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 equilibriaFree-energy and surprise

The free-energy principle Perception and generative modelsHierarchies and predictive coding

Perception Birdsong and categorizationSimulated lesions

Attention Uncertainty and precisionModeling the Posner paradigmBehavioral and ERP simulations

tem

pera

ture

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?

A

( )s g

…entropy is just average surprise

Low surprise (we are usually here)

High surprise (I am never here)

0

( ) ( | ) ln ( | )

ln ( | )

H L

L

T

dt t p m p m d

p s m

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?

?

( ) ( )F Lt t

( )s g

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?

( , ) ( ) (ln )F Gq qs Energy Entropy q E E

( , ) ln ( , | ) ln ( | , ) ln ( | )s p s m p s m p m G

Action

( )( ) ss g

argmin ( , )a

a s F

External states in the world

Internal states of the agent (m)

Sensations

argmin ( , )s

F( )( , )a f

More formally,

Backward(modulatory)

Forward(driving)

lateral

)1(~x )1(

s

)2((2)

(1)

)2(~x

)2(~v

)1(~v

( 1) ( ) ( , )

( ) ( ) ( , )D

i i v i

i i x i

v g

x f

{ ( ), ( ), , }x t v t

Hierarchal models in the brain

( , )x v ( )

( )Synaptic gain

Synaptic activity Synaptic efficacy

Activity-dependent plasticity

Functional specialization

Attentional gain

Enabling of plasticity

( ) ( )( )

G

Perception and inference Learning and memory

The proposal density and its sufficient statistics

( ) ( )( )

G

( ) ( )( )

( ) ( )( )

GD

GD

x xx

v vv

( | ) ( , ( ))q NLaplace 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

( , ) ( , ) ( ) ( ) ( , 1)

( , ) ( , ) ( ) ( )

D

D

v i v i i T i v iv

x i x i i T ix

( ) ( )12 ( ( ( )))T

i itr R ( )

i

Ti

Synaptic plasticity

( ,1)x

( ,1)x

( ,1)v

( ,2)v

( )s t

( ,1)v( ,2)x

( ,2)x

( ,2)v

( ,3)v

Synaptic gain

David Mumford

More formally,

cf Hebb's Law cf Rescorla-Wagnercf Predictive coding

( , ) ( , ) ( , ) ( , ) ( , 1) ( )

( , ) ( , ) ( , ) ( , ) ( , ) ( )

( )

( )

v i v i v i v i v i i

x i x i x i x i x i i

g

f

D

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 equilibriaFree-energy and surprise

The free-energy principle Perception and generative modelsHierarchies and predictive coding

Perception Birdsong and categorizationSimulated lesions

Attention Uncertainty and precisionModeling the Posner paradigmBehavioral and ERP simulations

Making bird songs with Lorenz attractors

SyrinxVocal centre

time (sec)

Freq

uenc

y

Sonogram

0.5 1 1.5causal states

hidden states

1

2

vv

v

(1) (1)2 1

(1) (1) (1) (1) (1) (1)1 1 3 1 2

(1) (1) (1) (1)1 2 2 3

18 18

2

2

x x

f v x x x x

x x v x

( )x

( )x

( )v( )s t

( )v

10 20 30 40 50 60-5

0

5

10

15

20prediction and error

10 20 30 40 50 60-5

0

5

10

15

20hidden states

Backward predictions

Forward prediction error

10 20 30 40 50 60-10

-5

0

5

10

15

20

causal states

Predictive coding and message passing

stimulus

0.2 0.4 0.6 0.82000

2500

3000

3500

4000

4500

5000

time (seconds)

Perceptual categorization

Freq

uenc

y (H

z) Song a

time (seconds)

Song b Song c

( )1v

( )2v

Hierarchical (itinerant) birdsong: sequences of sequences

SyrinxNeuronal hierarchy

Time (sec)

Freq

uenc

y (K

Hz)

sonogram

0.5 1 1.5

(1)1(1)2

v

v

(2) (2)2 1

(2) (2) (2) (2) (2)1 3 1 2

(2) (2) (2)81 2 33

18 18

32 2

2

x x

f x x x x

x x x

(1) (1)2 1

(1) (1) (1) (1) (1) (1)1 1 3 1 2

(1) (1) (1) (1)1 2 2 3

(1)1(1) 2

(1)23

18 18

2

2

x x

f v x x x x

x x v x

sxg

sx

(2) (1)(2) 2 1

(2) (1)3 2

x vg

x v

Freq

uenc

y (H

z)

percept

Freq

uenc

y (H

z)no top-down messages

time (seconds)

Freq

uenc

y (H

z)

no lateral messages

0.5 1 1.5

-40

-20

0

20

40

60

LFP

(micr

o-vo

lts)

