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How much about our interaction with – and experience of – our world can be deduced from basic principles? This talk reviews recent attempts to understand the self-organised behaviour of embodied agents, like ourselves, as satisfying basic imperatives for sustained exchanges with the environment. In brief, one simple driving force appears to explain many aspects of action and perception. This driving force is the minimisation of surprise or prediction error. In the context of perception, this corresponds to Bayes-optimal predictive coding that suppresses exteroceptive prediction errors. In the context of action, motor reflexes can be seen as suppressing proprioceptive prediction errors. We will look at some of the phenomena that emerge from this scheme, such as hierarchical message passing in the brain and the perceptual inference that ensues. I hope to illustrate these points using simple simulations of perception, action and action observation.. Life as we know it Karl Friston, University College London

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Overview The statistics of life Markov blankets and ergodic systems simulations of a primordial soup The anatomy of inference graphical models and predictive coding canonical microcircuits Action and perception perceptual omission responses simulations of action observation

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“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

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

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Phase-boundary The Fokker-Planck equation (a.k.a. the Kolmogorov forward equation) describes the evolution of the probability density over states This density depends upon flow, which can always be expressed in terms of curl-free and divergence-free components – by the Helmholtz decomposition (a.k.a. the fundamental theorem of vector calculus) lemma : any ergodic random dynamical system (m) that possesses a Markov blanket will appear to actively maintain its structural and dynamical integrity

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This means that action will appear to maximize Bayesian model evidence – and the entropy (dispersion) of the internal states and their Markov blanket. This is exactly consistent with the good regulator theorem (every good regulator is a model of its environment) External statesInternal states But what about the Markov blanket?

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In summary, for any ergodic random dynamical system: 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. Active inference : internal states appear to infer the hidden causes of sensory states (by maximizing Bayesian evidence). By the circular causality induced by the Markov blanket, sensory states depend on active states, rendering inference active or embodied. Autopoiesis : Because active states change – but are not changed by – external states they will appear to minimize the dispersion (entropy) of internal states and their Markov blanket. This means active states will appear to maintain the structural and functional integrity of the Markov blanket.

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Overview The statistics of life Markov blankets and ergodic systems simulations of a primordial soup The anatomy of inference graphical models and predictive coding canonical microcircuits Action and perception perceptual omission responses simulations of action observation

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

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Element Adjacency matrix 20406080100120 20 40 60 80 100 120 Markov Blanket Hidden states Sensory states Active states Internal states Markov Blanket = [ B · [eig(B) > τ]] Markov blanket matrix encodes the children, parents and parents of children Finding the (principal) Markov blanket

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Active inference – a prebiotic stimulation experiment

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Autopoiesis and oscillator death – a prebiotic lesion experiment

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Overview The statistics of life Markov blankets and ergodic systems simulations of a primordial soup The anatomy of inference graphical models and predictive coding canonical microcircuits Action and perception perceptual omission responses simulations of action observation

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“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

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The principle of least free energy (and action), Bayesian inference and predictive coding minimising prediction error = maximising Bayesian model evidence surprisedivergence entropyenergy prediction error complexity

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How can we minimize free energy (prediction error)? Change sensations sensations – predictions Prediction error Change predictions Action Perception

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A simple hierarchy Predictions and generative models whatwhere Sensory fluctuations

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Generative model Model inversion (inference) A simple hierarchy Expectations: Predictions: Prediction errors: Descending predictions Descending predictions Ascending prediction errors From models to perception and predictive coding

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Haeusler and Maass: Cereb. Cortex 2006;17:149-162Bastos et al: Neuron 2012; 76:695-711 Canonical microcircuits for predictive coding

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

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

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Overview The statistics of life Markov blankets and ergodic systems simulations of a primordial soup The anatomy of inference graphical models and predictive coding canonical microcircuits Action and perception perceptual omission responses simulations of action observation

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Perceptual inference and sequences of sequences Syrinx Neuronal hierarchy Time (sec) Frequency (KHz) sonogram 0.511.5

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omission and violation of predictions Stimulus but no percept Percept but no stimulus Frequency (Hz) stimulus (sonogram) 2500 3000 3500 4000 4500 Time (sec) Frequency (Hz) percept 0.511.5 2500 3000 3500 4000 4500 5000 500100015002000 -100 -50 0 50 100 peristimulus time (ms) LFP (micro-volts) ERP (error) without last syllable Time (sec) percept 0.511.5 500100015002000 -100 -50 0 50 100 peristimulus time (ms) LFP (micro-volts) with omission

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Overview The statistics of life Markov blankets and ergodic systems simulations of a primordial soup The anatomy of inference graphical models and predictive coding canonical microcircuits Action and perception perceptual omission responses simulations of action observation

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proprioceptive input Action with point attractors visual input Descending proprioceptive predictions Descending proprioceptive predictions

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00.20.40.60.811.21.4 0.4 0.6 0.8 1 1.2 1.4 action position (x) position (y) 00.20.40.60.811.21.4 observation position (x) Heteroclinic cycle (central pattern generator) Descending proprioceptive predictions Descending proprioceptive predictions

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“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

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Thank you And thanks to collaborators: Rick Adams Andre Bastos Sven Bestmann Harriet Brown Jean Daunizeau Mark Edwards Xiaosi Gu Lee Harrison Stefan Kiebel James Kilner Jérémie Mattout Rosalyn Moran Will Penny Lisa Quattrocki Knight Klaas Stephan And colleagues: Andy Clark Peter Dayan Jörn Diedrichsen Paul Fletcher Pascal Fries Geoffrey Hinton James Hopkins Jakob Hohwy Henry Kennedy Paul Verschure Florentin Wörgötter And many others

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Perception and Action: The optimisation of neuronal and neuromuscular activity to suppress prediction errors (or free- energy) based on generative models of sensory data. Learning and attention: The optimisation of synaptic gain and efficacy over seconds to hours, to encode the precisions of prediction errors and causal structure in the sensorium. This entails suppression of free-energy over time. Neurodevelopment: Model optimisation through activity- dependent pruning and maintenance of neuronal connections that are specified epigenetically Evolution: Optimisation of the average free-energy (free-fitness) over time and individuals of a given class (e.g., conspecifics) by selective pressure on the epigenetic specification of their generative models. Time-scale Free-energy minimisation leading to…

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Searching to test hypotheses – life as an efficient experiment Free energy principleminimise uncertainty

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