Free energy and active inference Karl Friston, University College London

1. Free energy and active inference Karl Friston, University College London 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 implications for the anatomy of this active inference – in terms of large-scale anatomical graphs and canonical microcircuits – and then turn to some examples of active inference – such as perceptual categorisation, action perception and visual searches.

2. Overview The free-energy principleaction and perception predictive coding with reflexes The anatomy of inference graphical models canonical microcircuits Some examples perceptual categorization omission responses action observation visual searches

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 Hermann von Helmholtz Richard Gregory Geoffrey Hinton From the Helmholtz machine to the Bayesian brain and self-organization Thomas Bayes Richard Feynman Ross Ashby

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

5. The principle of least free energy (and minimising surprise) Self organisation and the principle of least action Ergodic theorem surprise divergence energy entropy prediction error complexity minimising surprise = maximising Bayesian model evidence

6. How canwe minimize free energy (prediction error)? sensations – predictions Prediction error Action Perception Change sensations Change predictions

7. Action as inference – the “Bayesian thermostat” Posterior distribution Prior distribution Likelihood distribution 20 40 60 80 100 120 temperature Perception Action

8. Overview The free-energy principleaction and perception predictive coding with reflexes The anatomy of inference graphical models canonical microcircuits Some examples perceptual categorization omission responses action observation visual searches

9. Generative models what where A simple hierarchy Sensory fluctuations

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

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

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

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. Overview The free-energy principleaction and perception predictive coding with reflexes The anatomy of inference graphical models canonical microcircuits Some examples perceptual categorization omission responses action observation visual searches

15. Generating bird songs with attractors HVC Syrinx Sonogram Frequency 0.5 1 1.5 Hidden causes Hidden states time (sec)

16. Predictive coding prediction and error 20 15 10 5 0 -5 10 20 30 40 50 60 Backward predictions causal states 20 15 stimulus 10 5000 5 4500 Forward prediction error 0 4000 -5 3500 -10 10 20 30 40 50 60 3000 hidden states 20 2500 2000 15 0.2 0.4 0.6 0.8 time (seconds) 10 5 0 -5 10 20 30 40 50 60

17. Perceptual categorization Song a Song b Song c Frequency (Hz) time (seconds)

18. Sequences of sequences Neuronal hierarchy Syrinx sonogram Frequency (KHz) 0.5 1 1.5 Time (sec)

19. 4500 4000 3500 Frequency (Hz) 3000 stimulus (sonogram) without last syllable 2500 5000 omission and violation of predictions 4500 4000 3500 Frequency (Hz) 3000 percept percept 2500 0.5 1 1.5 0.5 1 1.5 Time (sec) Time (sec) ERP (error) with omission 100 100 50 50 Stimulus but no percept 0 0 LFP (micro-volts) LFP (micro-volts) Percept but no stimulus -50 -50 -100 -100 500 1000 1500 2000 500 1000 1500 2000 peristimulus time (ms) peristimulus time (ms)

20. Overview The free-energy principleaction and perception predictive coding with reflexes The anatomy of inference graphical models canonical microcircuits Some examples perceptual categorization omission responses action observation visual searches

21. Action as inference – the “Bayesian thermostat” Prior distribution 20 40 60 80 100 120 temperature Perception: Action:

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

23. Heteroclinic cycle (central pattern generator) Descending proprioceptive predictions action observation 0.4 0.6 0.8 position (y) 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 position (x) position (x)

24. Overview The free-energy principleaction and perception predictive coding with reflexes The anatomy of inference graphical models canonical microcircuits Some examples perceptual categorization omission responses action observation visual searches

25. If percepts are hypotheses, where do we look for evidence? Richard Gregory

26. Sampling the world to minimise uncertainty Free energy minimisation minimise uncertainty visual input stimulus salience sampling Perception as hypothesis testing – saccades as experiments

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

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

29. Hermann von Helmholtz “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

30. 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

31. Time-scale Free-energy minimisation leading to… 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.

32. Searching to test hypotheses – life as an efficient experiment Free energy principle minimise uncertainty

33. Epilogue (what we have not covered)

34. Posterior beliefs and sufficient statistics Learning and memory Perception and inference Learning and memory Perception and inference Synaptic activity Synaptic efficacy Synaptic gain Attention and affordance Sensory attenuation Attention and precision

35. Fokker-Planck equation = ensemble dynamics Random dynamical attractors and ergodic theorem (path integral formulations and principle of least action) The free energy principle Discrete formulations and Markovian processes (optimal decision theory) Continuous formulations and dynamical systems theory (self-organised criticality) Variational Bayes = ensemble learning Generalized Bayesian filtering = predictive coding

36. Sleeping and dreaming (complexity minimisation and synaptic homoeostasis) Predictive coding and embodied cognition (philosophy) The free energy principle Interoception and predictive coding (emotional valence and self-awareness) Neuropsychiatry (false inference and failures of sensory attenuation)