence (AI) and machine learning (ML) aim at generating intelligent systems including such for perception, cognition, and learning. This overlaps with IFT, which is designed to address perception, reasoning, and inference tasks. Here, the relation between concepts and tools in IFT and those in AI and ML research are discussed. In the context of IFT, fields denote physical quantities that change continuously as a function of space (and time) and information theory refers to Bayesian probabilistic logic equipped with the associated entropic information measures. Reconstructing a signal with IFT is a computational problem similar to training a generative neural network (GNN) in ML. In this paper, the process of inference in IFT is reformulated in terms of GNN training. In contrast to classical neural networks, IFT based GNNs can operate without pre-training thanks to incorporating expert knowledge into their architecture. Furthermore, the cross-fertilization of variational inference methods used in IFT and ML are discussed. These discussions suggests that IFT is well suited to address many problems in AI and ML research and application.

12 pages, three figures, invited talk at MaxEnt2020/2021, reviewed and published by Entropy

References in corpus (8)

• Estimating extragalactic Faraday rotation
• Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty
• Geometric variational inference
• Unified Radio Interferometric Calibration and Imaging with Joint Uncertainty Quantification
• Reconstructing non-repeating radio pulses with Information Field Theory
• A Bayesian method for pulsar template generation
• Field dynamics inference via spectral density estimation
• All-sky reconstruction of the primordial scalar potential from WMAP temperature data

Cited by in corpus (4)

• Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantification
• First spatio-spectral Bayesian imaging of SN1006 in X-ray
• Non-parametric Bayesian reconstruction of Galactic magnetic fields using Information Field Theory: The inclusion of line-of-sight information in ultra-high energy cosmic ray backtracking
• Inferring Evidence from Nested Sampling Data via Information Field Theory