Abstract: This overview of the free energy principle offers an account of embodied exchange with the world that associates conscious operations with actively inferring the causes of our sensations. Its agenda is to link formal (mathematical) descriptions of dynamical systems to a description of perception in terms of beliefs and goals. The argument has two parts: the first calls on the lawful dynamics of any (weakly mixing) ergodic system– from a single cell organism to a human brain. These lawful dynamics suggest that (internal) states can be interpreted as modelling or predicting the (external) causes of sensory fluctuations. In other words, if a system exists, its internal states must encode probabilistic beliefs about external states. Heuristically, this means that if I exist (am) then I must have beliefs (think). The second part of the argument is that the only tenable beliefs I can entertain about myself are that I exist. This may seem rather obvious; however, if we associate existing with ergodicity, then (ergodic) systems that exist by predicting external states can only possess prior beliefs that their environment is predictable. It transpires that this is equivalent to believing that the world – and the way it is sampled – will resolve uncertainty about the causes of sensations. We will conclude by looking at the epistemic behaviour that emerges under these beliefs, using simulations of active inference. Key words : active inference ∙ autopoiesis ∙ cognitive ∙ dynamics ∙ free energy ∙ epistemic value ∙ self-organization. I am therefore I think Karl Friston, University College London Free Energy Workshop 2015

Overview The statistics of life Markov blankets and ergodic systems Simulations of a primordial soup I am therefore I think The anatomy of inference Graphical models and predictive coding Canonical microcircuits Birdsong and generalized synchrony Active inference Minimizing expected uncertainty Saccadic searches and salience Anatomy of choice Markov decision processes Minimizing expected free energy Dopamine and precision Knowing your place Multi-agent games Morphogenesis

“How can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry?” (Erwin Schrödinger 1943) The Markov blanket as a statistical boundary (parents, children and parents of children) Internal states External states Sensory states Active states

The Markov blanket in biotic systems Active states External states Internal states Sensory states

The Fokker-Planck equation And its solution in terms of curl-free and divergence-free components lemma : any (ergodic random) dynamical system ( m ) that possesses a Markov blanket will appear to engage in active inference

But what about the Markov blanket? Reinforcement learning, optimal control and expected utility theory Information theory and minimum redundancy Self-organisation, synergetics and homoeostasis Bayesian brain, active inference and predictive coding Value Surprise Entropy Model evidence Pavlov Haken Helmholtz Barlow Perception Action

Overview The statistics of life Markov blankets and ergodic systems Simulations of a primordial soup I am therefore I think The anatomy of inference Graphical models and predictive coding Canonical microcircuits Birdsong and generalized synchrony Active inference Minimizing expected uncertainty Saccadic searches and salience Anatomy of choice Markov decision processes Minimizing expected free energy Dopamine and precision Knowing your place Multi-agent games Morphogenesis

Position Simulations of a (prebiotic) primordial soup Weak electrochemical attraction Strong repulsion Short-range forces

Element Adjacency matrix Markov Blanket Hidden states Sensory states Active states Internal states Markov Blanket = [ B · [eig(B) > τ]] Markov blanket matrix: encoding the children, parents and parents of children Finding the (principal) Markov blanket A Does action maintain the structural and functional integrity of the Markov blanket ( autopoiesis ) ? Do internal states appear to infer the hidden causes of sensory states ( active inference ) ?

Autopoiesis, oscillator death and simulated brain lesions

Decoding through the Markov blanket and simulated brain activation Christiaan Huygens

The existence of a Markov blanket necessarily implies a partition of states into internal states, their Markov blanket (sensory and active states) and external or hidden states. Because active states change – but are not changed by – external states they minimize the entropy of internal states and their Markov blanket. This means action will appear to maintain the structural and functional integrity of the Markov blanket ( autopoiesis ). Internal states appear to infer the hidden causes of sensory states (by maximizing Bayesian evidence) and influence those causes though action ( active inference ) Interim summary

res extensa (extensive flow) res cogitans (beliefs) Belief productionFree energy functional “I am [ergodic] therefore I think”

Overview The statistics of life Markov blankets and ergodic systems Simulations of a primordial soup I am therefore I think The anatomy of inference Graphical models and predictive coding Canonical microcircuits Birdsong and generalized synchrony Active inference Minimizing expected uncertainty Saccadic searches and salience Anatomy of choice Markov decision processes Minimizing expected free energy Dopamine and precision Knowing your place Multi-agent games Morphogenesis

“Objects are always imagined as being present in the field of vision as would have to be there in order to produce the same impression on the nervous mechanism” - von Helmholtz Thomas Bayes Geoffrey Hinton Richard Feynman The Helmholtz machine and the Bayesian brain Richard Gregory Hermann von Helmholtz

“Objects are always imagined as being present in the field of vision as would have to be there in order to produce the same impression on the nervous mechanism” - von Helmholtz Richard Gregory Hermann von Helmholtz Impressions on the Markov blanket…

Bayesian filtering and predictive coding prediction update prediction error

Making our own sensations Changing sensations sensations – predictions Prediction error Changing predictions Action Perception

the Descending predictions Descending predictions Ascending prediction errors A simple hierarchy whatwhere Sensory fluctuations Hierarchical generative models

frontal eye fields geniculate visual cortex retinal input pons oculomotor signals Top-down or backward predictions Bottom-up or forward prediction error proprioceptive input reflex arc Perception David Mumford Predictive coding with reflexes Action Prediction error (superficial pyramidal cells) Expectations (deep pyramidal cells)

