K C Y W D K D O P E D B A I Q S D F M K C N F A E …courses.cs.washington.edu/courses/cse528/05wi/Shadlen-slides.pdfDirection-Discrimination Task Reward for correct choice ... Positive

A Neural Mechanism for Decision MakingK C Y W D K D O P E D B A I Q S D F M K C N F A E O I E N C V N SE N C H P D N C O E N A S H Q E N D N C K R N D N Q I O M Z C P Q

What is a decision?

• A commitment to a proposition or selectionof an action

• Based on– evidence– prior knowledge– payoff

Why study decisions?

• They are a model of higher brain function• They are experimentally tractable

– Combined behavior and physiology in rhesusmonkeys

Direction-Discrimination TaskReaction-time version

Direction-Discrimination TaskDirection-Discrimination TaskReaction-time version



Direction-Discrimination Task

Reward for correct choice

Direction-Discrimination TaskReaction-time version

Psychometric function: Accuracy

Chronometric function: Speed

Rea

ctio

n tim

e [m

s]

Information is coded by spikes

Hubel, 1988 “Eye, brain and vision”

Sensory “Evidence”

Albright et al., 1984 J. Neurophysiol.

100 ms

120

60

0

60

Spikes/sec

120

60

0

Spatially-selective, eye movement-related,persistent activity in area LIP

LIP activity during directiondiscrimination task



Average LIP activity in RT motion task

Roitman & Shadlen, 2002 J. Neurosci.

choose Tin

choose Tout

High motion strength

High motion stre

ngth

Low motion strength

Time~1 secStimulus

onStimulus

off

Spikes/s

Time~1 secStimulus

onStimulus

off

Spikes/s

Low motion strength

A Neural Integrator for Decisions?

MT: Sensory Evidence

Motion energy“step”

LIP: Decision Formation

Accumulation of evidence “ramp”

Threshold

Diffusion to bound modelPositive bound

Negative bound

Proposed by Wald, 1947 and Turing (WW II, classified); Stone, 1960; then Laming, Link, Ratcliff, Smith, . . .

Diffusion to bound modelPositive bound or Criterion to answer “1”

Negative bound or Criterion to answer “2”

Momentary evidencee.g.,

∆Spike rate:MTRight– MTLeft

Accumulated evidencefor Rightward

andagainst Leftward

Criterion to answer “Right”

Criterion to answer “Left”

Diffusion to bound model

Shadlen & Gold (2004)Palmer et al (in press)

µ = kC

C is motion strength (coherence)

Best fitting chronometric function“Diffusion to bound”

t(C) =B

kCtanh(BkC) + t

nd

Predicted psychometric function “Diffusion to bound”

P =1

1+ e!2k C B

µ = kC






andagainst Leftward

Time (ms)

µ = kC






andagainst Leftward

• LIP represents ∫ dt of momentary motion evidence

• Momentary evidence is a spike rate difference from area MT• The accumulated evidence used by the monkey is in area LIP• How and where is the integral computed?• How is the bound set?• How is a bound crossing detected?

• More RIGHT choices

• Faster RIGHT choices• Slower LEFT choices

• More RIGHT choices• Faster RIGHT choices• Slower LEFT choices

Bound for RIGHT choice

Bound for LEFT choice

Bound for RIGHT choice

Bound for LEFT choice

Stimulate RIGHTWARDMT neurons

The momentary evidence is a ∆ between opposite direction signals in area MT

The accumulated evidence used by the monkey is in area LIP

Stimulate RIGHT CHOICELIP neurons

µ = kC






andagainst Leftward

• LIP represents ∫ dt of momentary motion evidence

• Momentary evidence is a spike rate difference from area MT• The accumulated evidence used by the monkey is in area LIP• How and where is the integral computed?• How is the bound set?• How is a bound crossing detected?

Fixation

1st Stim &Targets

2nd Stim

3rd Stim

4th Stim

Delay & Sacade

0 ms

500 ms

1000 ms

1500 ms

2000 ms

Time

Probabilistic categorization task:4-card stud

Tianming Yang

- -0.9 -0.7 -0.5 -0.3 0.3 0.5 0.7 0.9 +

FavoringGreen

FavoringRed

0.9 -0.9

0.7-0.9-0.2

0.61 0.39

Weight of evidence in favor of red(log10 likelihood ratio)

From sensorimotor integration tocognition and its disorders

Sensoryevidence

Motoroutput

Prior knowledgeExpected payoff

Urgency

Potentialbehavioror plan


Sensoryevidence

MotorresponseArea LIP


Sensoryevidence

MotoroutputArea MT Area LIP Oculomotor System


Leaky integration confusion

Evanescentsensory stream

Plans forthe future

dt!

