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 suggest that IFT is well suited to address many problems in AI and ML research and application.

The first spatio-spectral Bayesian imaging of SN1006 in X-rays

“…Here, R ′ denotes a mask, which assures that the additional background field is added in BI chip regions only. By expressing the transformation into the standardized coordinate system as a function s i with i ∈ d, p, b, we obtain a generative model for each component as described in Enßlin (2022).…”

Inferring Evidence from Nested Sampling Data via Information Field Theory

“…In NIFTy [16] we represent our reconstruction priors via generative models as described in [18]. More precisely we use the reparametrisation trick by [19] according to [20] to describe the field τ with correlation structure T in Equation ( 12) as a generative process,…”