# Applications of the Free Energy Principle to Machine Learning and Neuroscience

arXiv: https://arxiv.org/abs/2107.00140 · HTML: https://mlsanity.com/paper/2107.00140/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 72 of its 280 references that are in the map.
- First posted on arXiv 30 Jun 2021.

## Builds on (most cited first, 30 of 72)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Rainbow: Combining Improvements in Deep Reinforcement Learning](https://mlsanity.com/paper/1710.02298/) (2017)
- [Dueling Network Architectures for Deep Reinforcement Learning](https://mlsanity.com/paper/1511.06581/) (2015)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning](https://mlsanity.com/paper/1708.02596/) (2017)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Deep Dynamics Models for Learning Dexterous Manipulation](https://mlsanity.com/paper/1909.11652/) (2019)
- [Deep Predictive Coding Networks for Video Prediction and Unsupervised Learning](https://mlsanity.com/paper/1605.08104/) (2016)
- [Efficient Exploration via State Marginal Matching](https://mlsanity.com/paper/1906.05274/) (2019)

## Built on by (most cited first, 9 of 9)

- [Predictive Coding Networks and Inference Learning: Tutorial and Survey](https://mlsanity.com/paper/2407.04117/) (2024)
- [Deep Active Inference Agents for Delayed and Long-Horizon Environments](https://mlsanity.com/paper/2505.19867/) (2025)
- [Successor Representation Active Inference](https://mlsanity.com/paper/2207.09897/) (2022)
- [Sophisticated Learning: A novel algorithm for active learning during model-based planning](https://mlsanity.com/paper/2308.08029/) (2023)
- [Active Inference Meeting Energy-Efficient Control of Parallel and Identical Machines](https://mlsanity.com/paper/2406.09322/) (2024)
- [Is the `Agent' Paradigm a Limiting Framework for Next-Generation Intelligent Systems?](https://mlsanity.com/paper/2509.10875/) (2025)
- [Distributional Active Inference](https://mlsanity.com/paper/2601.20985/) (2026)
- [Quantitative Promise Theory: Intentionality and Inference in Autonomous Agents](https://mlsanity.com/paper/2606.08552/) (2026)
- [Active Inference as Context Acquisition for AI Agents](https://mlsanity.com/paper/2608.19202/) (2026)

## Abstract (arXiv)

In this PhD thesis, we explore and apply methods inspired by the free energy principle to two important areas in machine learning and neuroscience. The free energy principle is a general mathematical theory of the necessary information-theoretic behaviours of systems that maintain a separation from their environment. A core postulate of the theory is that complex systems can be seen as performing variational Bayesian inference and minimizing an information-theoretic quantity called the variational free energy. The thesis is structured into three independent sections. Firstly, we focus on predictive coding, a neurobiologically plausible process theory derived from the free energy principle which argues that the primary function of the brain is to minimize prediction errors, showing how predictive coding can be scaled up and extended to be more biologically plausible, and elucidating its close links with other methods such as Kalman Filtering. Secondly, we study active inference, a neurobiologically grounded account of action through variational message passing, and investigate how these methods can be scaled up to match the performance of deep reinforcement learning methods. We additionally provide a detailed mathematical understanding of the nature and origin of the information-theoretic objectives that underlie exploratory behaviour. Finally, we investigate biologically plausible methods of credit assignment in the brain. We first demonstrate a close link between predictive coding and the backpropagation of error algorithm. We go on to propose novel and simpler algorithms which allow for backprop to be implemented in purely local, biologically plausible computations.