Abstract This presentation will look at action, perception and cognition as emergent phenomena under a unifying perspective: This Helmholtzian perspective regards the brain as a (generative) model of its environment. The imperative for any brain is then to optimize a free energy bound on the (Bayesian) evidence for its model of the world. We will see that this is not just mandated for the brain but for any self-organizing system that resists a natural tendency to disorder in a changing environment. More specifically, maximizing Bayesian evidence leads in a fairly straightforward way to an understanding of action as active inference, and perception in terms of predictive coding. I hope to illustrate these points using simulations of perceptual categorization and action observation. Free energy: from Feynman to Freud Karl Friston University College London

“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” - Hermann Ludwig Ferdinand von Helmholtz Thomas Bayes Geoffrey Hinton Richard Feynman From the Bayesian brain to free energy Sigmund Freud Richard Gregory

Overview Ensemble dynamics Entropy and equilibria Free-energy and surprise Free-energy principle Action and perception Hierarchies and generative models Perception Birdsong and categorization False inference Action Active inference Action observation

temperature What is the difference between a snowflake and a bird? Phase-boundary …a bird can move (to avoid surprises)

What is the difference between snowfall and a flock of birds? Ensemble dynamics, clumping and swarming …birds (biological agents) stay in the same place They resist the second law of thermodynamics, which says that their entropy should increase

This means biological agents must self-organize to minimize surprise - to ensure they occupy a limited number of states (cf homeostasis). But what is the entropy? …entropy is just average surprise Low surprise (we are usually here) High surprise (I am never here)

But there is a small problem… agents cannot measure their surprise But they can measure their free-energy, which is always bigger than surprise This means agents should minimize their free-energy ?

Change sensory input sensations – predictions Prediction error Change predictions Action Perception action and perception to suppress prediction errors and minimise surprise What is free-energy? …free-energy is basically prediction error

Action to minimise a bound on surprisePerception to optimise the bound Action External states in the world Internal states of the agent ( m ) Sensations More formally, Free-energy rests a generative model comprising a likelihood and prior: so what models might the brain use?

Backward (modulatory) Forward (driving) lateral Hierarchal models in the brain And their hidden states, causes and parameters

Synaptic gain Synaptic activity Synaptic efficacy Activity-dependent plasticity Functional specialization Attentional gain Enabling of plasticity Perception and inference Learning and memory The proposal density and its sufficient statistics Laplace approximation: Attention and salience

Backward predictions Forward prediction error Synaptic activity and message-passing David Mumford Predictive coding

Adjust hypotheses sensory input Backward connections return predictions …by hierarchical message passing in the brain prediction Forward connections convey feedback Perceptual inference hierarchical message passing Prediction errors Predictions

Summary Biological agents resist the second law of thermodynamics They must 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 optimise predictions Action makes predictions come true (and minimises surprise)

Overview Ensemble dynamics Entropy and equilibria Free-energy and surprise Free-energy principle Action and perception Hierarchies and generative models Perception Birdsong and categorization False inference Action Active inference Action observation

Generating bird songs with attractors Syrinx Vocal centre time (sec) Frequency Sonogram causal states hidden states

prediction and error hidden states Backward predictions Forward prediction error causal states Perception and message passing stimulus time (seconds)

Perceptual categorization Frequency (Hz) Song a time (seconds) Song bSong c

Hierarchical (deep) birdsong: sequences of sequences Syrinx Neuronal hierarchy Time (sec) Frequency (KHz) sonogram

Frequency (Hz) percept Frequency (Hz) no top-down messages time (seconds) Frequency (Hz) no lateral messages LFP (micro-volts) LFP LFP (micro-volts) LFP peristimulus time (ms) LFP (micro-volts) LFP Simulated lesions and false inference no structural priors no dynamical priors

Overview Ensemble dynamics Entropy and equilibria Free-energy and surprise Free-energy principle Action and perception Hierarchies and generative models Perception Birdsong and categorization False inference Action Active inference Action observation

predictions Reflexes to action action dorsal root ventral horn sensory error Active inference Action can only suppress (sensory) prediction error. This means action fulfils our (sensory) predictions

Proprioceptive forward model Motor commands Easy inverse problem Proprioceptive cuesVisual cues Visual forward model Exteroception Classical reflex arc Proprioception Sensorimotor contingencies and schema

Descending proprioceptive predictions visual input proprioceptive input Action, predictions and priors Exteroceptive predictions

Autonomous behavior and action-observation action position (x) position (y) observation position (x) Descending predictions hidden attractor states (Lotka-Volterra)

Proprioceptive forward model Easy inverse problem Proprioceptive cuesVisual cues Speech and behaviour Visceral cues Exteroceptive forward model Interoceptive forward model suppression excitation Conscious (reportable) Unconscious (not reportable) Freud and free energy

Thank you And thanks to collaborators: Rick Adams Sven Bestmann Jean Daunizeau Harriet Brown Lee Harrison Stefan Kiebel James Kilner Jérémie Mattout Klaas Stephan And colleagues: Peter Dayan Jörn Diedrichsen Paul Verschure Florentin Wörgötter And many others

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…