1. Abstract Predictive coding models and the free-energy principle, suggests that cortical activity in sensory brain areas reflects the precision of prediction errors and not just the sensory evidence or prediction errors per se. If we assume that neuronal activity encodes a probabilistic representation of the world that optimizes free-energy in a Bayesian fashion, then, because free-energy bounds surprise or the (negative) log-evidence for internal models of the world, this optimization can be regarded as evidence accumulation or (generalized) predictive coding. Crucially, both predictions about the state of the world generating sensory data and the precision of those data have to be optimized. In other words, we have to make predictions (test hypotheses) about the content of the sensorium and predict our confidence in those hypotheses. I hope to demonstrate the meta-representational aspect of inference using simulations of visual searches and action selection - to illustrate their nature and promote discussion about its role in high-order cognition. November 29th 4:30 – 6:00pm Old Library Karl Friston Meta-cognition, prediction, precision (Discussant, Andreas Roepstorff, Aarhus) SEMINARS ON META-COGNITION, 2012–2013

2. The basic idea: active inference and free energy Beliefs about beliefs: beliefs about uncertainty Beliefs about beliefs: beliefs about precision and agency

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 What we need to explain: how do we minimise the dispersion of sensory states (homoeostasis)?

6. The principle of least action The principle of least free energy (minimising surprise) Self organisation Ergodic theorem Bayesian inference Maximum entropy principle

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. Attention 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. Beliefs about beliefs: beliefs about uncertainty Perception as hypothesis testing – action as experiments But how do we think action will change our beliefs? Searching, salience and saccades

15. Where do I expect to look?

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

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

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

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

20. Beliefs about beliefs: beliefs about precision If beliefs cause movement, how can I move when sensory evidence compels me to believe that I am not moving? Sensory attenuation, illusions and agency

21. Generative process Generative model Making your own sensations

22. Motor reflex arc thalamus sensorimotor cortex prefrontal cortex descending predictions ascending prediction errors descending modulation

25. 102030405060 -0.5 0 0.5 1 1.5 2 hidden states Force matching illusion 102030405060 -0.5 0 0.5 1 1.5 2 prediction and error Time (bins) Sensory attenuation 102030405060 -0.5 0 0.5 1 1.5 hidden causes Time (bins) 102030405060 -0.5 0 0.5 1 1.5 Time (bins) perturbation and action

26. 00.511.522.53 0 0.5 1 1.5 2 2.5 3 External (target) force Self-generated(matched) force External (target) force Self-generated(matched) force SimulatedEmpirical (Shergill et al) Failures of sensory attenuation, with compensatory increases in non-sensory precision

27. A failure of sensory attenuation and delusions of control 102030405060 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 prediction and error Time (bins) 102030405060 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 hidden states Time (bins) 102030405060 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 hidden causes Time (bins) 102030405060 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 Time (bins) perturbation and action

28. Thank you And thanks to collaborators: Rick Adams Andre Bastos Sven Bestmann Jean Daunizeau Mark Edwards 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

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

30. 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…