2. 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 and its perception. Hierarchal brain architectures and the Bayesian brain Karl Friston, University College London

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

4. “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 Richard Gregory Hermann von Helmholtz Ross Ashby

5. Minimizing prediction error Change sensations sensations – predictions Prediction error Change predictions Action Perception

6. Prior distribution Posterior distribution Likelihood distribution temperature Action as inference – the ‘Bayesian thermostat’ 20406080100120 Perception Action

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

8. A simple hierarchy Generative models whatwhere Sensory fluctuations

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

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

11. frontal eye fields geniculate visual cortex retinal input pons oculomotor signals Errors (superficial pyramidal cells) Expectations (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

12. superficial deep Errors (superficial pyramidal cells) Expectations (deep pyramidal cells) 020406080100120 0 0.05 0.1 0.15 0.2 0.25 0.3 020406080100120 0 1 2 x 10 -4 frequency (Hz) 020406080100 0 0.5 1 1.5 2 2.5 3 spectral power V1 Autospectra (SPC) 020406080100 0 2 4 6 8 10 12 14 spectral power Forward transfer function 020406080100 0 5 10 15 20 frequency (Hz) spectral power V4 Autospectra (DPC) 020406080100 0 1 2 3 4 5 6 frequency (Hz) spectral power Backward transfer function

13. Errors (superficial pyramidal cells) Expectations (deep pyramidal cells) Linear or driving connections Nonlinear or modulatory connections superficial deep NMDA receptor density

14. 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)

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

16. Generating bird songs with attractors Syrinx HVC time (sec) Frequency Sonogram 0.511.5 Hidden causesHidden states

17. 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)

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

19. Perceptual inference and sequences of sequences SyrinxNeuronal hierarchy Time (sec) Frequency (KHz) sonogram 0.511.5 Prediction errorSensory statesHidden states

20. 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 500100015002000 -100 -50 0 50 100 peristimulus time (ms) LFP (micro-volts) ERP (prediction error) without last syllable Time (sec) percept 0.511.5 500100015002000 -100 -50 0 50 100 peristimulus time (ms) LFP (micro-volts) with omission

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

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

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

24. 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

25. “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

26. 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

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

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

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

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

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

32. 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…

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

34. Epilogue (what we have not covered)

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

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

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