Predictive coding

Fancy analogy for brains

Maybe related (?) prediction processes. To learn: Is this what the information-dynamics folks are wondering about also, e.g. Ay et al. (2008) or Tishby and Polani (2011)?

There is some interesting hype in this area, along the lines of understanding biological learning as machine learning: Predictive Coding has been Unified with Backpropagation, concerning Millidge, Tschantz, and Buckley (2020b).. I have not read the article or the explanation properly, but at first glance it indicates that perhaps I do not understand this area properly. The assertion, skim-read, seems to be that predictive coding, which I imagined was some form of variational inference, can approximate minimum loss learning by backpropagation in some sense. While not precisely trivial, this would seem like well-trodden ground— unless I have failed ot understand how they are using the terms, which seems likely. TBC.

Free energy

This term, with an analogous definition to the use in variational inference appears to pop up in a “free energy principle” which AFAICT is some weird phrasing of predictive coding through the lense of variational Bayes.

Here is the most compact version I could find:

The free energy principle (FEP) claims that self-organization in biological agents is driven by variational free energy (FE) minimization in a generative probabilistic model of the agent’s environment.

The chief pusher of this wheelbarrow appears to be Karl Friston. He starts his Nature Reviews Neuroscience piece with this statement of the principle:

The free-energy principle says that any self-organizing system that is at equilibrium with its environment must minimize its free energy.

Is that “must” in

  • the sense of moral obligation, or is it
  • a testable conservation law of some kind?

If the latter, self-organising in what sense? What type of equilibrium? For which definition of the free energy? What is our chief experimental evidence for this hypothesis?

I think it means that

any right thinking brain, seeking to avoid the vice of slothful and decadent perception after the manner of foreigners and compulsive masturbators, would do well to seek to maximise its free energy before partaking of a stimulating and refreshing physical recreation such as a game of cricket.

There are dozens of Friston papers with minor variations on the theme and it is not clear where to start. If I wanted a better grasp here, I would recommend the clearer explanation in Millidge, Tschantz, and Buckley (2020a) which summarises many of the ideas in language I am more used to.

See also: the Slate Star Codex Friston dogpile, based on an exposition by Wolfgang Schwarz.


Aguilera, Miguel, Beren Millidge, Alexander Tschantz, and Christopher L. Buckley. 2021. “How Particular Is the Physics of the Free Energy Principle?” arXiv:2105.11203 [q-Bio], May.
Ay, N., N. Bertschinger, R. Der, F. Güttler, and E. Olbrich. 2008. “Predictive Information and Explorative Behavior of Autonomous Robots.” The European Physical Journal B - Condensed Matter and Complex Systems 63 (3): 329–39.
Carhart-Harris, Rl, and Dj Nutt. 2017. “Serotonin and Brain Function: A Tale of Two Receptors.” Journal of Psychopharmacology 31 (9): 1091–1120.
Clark, Andy. 2015. Surfing Uncertainty: Prediction, Action, and the Embodied Mind. Illustrated edition. Oxford ; New York: Oxford University Press.
Da Costa, Lancelot, Karl Friston, Conor Heins, and Grigorios A. Pavliotis. 2021. “Bayesian Mechanics for Stationary Processes.” arXiv:2106.13830 [Math-Ph, Physics:nlin, q-Bio], June.
Friston, Karl. 2010. “The Free-Energy Principle: A Unified Brain Theory?” Nature Reviews Neuroscience 11 (2): 127.
———. 2013. “Life as We Know It.” Journal of The Royal Society Interface 10 (86).
Kay, Kenneth, Jason E. Chung, Marielena Sosa, Jonathan S. Schor, Mattias P. Karlsson, Margaret C. Larkin, Daniel F. Liu, and Loren M. Frank. 2020. “Constant Sub-second Cycling between Representations of Possible Futures in the Hippocampus.” Cell 180 (3): 552–567.e25.
Millidge, Beren, Alexander Tschantz, and Christopher L. Buckley. 2020a. “Whence the Expected Free Energy?” arXiv:2004.08128 [Cs], September.
———. 2020b. “Predictive Coding Approximates Backprop Along Arbitrary Computation Graphs.” arXiv:2006.04182 [Cs], October.
Tishby, Naftali, Fernando C Pereira, and William Bialek. 2000. “The Information Bottleneck Method.” arXiv:physics/0004057, April.
Tishby, Naftali, and Daniel Polani. 2011. “Information Theory of Decisions and Actions.” In PERCEPTION-ACTION CYCLE, 601–36. Springer.
Williams, Daniel. 2020. “Predictive Coding and Thought.” Synthese 197 (4): 1749–75.

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