2. Abstract How much about our interactions 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 that – in the context of perception – corresponds to Bayes-optimal predictive coding (that suppresses exteroceptive prediction errors) and – in the context of action – reduces to classical motor reflexes (that suppress proprioceptive prediction errors). We will look at some of the phenomena that emerge from this single principle; such as the perceptual encoding of sensory trajectories (bird song and action perception). These perceptual abilities rest upon prior beliefs about the world – but where do these beliefs come from? I will finish by discussing recent proposals about the nature of prior beliefs and how they underwrite the active sampling of the sensorium. Put simply, to minimise surprising states of the world, it is necessary to sample inputs that minimise uncertainty about the causes of sensory input. When this minimisation is implemented via prior beliefs – about how we sample the world – the resulting behaviour is remarkably reminiscent of searches of the sort seen in exploration and visual searches. Free energy and active inference Karl Friston University College London The Statistical Physics of Inference and Control Theory Granada, Spain September 12-16, 2012

3. “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 From the Helmholtz machine to the Bayesian brain and self-organization Hermann Haken Richard Gregory Hermann von Helmholtz

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

5. Hidden states in the worldInternal states of the agent Sensations Action External states Fluctuations Posterior expectations The basic ingredients

6. Self organisation and the principle of least action Maximum entropy principle The principle of least free energy (minimising surprise) Minimum entropy principle Ergodic theorem

7. How can we minimize surprise (prediction error)? Change sensations sensations – predictions Prediction error Change predictions Action Perception …action and perception minimise free energy

8. Prior distribution Posterior distribution Likelihood distribution temperature Action as inference – the “Bayesian thermostat” 20406080100120 Perception: Action:

9. Hidden states in the worldInternal states of the agent Sensations Action External states Fluctuations Posterior expectations How might the brain minimise free energy (prediction error)? By using predictive coding (and reflexes)

10. Free energy minimisationGenerative modelPredictive coding with reflexes

11. Expectations: Predictions: Prediction errors: Generative model Model inversion (inference) A simple hierarchy Outward prediction stream Inward error stream From models to perception

12. occipital cortex 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 David Mumford Predictive coding with reflexes Action Perception

13. 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 optimize predictions Action makes predictions come true (and minimizes surprise)

14. Generating bird songs with attractors Syrinx HVC time (sec) Frequency Sonogram 0.511.5 causal states hidden states

15. 102030405060 -5 0 5 10 15 20 prediction and error 102030405060 -5 0 5 10 15 20 hidden states Backward predictions Forward prediction error 102030405060 -10 -5 0 5 10 15 20 causal states Predictive coding stimulus 0.20.40.60.8 2000 2500 3000 3500 4000 4500 5000 time (seconds)

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

17. Prior distribution temperature Action as inference – the “Bayesian thermostat” 20406080100120 Perception: Action:

18. visual input proprioceptive input Action with point attractors Descending proprioceptive predictions Exteroceptive predictions

19. 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

20. Where do I expect to look?

21. saliencevisual inputstimulussampling Sampling the world to minimise uncertainty Perception as hypothesis testing – saccades as experiments Free energy principleminimise uncertainty

22. Hidden states in the worldInternal states of the agent Sensations Action External states Fluctuations Posterior expectations Prior expectations

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

24. Saccadic fixation and salience maps Visual samples Conditional expectations about hidden (visual) states And corresponding percept Saccadic eye movements Hidden (oculomotor) states

25. Thank you And thanks to collaborators: Rick Adams Andre Bastos Sven Bestmann Jean Daunizeau Harriet Brown Lee Harrison Stefan Kiebel James Kilner Jérémie Mattout Rosalyn Moran Will Penny 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

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

27. 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…