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A repository for major/influential FEP and active inference papers.
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README.md

FEP and Active Inference Paper Repository

This repository provides a list of papers that I believe are interesting and influential on the Free-Energy-Principle, or in Active Inference. If you believe I have missed any papers, please contact me or make a pull request with the information about the paper. I will be happy to include it.

FEP Outline

This list is of papers focused specifically on the abstract mathematical form of the Free-Energy-Principle (FEP)

Surveys

This is Karl's magisterial monograph, and contains the most comprehensive description of the FEP to date

This is a great review which introduces the basics of predictive coding and the FEP, including the maths and contains MATLAB sample code. If you are totally new, I would start here.

This is a fantastic review which presents a complete walkthrough of the mathematical basis of the Free Energy Principle and Variational Inference, and derives predictive coding and (continuous time and state) active inference. I would reccomend this as a second thing to read (although be prepared -- it is a long and serious read)

This provides a great overview for the initial intuitions behind the FEP and its application to biological systems.

Classics

A great interview with Karl. Goes into a lot of his personal motivations underlying his work on the FEP. I would reccomend this perhaps as an initial place to start out if you know nothing of the FEP to grasp the underlying motivations of *what* it is trying to explain.

Mathematical paper by Karl and Ping Ao which begins fleshing out formally the notion of desires as attractors

Goes deep into the neuroscientific intuitions behind why you might want to think about action as a predicted observation and not a latent variable for biological brains. Presents Karl's view that action happens primarily at the periphery through simple 'reflex arcs' while all the real work is done by the generative models generating predictions.

Makes a conjectured link between precision in predictive coding and attention in the brain.

The earliest paper (I think) on active inference. Introduces the motivation behind the continuous state and time formulation of active inference. Shows how predictive coding can be used to learn actions as well as observations (by treating them the same)

Presents the 'full-construct' predictive coding model with both hierarchies and generalised coordinates.

Extends predictive coding to generalised coordinates, and derives the necessary inference algorithms for working with them -- i.e. DEM, dynamic expectation maximisation.

Perhaps the earliest paper describing the FEP. Provides a great description of the fundamental intuitions behind the theory (in needs of living systems to reduce their internal entropy to keep conditions within homeostatic bounds)

An early but complete description of predictive coding as an application of the FEP and variational inference under Gaussian and Laplace assumptions. Also surprisingly readable. This is core reading on predictive coding and the FEP

Philosophical Analyses

Self-Organisation and Markov Blankets

Information Geometry

Active Inference Outline

Active Inference is a process theory of neurobiological function inspired by and closely related to the FEP. However Active Inference stands independent of the FEP and can be true even if the FEP is not, and similarly can potentially be falsified without impacting the FEP. The core idea behind Active Inference is the idea that the brain performs both action and perception by variational inference on a unified objective function

Surveys and Tutorials

This is a great and thorough tutorial on discrete-state-space active inference. I would reccomend it to everybody new to the field.

Discrete State Space Formulation

Discusses the relationship between active inference and dynamic programming solutions to reinforcement learning problems (i.e. Q learning, value functions etc). Shows that they are largely equivalent except with different objectives (Expected Free Energy vs Expected Discounted Reward).

Provides a very good and thorough description of discrete-state-space active inference and ties its updates closely to neural physiology. I would reccomend this after the Da Costa introduction.

Introduces the main intuitions behind active inference, as well as the crucial epistemic foraging behaviour of the expected free energy. Illustrated on a simple T-maze task.

The first (I think) discrete-state-space paper on active inference. Notable for using the standard variational free energy as objective function and not the expected free energy. Describes some of the intuitions behind active inference.

Continuous Time Formulation

The earliest paper (I think) on active inference. Introduces the motivation behind the continuous state and time formulation of active inference. Shows how predictive coding can be used to learn actions as well as observations (by treating them the same)

Message Passing and Free Energies

Discusses whether we can derive the expected free energy objective function on principled ground from the FEP, and discusses different potential objective functions for active inference.

Discusses the relationship between Active Inference and Control as Inference, a variational framework for understanding action selection which has emerged from RL.

Discusses in depth the different potential message passing inference algorithms which can be used to implement active inference on factor graphs.

Introduces the Bethe free energy, as a result of making the Bethe approximation instead of the mean-field variational assumption to derive the message passing algorithms.

Contributing

To contribute, please make pull requests adding entries to the bibtex file.

The README file was generated from bibtex using the bibtex_to_md.py file. The keywords to use for each classification (Survey, Discrete-state-space etc) can be found at the bottom of the .py file.

This code and structure is heavily inspired by https://github.com/optimass/continual_learning_papers.