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108 | 2008
Annuaire du Collège de France 2007-2008
Résumé des cours et travaux 108e année
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A Free energy principle for the brain

Résumé des conférences du Collège de France (2007-2008)
Karl Friston
p. 927-929

Texte intégral

Action, perception and free-energy (Thursday May 29th)

1Value-learning and perceptual learning have been an important focus over the past decade, attracting the concerted attention of experimental psychologists, neurobiologists and the machine learning community. Despite some formal connections; e.g., the role of prediction error in optimising some function of sensory states, both fields have developed their own rhetoric and postulates.  In work, we show that perceptual learning is, literally, an integral part of value learning; in the sense that perception is necessary to integrate out dependencies on the inferred causes of sensory information. This enables the value of sensory trajectories to be optimised through action. Furthermore, we show that acting to optimize value and perception are two aspects of exactly the same principle; namely the minimisation of a quantity [free energy] that bounds the probability of sensory input, given a particular agent or phenotype. This principle can be derived, in a straightforward way, from the very existence of agents, by considering the probabilistic behaviour of an ensemble of agents belonging to the same class.

2This treatment unifies value and perceptual learning and suggests that value is simply the probability of sensory input expected by an agent. This means that acting to maximise value is the same as acting to minimise surprise; in other words, sampling the environment so that is conforms to our expectations. In this way, exchange or interactions with the environment are maintained within bounds that preserve the integrity of the agent. Clearly, the surprise of a sensory exchange depends on some representation or perceptual model of that exchange. We show that this model emerges naturally as the internal states of the agent optimise the free energy bound above.

3This formulation is important because it places the mechanisms of value-learning and reinforcement in the larger context of perceptual learning. For example, conditioning paradigms (both classical and operant) can be regarded as introducing statistical regularities into the sensorium. These are learned in the same way we learn the causal structure of sensory contingencies. In this view, rewards are simply predictable stimuli (and aversive stimuli are, be definition, surprising). Furthermore, the neurobiological substrates of value-learning become accountable to the larger problem of perceptual inference in the brain. For example, dopamine may not just signal reward but have a much more generic and role encoding the conditional certainty or precision of our predictions. This is consistent with a role in modulating the balance between bottom-up sensory information and top-down empirical priors, during perpetual inference.

Variational filtering and inference (Friday May 30th, NeuroSpin)

4We present a variational treatment of dynamic models that furnishes the time-dependent conditional densities of a system’s states and the time-independent densities of its parameters. These obtain by maximising the variational free energy of the system with respect to the conditional densities. The ensuing free energy represents a lower-bound approximation to the models marginal likelihood or log-evidence required for model selection and averaging. This approach rests on formulating the optimisation of free energy dynamically, in generalised co-ordinates of motion. The resulting scheme can be used for online Bayesian inversion of nonlinear dynamic causal models and eschews some limitations of existing approaches, such as Kalman and particle filtering. We refer to this approach as dynamic expectation maximisation (DEM).

Perceptual inference and learning (Monday June 1st)

5This talk summarizes our recent attempts to integrate action and perception within a single optimization framework. We start with a statistical formulation of Helmholtz’s ideas about neural energy to furnish a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring what cause our sensory inputs and learning causal regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain’s organization and responses.

6Here, we suggest that these perceptual processes are just one aspect of systems that conform to a free-energy principle.  The free-energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. A system can minimize free-energy by changing its configuration to change the way it samples the environment, or to change its expectations. These changes correspond to action and perception respectively and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment implies that the system’s state and structure encode an implicit and probabilistic model of the environment and that its actions suppress surprising exchanges with it. Furthermore, it suggests that free-energy, surprise and [negative] value are all the same thing. We will look at models entailed by the brain and how minimization of free-energy can explain its dynamics and structure.

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Cours et travaux du Collège de France. Annuaire 108e année, Collège de France, Paris, décembre 2008, p. 927-929. ISBN 978-2-7226-0082-9

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Karl Friston, « A Free energy principle for the brain », L’annuaire du Collège de France [En ligne], 108 | 2008, mis en ligne le , consulté le 19 décembre 2018. URL :

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Karl Friston

Professeur, University College London (Grande Bretagne)

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Collège de France

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