LFP

-60

-40

-20

0

20

40

60

LFP

(micr

o-vo

lts)

LFP

0 500 1000 1500 2000-60

-40

-20

0

20

40

60

peristimulus time (ms)

LFP

(micr

o-vo

lts)

LFP

Simulated lesions and false inference

no structural priors

no dynamical priors

Overview

( )( )ig first order predictions

second order predictions( )( )i

Attention and precision

Perception Birdsong and categorizationSimulated lesions

Attention Uncertainty and precisionModeling the Posner paradigmBehavioral and ERP simulations

precision and prediction error

( , ) ( , ) ( , ) ( , 1) ( )( )( ( ))v i v i x i v i ig first order predictions (AMPA)

second order predictions (NMDA)

( )s t

( ,1)v( )( )ig

( )( )i

Backward predictions

( , 1)v i

( , )v i

( )( )ig

( )( )i

Forward prediction error

( ,1)x

( ,1)x

( ,1)v

( ,2)v

( , )v i

( ,2)x

( ,2)x

( ,2)v

( ,3)v

cue

target

stimuli

A generative model of precision and attention

exogenous endogenous decay

(1) ( ,1)

(1)(1) (1) (1) (1) (1)1 1 1 1

4 4 2 32(1)

(1)

(1) (1) ( ,2)

(1)

(1)( ,1)

(1)

( ,2)

1 1 1

1 1 1

exp( )~ (0, )

( ) 1~ (0, )

exp

N

N

Lv

C

R

LL R C

R

Lv

C

R

Lv

v

s

s s v

s

xx v v v x

x

v

v v

v

x

I

(1)( )Rx

stimuli

Predictive coding

-1.5

-1

-0.5

0

0.5

1

1.5

100 200 300 400 500 600time (ms)

Striate cortex

Extrastriate cortex

Rs

( ,1)vv

Parietal cortex

Rs

( ,1)vv

Cs

( ,1)vv

Ls

( ,1)vv

( ,1)vC

( , )v RC

hidden causes

hidden states

cue

target

hidden causes

( ,1)xR

( ,1)xR

( ,1)xL

( ,1)xL

( ,1)vL

( ,2)vL

( ,1)vR

( ,2)vR

( ,1)xR

( ,1)xR

( ,1)xL

( ,1)xL

-1.5

-1

-0.5

0

0.5

1prediction and error

-2

-1

0

1

2hidden states

-1.5

-1

-0.5

0

0.5

1

1.5hidden causes

Valid cue

100 200 300 400 500 600time (ms)

100 200 300 400 500 600time (ms)

100 200 300 400 500 600time (ms)

( ,1)x

( ,1)v

(1)( )g

stimuli

-1.5

-1

-0.5

0

0.5

1

1.5prediction and error

-2

-1

0

1

2hidden states

-1.5

-1

-0.5

0

0.5

1

1.5hidden causes

100 200 300 400 500 600-2

-1

0

1

2

time (ms)

Inference with valid and invalid cues

Invalid cue

100 200 300 400 500 600time (ms)

100 200 300 400 500 600time (ms)

100 200 300 400 500 600time (ms)

validity costs and benefits

250

300

350

400

Reac

tion

time

(ms)

validinvalid neutral

Reaction times and conditional confidence

100 200 300 400 500 600

time (ms)

Valid and invalid cues

Empirical timing effects

Invalid

Neutral

Valid

Simulated timing effects

Invalid

Neutral

Valid

Posner et al, (1978)

Behavioural simulations

100 200 300 400 500 600time (ms)

Foreperiod

prediction errors (sensory states)

prediction errors (hidden states)

Mangun and Hillyard (1991)

ValidInvalid

0 200 400 600

-2 V

+Peristimulus time (ms)

P1

P3

N1

-100 0 100 200 300-2

-1

0

1

2

3

-0.01

-0.005

0

0.005

0.01

-200

-100 0 100 200 300

Peristimulus time (ms)-200

Peristimulus time (ms)-100 0 100 200 300

-2

-1

0

1

2

3

-0.01

-0.005

0

0.005

0.01

-200

-100 0 100 200 300

Peristimulus time (ms)-200

( ,1)vR

( ,1)xR

Peristimulus time (ms)

( ,1)vR

( ,1)vR

( ,1)xR

( ,1)xR

Electrophysiological simulations

Thank you

And thanks to collaborators:

Rick AdamsJean DaunizeauHarriet Feldman

Lee HarrisonStefan KiebelJames Kilner

Jérémie MattoutKlaas Stephan

And colleagues:

Peter DayanJörn DiedrichsenPaul Verschure

Florentin Wörgötter

And many others