# Free Energy Minimization: A Unified Framework for Modelling, Inference, Learning,and Optimization

arXiv: https://arxiv.org/abs/2011.14963 · HTML: https://mlsanity.com/paper/2011.14963/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2020.

## Built on by (most cited first, 4 of 4)

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- [Transgressing the boundaries: towards a rigorous understanding of deep learning and its (non-)robustness](https://mlsanity.com/paper/2307.02454/) (2023)

## Abstract (arXiv)

The goal of these lecture notes is to review the problem of free energy minimization as a unified framework underlying the definition of maximum entropy modelling, generalized Bayesian inference, learning with latent variables, statistical learning analysis of generalization,and local optimization. Free energy minimization is first introduced, here and historically, as a thermodynamic principle. Then, it is described mathematically in the context of Fenchel duality. Finally, the mentioned applications to modelling, inference, learning, and optimization are covered starting from basic principles.