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. 8th Biannual Scientific Meeting on Attention “RECA VIII” Attention, uncertainty and free-energy Karl Friston

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

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

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

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 entropy should increase

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

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? ?

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

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? Action External states in the world Internal states of the agent ( m ) Sensations More formally,

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

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

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

Backward predictions Forward prediction error Synaptic activity and message-passing Synaptic plasticitySynaptic gain David Mumford More formally, cf Hebb's Lawcf Rescorla-Wagnercf Predictive coding

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

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

Making bird songs with Lorenz attractors Syrinx Vocal centre time (sec) Frequency Sonogram causal states hidden states

prediction and error hidden states Backward predictions Forward prediction error causal states Predictive coding and message passing stimulus time (seconds)

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

Hierarchical (itinerant) birdsong: sequences of sequences Syrinx Neuronal hierarchy Time (sec) Frequency (KHz) sonogram

Frequency (Hz) percept Frequency (Hz) no top-down messages time (seconds) Frequency (Hz) no lateral messages LFP (micro-volts) LFP LFP (micro-volts) LFP peristimulus time (ms) LFP (micro-volts) LFP Simulated lesions and false inference no structural priors no dynamical priors

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

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

cue target stimuli A generative model of precision and attention exogenousendogenousdecay

stimuli Predictive coding time (ms) Striate cortex Extrastriate cortex Parietal cortex hidden causes hidden states cue target hidden causes

validity costs and benefits Reaction time (ms) validinvalidneutral Reaction times and conditional confidence time (ms) Validand invalid cues

Empirical timing effects Invalid Neutral Valid Simulated timing effects Invalid Neutral Valid Posner et al, (1978) Behavioural simulations time (ms) Foreperiod

prediction errors (sensory states) prediction errors (hidden states) Mangun and Hillyard (1991) Valid Invalid  V + Peristimulus time (ms) P1 P3 N Peristimulus time (ms) -200 Peristimulus time (ms) Peristimulus time (ms) -200 Peristimulus time (ms) Electrophysiological simulations

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