# Information Field Theory and Artificial Intelligence

arXiv: https://arxiv.org/abs/2112.10133 · HTML: https://mlsanity.com/paper/2112.10133/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 55 references that are in the map.
- First posted on arXiv 19 Dec 2021.

## Builds on (most cited first, 15 of 15)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Metric Gaussian Variational Inference](https://mlsanity.com/paper/1901.11033/) (2019)
- [Geometric variational inference](https://mlsanity.com/paper/2105.10470/) (2021)
- [Optimal Belief Approximation](https://mlsanity.com/paper/1610.09018/) (2016)
- [Encoding prior knowledge in the structure of the likelihood](https://mlsanity.com/paper/1812.04403/) (2018)
- [A Bayesian Model for Bivariate Causal Inference](https://mlsanity.com/paper/1812.09895/) (2018)
- [Field dynamics inference for local and causal interactions](https://mlsanity.com/paper/1902.02624/) (2019)
- [Field dynamics inference via spectral density estimation](https://mlsanity.com/paper/1708.05250/) (2017)
- [Towards information optimal simulation of partial differential equations](https://mlsanity.com/paper/1709.02859/) (2017)
- [Operator Calculus for Information Field Theory](https://mlsanity.com/paper/1605.00660/) (2016)
- [Correlated signal inference by free energy exploration](https://mlsanity.com/paper/1612.08406/) (2016)
- [Separating diffuse from point-like sources - a Bayesian approach](https://mlsanity.com/paper/1804.05591/) (2018)
- [Bayesian Reasoning with Trained Neural Networks](https://mlsanity.com/paper/2001.11031/) (2020)

## Built on by (most cited first, 1 of 1)

- [Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantification](https://mlsanity.com/paper/2301.07609/) (2023)

## Abstract (arXiv)

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.