Biological agents minimize their average surprise (entropy) They minimize surprise by suppressing prediction error Prediction error can be reduced by changing predictions (perception) Prediction error can be reduced by changing sensations (action) Perception entails recurrent message passing to optimize predictions Action makes predictions come true (and minimizes surprise) Interim summary

Overview The statistics of life Markov blankets and ergodic systems Simulations of a primordial soup I am therefore I think The anatomy of inference Graphical models and predictive coding Canonical microcircuits Birdsong and generalized synchrony Active inference Minimizing expected uncertainty Saccadic searches and salience Anatomy of choice Markov decision processes Minimizing expected free energy Dopamine and precision Knowing your place Multi-agent games Morphogenesis

Thalamus Area X Higher vocal centre Hypoglossal Nucleus creating your own sensations: Listening time (sec) Frequency (Hz) sensations

Thalamus Area X Higher vocal centre Hypoglossal Nucleus creating your own sensations: Singing Motor commands (proprioceptive predictions) Corollary discharge ( exteroceptive predictions) time (sec) Frequency (Hz) sensations

time (sec) Frequency (Hz) percept time (seconds) First level expectations (hidden states) time (seconds) Second level expectations (hidden states) Singing alone

Mutual prediction and synchronization of chaos synchronization manifold

Overview The statistics of life Markov blankets and ergodic systems Simulations of a primordial soup I am therefore I think The anatomy of inference Graphical models and predictive coding Canonical microcircuits Birdsong and generalized synchrony Active inference Minimizing expected uncertainty Saccadic searches and salience Anatomy of choice Markov decision processes Minimizing expected free energy Dopamine and precision Knowing your place Multi-agent games Morphogenesis

saliencevisual inputstimulussampling Perception as hypothesis testing – saccades as experiments Sampling the world to minimise expected uncertainty “I am [ergodic] therefore I think”  “I think therefore I am [ergodic]” LikelihoodEmpirical priorsPrior beliefs

Frontal eye fields Pulvinar salience map Fusiform (what) Superior colliculus Visual cortex oculomotor reflex arc Parietal (where)

Visual samples Conditional expectations about hidden (visual) states And corresponding percept Saccadic eye movements Hidden (oculomotor) states vs.

Overview The statistics of life Markov blankets and ergodic systems Simulations of a primordial soup I am therefore I think The anatomy of inference Graphical models and predictive coding Canonical microcircuits Birdsong and generalized synchrony Active inference Minimizing expected uncertainty Saccadic searches and salience Anatomy of choice Markov decision processes Minimizing expected free energy Dopamine and precision Knowing your place Multi-agent games Morphogenesis

Generative models Hidden states Action Control states Continuous states Discrete states Bayesian filtering (predictive coding) Variational Bayes (belief updating)

Full priors – control states Empirical priors – hidden states Likelihood The (normal form) generative model Hidden states Action Control states

KL or risk-sensitive control In the absence of ambiguity: Expected utility theory In the absence of uncertainty or risk: Bayesian surprise and Infomax In the absence of prior beliefs about outcomes: Prior beliefs about policies Quality of a policy = (negative) Expected free energy Extrinsic value Epistemic value, information gain or reduction of expected uncertainty Predicted divergence Extrinsic value Bayesian surprise Predicted mutual information

midbrain motor Cortex occipital Cortex striatum Variational updates Perception Action selection Incentive salience Functional anatomy prefrontal Cortex hippocampus Performance Prior preference success rate (%) FE KL RL DA Simulated behaviour

Simulating conditioned responses and dopamine release (precision updates)

Overview The statistics of life Markov blankets and ergodic systems Simulations of a primordial soup I am therefore I think The anatomy of inference Graphical models and predictive coding Canonical microcircuits Birdsong and generalized synchrony Active inference Minimizing expected uncertainty Saccadic searches and salience Anatomy of choice Markov decision processes Minimizing expected free energy Dopamine and precision Knowing your place Multi-agent games Morphogenesis

Generative model Intercellular signaling Intrinsic signals Exogenous signals Endogenous signals Knowing your place: multi-agent games and morphogenesis

Extracellular target signal position (Genetic) encoding of target morphology Position (place code) Signal expression (genetic code) Target form position

Expectations time time Action Morphogenesis

Dysmorphogenesis Gradient IntrinsicExtrinsic TARGET

Regeneration

“Each movement we make by which we alter the appearance of objects should be thought of as an experiment designed to test whether we have understood correctly the invariant relations of the phenomena before us, that is, their existence in definite spatial relations.” ‘The Facts of Perception’ (1878) in The Selected Writings of Hermann von Helmholtz, Ed. R. Karl, Middletown: Wesleyan University Press, 1971 p. 384 Hermann von Helmholtz

And thanks to collaborators: Rick Adams Ryszard Auksztulewicz Andre Bastos Sven Bestmann Harriet Brown Jean Daunizeau Mark Edwards Chris Frith Thomas FitzGerald Xiaosi Gu Stefan Kiebel James Kilner Christoph Mathys Jérémie Mattout Rosalyn Moran Dimitri Ognibene Sasha Ondobaka Will Penny Giovanni Pezzulo Lisa Quattrocki Knight Francesco Rigoli Klaas Stephan Philipp Schwartenbeck And colleagues: Micah Allen Felix Blankenburg Andy Clark Peter Dayan Ray Dolan Allan Hobson Paul Fletcher Pascal Fries Geoffrey Hinton James Hopkins Jakob Hohwy Mateus Joffily Henry Kennedy Simon McGregor Read Montague Tobias Nolte Anil Seth Mark Solms Paul Verschure And many others Thank you