Attention, Uncertainty, and Free-Energy: Neuronal Simulations Supporting a Bayesian Understanding of Attention

1. 8th Biannual Scientific Meeting on Attention “RECA VIII” Attention, uncertainty and free-energy Karl Friston Abstract We suggested recently that attention can be understood as inferring the level of uncertainty or precision during hierarchical perception.  In this talk, I will try to substantiate this claim using neuronal simulations of directed spatial attention and biased competition.  These simulations assume that neuronal activity encodes a probabilistic representation of the world that optimises free-energy in a Bayesian fashion.  Because free-energy bounds surprise or the (negative) log evidence for internal models of the world, this optimisation can be regarded as evidence accumulation or (generalised) predictive coding.  Crucially, both predictions about the state of the world generating sensory data and the precision of those data have to be optimised.  Here, we show that if the precision depends on the states, one can explain many aspects of attention.  We illustrate this in the context of the Posner paradigm, using simulations to generate both psychophysical and electrophysiological responses.  These simulated responses are consistent with attentional bias or gating, competition for attentional resources, attentional capture and associated speed-accuracy tradeoffs.  Furthermore, if we present both attended and non-attended stimuli simultaneously, biased competition for neuronal representation emerges as a principled and straightforward property of Bayes-optimal perception.

2. “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 Richard Gregory Geoffrey Hinton From the Helmholtz machine to the Bayesian brain and self-organization Thomas Bayes Richard Feynman Hermann Haken

3. Overview Ensemble dynamics Entropy and equilibria Free-energy and surprise The free-energy principle Perception and generative models Hierarchies and predictive coding Perception Birdsong and categorization Simulated lesions Attention Uncertainty and precision Modeling the Posner paradigm Behavioral and ERP simulations

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

5. 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 entropyshould increase

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

7. 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. So what is free-energy?

8. What is free-energy? …free-energy is basically prediction error sensations – predictions = prediction error where small errors mean low surprise

9. More formally, Sensations External states in the world Internal states of the agent (m) Action Free-energy is a function of sensations and a proposal density over hidden causes and can be evaluated, given a generative model (Gibbs Energy) or likelihood and prior: So what models might the brain use?

10. Hierarchal models in the brain lateral Backward (modulatory) Forward (driving)

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

12. So how do prediction errors change predictions? sensory input Forward connections convey feedback Prediction errors Adjust hypotheses Predictions prediction Backward connections return predictions …by hierarchical message passing in the brain

13. David Mumford More formally, Synaptic activity and message-passing Forward prediction error Backward predictions Synaptic plasticity Synaptic gain cf Hebb's Law cf Predictive coding cf Rescorla-Wagner

14. 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 Predictions depend upon the precision of prediction errors

15. Overview Ensemble dynamics Entropy and equilibria Free-energy and surprise The free-energy principle Perception and generative models Hierarchies and predictive coding Perception Birdsong and categorization Simulated lesions Attention Uncertainty and precision Modeling the Posner paradigm Behavioral and ERP simulations

16. Making bird songs with Lorenz attractors Vocal centre Syrinx Sonogram Frequency causal states 0.5 1 1.5 time (sec) hidden states

17. Predictive coding and message passing 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

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

19. Hierarchical (itinerant) birdsong: sequences of sequences Neuronal hierarchy Syrinx sonogram Frequency (KHz) 0.5 1 1.5 Time (sec)

20. Simulated lesions and false inference percept LFP 60 40 20 Frequency (Hz) LFP (micro-volts) 0 -20 -40 no top-down messages LFP 60 40 20 no structural priors Frequency (Hz) LFP (micro-volts) 0 -20 -40 -60 no lateral messages LFP 60 40 20 no dynamical priors Frequency (Hz) LFP (micro-volts) 0 -20 -40 -60 0.5 1 1.5 0 500 1000 1500 2000 time (seconds) peristimulus time (ms)

21. Overview Perception Birdsong and categorization Simulated lesions Attention Uncertainty and precision Modeling the Posner paradigm Behavioral and ERP simulations first order predictions Attention and precision second order predictions

22. Forward prediction error Backward predictions precision and prediction error first order predictions (AMPA) second order predictions (NMDA)

23. stimuli A generative model of precision and attention target cue exogenous endogenous decay

24. 1.5 1 0.5 0 -0.5 -1 -1.5 100 200 300 400 500 600 stimuli time (ms) Predictive coding hidden causes target hidden states cue hidden causes Parietal cortex Extrastriate cortex Striate cortex

25. prediction and error hidden states prediction and error hidden states 1.5 2 1 2 1 0.5 1 1 0.5 0 0 0 0 -0.5 -0.5 -1 -1 -1 -1 -1.5 -2 -1.5 -2 100 200 300 400 500 600 100 200 300 400 500 600 100 200 300 400 500 600 time (ms) time (ms) time (ms) Valid cue Invalid cue Inference with valid and invalid cues hidden causes hidden causes 1.5 2 1.5 1 1 1 stimuli 0.5 0.5 0 0 0 -0.5 -0.5 -1 -1 -1 -1.5 -2 -1.5 100 200 300 400 500 600 100 200 300 400 500 600 100 200 300 400 500 600 time (ms) time (ms) time (ms) 100 200 300 400 500 600 time (ms)

26. validity costs and benefits 400 350 Reaction time (ms) 300 invalid neutral valid 250 Valid and invalid cues 100 200 300 400 500 600 time (ms) Reaction times and conditional confidence

27. Simulated timing effects Empirical timing effects Invalid Invalid Neutral Neutral Valid Valid 100 200 300 400 500 600 time (ms) Behavioural simulations Foreperiod Posner et al, (1978)

28. Valid Invalid Electrophysiological simulations 3 3 0.01 0.01 prediction errors (sensory states) prediction errors (hidden states) 2 2 0.005 0.005 1 1 0 0 0 0 -0.005 -0.005 -1 -1 -2 -2 -0.01 -0.01 -200 -200 -100 -100 0 0 100 100 200 200 300 300 -200 -200 -100 -100 0 0 100 100 200 200 300 300 Peristimulus time (ms) Peristimulus time (ms) Peristimulus time (ms) Peristimulus time (ms) N1 P1 - 2 V + P3 Mangun and Hillyard (1991) 0 200 400 600 Peristimulus time (ms)

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