Sensoryevidence

Motorresponse

Turing’s strategy: sequential analysis

WOE =

10 log10

113( )126( )

!

" # #

$

% & &

= +3.0 db match

10 log10

1213( )2526( )

!

" # #

$

% & &

= '0.17db non -match

(

)

* *

+

* *

Weight of evidencein favor of

common rotor setting

Hypothesis: Messages encrypted by Enigma devices in same stateK C Y W D K D O P E D B A I Q S D F M K C N F A E O I E N C V N S D F NE N C H P D N C O E N A S H Q E N D N C K R N D N Q I O M Z F J K C P Q

0

5

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WOE =

10 log10

113( )126( )

!

" # #

$

% & &

= +3.0 db match

10 log10

1213( )2526( )

!

" # #

$

% & &


(

)

* *

+

* *



Hypothesis: Messages encrypted by Enigma devices in same stateK C Y W D K D O P E D B A I Q S D F M K C N F A E O I E N C V N S D F NE N C H P D N C O E N A S H Q E N D N C K R N D N Q I O M Z F J K C P Q

0

5

Wei

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favo

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K C Y W D K D O P E D B A I Q S D F M K C N F A E O I E N C V N S D F NE N C H P D N C O E N A S H Q E N D N C K R N D N Q I O M Z F J K C P Q

0

5

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ght o

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favo

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setti

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(dec

iban

s) K C Y W D K D O P E D B A I Q S D F M K C N F A E O I E N C V N S D F NE N C H P D N C O E N A S H Q E N D N C K R N D N Q I O M Z F J K C P Q

WOE =

10 log10

113( )126( )

!

" # #

$

% & &

= +3.0 db match

10 log10

1213( )2526( )

!

" # #

$

% & &


(

)

* *

+

* *




0 10 20 30 40 500

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Response (spikes/sec)

Pro

ba

bili

ty

Response (spikes/s)

Frequency ofoccurrence

LEFT preferringMT neurons

RIGHT preferringMT neurons

Variable response to weak RIGHTWARD motion

-40 -20 0 20 400

0.01

0.02

0.03

0.04

0.05

0.06

Frequency ofoccurrence

Response difference (spikes/s)

Difference in spike rate is proportionalto the logarithm of the likelihood ratio

Distribution ofresponseDIFFERENCES,right-left, forrightward motion

0 0.2 0.4 0.6 0.8

0

Time (s)

Accumulateddifference (R-L)

Amount of accumulatedevidence required tochoose “LEFT”

Weight ofevidence

Decibans

Belief

Log ofLikelihood

Ratio

Amount of accumulatedevidence required tochoose “RIGHT”

Yn= X

i

i=1

n

! random walk or diffusion

MX(!) " E e!X#$ %& = f (x)e!xdx

'(

(

) def. of MGF for X

MYn

(!) = MX

n(!) MGF for sums

M!Y(!) = P

+e!A

+ (1" P+)e

"!A MFG for !Y

!Y ! stopped accumulation

Random walk to bounds at ±A

Stochastic processes: partial sums andWald’s martingale

Stochastic processes: partial sums andWald’s martingale

E Zn[ ] = E M

X

!n(")e"Yn#$ %&!!!!!!!

= MX

!n(")E e

"Yn#$ %&

= MX

!n(")M

Yn

(")

= 1

E Zn+1

Y1,Y2,…,Y

n!" #$ = E M

X

%(n+1)(&)e&Yn+1 Y

1,Y2,…,Y

n!" #$

= E MX

%(n+1)(&)e& (Yn +Xn+1 )!" #$

= E[MX

%1(&)M

X

%n(&)e&Yn e&Xn+1 ]

= E[ZnM

X

%1(&)e&Xn+1 ]!!!

= MX

%1(&)Z

nE e

&Xn+1!" #$

= Zn

Wald’s martingale & identity

E !Z!" #$ = E Z

n[ ] = 1

E M

X

!n(")e"

!Y#$

%& = 1

If there were a value for ! such that MX(!) = 1 , it no longer matters

that n is a random number. At this special value, !1 ,

E e

!1 !Y"#

$% = 1

E.g., for the Normal distribution, with mean ! and variance !2, "

1= #

2µ

!2

M!Y(!1) = P

+e!1A + (1" P

+)e

"!1A = 1

P+=

1

1+ e!1A

Use Wald’s martingale to simplify

M!Y(!)

Documents

K C Y W D K D O P E D B A I Q S D F M K C N F A E …courses.cs.washington.edu/courses/cse528/05wi/Shadlen-slides.pdfDirection-Discrimination Task Reward for correct choice ... Positive