Information Field Theory and Artificial Intelligence

TL;DR

This paper explores the connection between information field theory (IFT) and artificial intelligence, showing how IFT can enhance AI systems by enabling inference without pre-training and integrating expert knowledge.

Contribution

It reformulates IFT inference as generative neural network training and discusses how variational inference bridges IFT and ML, highlighting IFT's potential in AI applications.

Findings

IFT-based GNNs can operate without pre-training

IFT and ML variational inference methods are compatible

IFT is suitable for various AI and ML problems

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.