Decision Dynamics and Decision States: - PowerPoint Presentation

Slide1

Decision Dynamics and Decision States:the Leaky Competing Accumulator Model

Psychology 209

March 4, 2013

Slide2

Is the rectangle longer toward the northwest or longer toward the northeast?

Slide3

Longer toward the Northeast!

2.00”

1.99”

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A Classical Model of Decision Making:

The Drift Diffusion Model of Choice Between Two Alternative Decisions

At each time step a small sample of noisy information is obtained; each sample adds to a cumulative relative evidence variable.

Mean of the noisy samples is +

m

for one alternative, –

m

for the other, with standard deviation s.When a bound is reached, the corresponding choice is made.Alternatively, in ‘time controlled’ or ‘interrogation’ tasks, respond when signal is given, based on value of the relative evidence variable.

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The DDM is an optimal model, and it is consistent with some data from neurophysiologyIt achieves the fastest possible decision on average for a given level of accuracy

It can be tuned to optimize performance under different kinds of task conditions

Different prior probabilities

Different costs and payoffs

Variation in the time between trials…

The activity of neurons in a brain area associated with decision making seems to reflect the DD process

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Neural Basis of Decision Making in Monkeys (Shadlen & Newsome; Roitman & Shadlen, 2002)

RT task paradigm of R&T.

Motion coherence and

direction is varied from

trial to trial.

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Neural Basis of Decision Making in Monkeys: Results

Data are averaged over many different neurons that are

associated with intended eye movements to the location

of target.

Slide8

Hard

Prob. Correct

Easy

A Problem with the DDM

Accuracy should gradually improve toward ceiling levels as more time is allowed, even for very hard discriminations, but this is not what is observed in human data.

Two possible fixes:

Trial-to-trial variance in the direction of drift

Evidence accumulation may reach a bound and stop, even if more time is available

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Goals for a Neurally Inspired Model of Decision MakingIncorporate principles of neural processing

Build a bridge between abstract statistically-grounded approaches and details of physiology

Explain existing data

Make predictions and see if they are borne out in data

Offer a new way of thinking about the nature of decision states

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Usher and McClelland (2001)Leaky Competing Accumulator Model

Addresses the process of deciding

between two alternatives based

on external input, with leakage, mutual inhibition, and noise:

dy

1

/dt = I1-gy1–bf(y2)+x1 dy2/dt = I2-gy2–bf

(y1)+x2

f(y) = [y]+Participant chooses the most active accumulator when the go cue occurs

This is equivalent to choosing response 1 iff y

1

-y

2

> 0

Let y = (y

1

-y

2

). While y

1

and y

2

are positive, the model reduces to: dy/dt = I-ly+x [I=I

1

-I

2

; l

=

g

-b; x=x1-x2]

I

1

I

2

y

1

y

2

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Wong & Wang (2006)

~Usher & McClelland (2001)

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Slide13

The Full Non-Linear LCAi Model

y

1

y

2

Although the value of the difference

variable is not well-captured by the

linear approximation, the sign of the

difference is approximated very closely.

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Time-accuracy curves for different |k-b| or |l|

|k

-

b|

= 0

|k

-

b|

= .2

|k

-

b|

= .4

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Prob. Correct

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Kiani, Hanks and Shadlen 2008

Random motion stimuli of different coherences.

Stimulus duration follows an exponential distribution.

‘go’ cue can occur at stimulus offset; response must occur within 500 msec to earn reward.

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The earlier the pulse, the more it matters(Kiani et al, 2008)

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These results rule out leak dominance

X

Still viable

Slide19

Quasi-Continuous, Quasi-Discrete, Reversible Decision States in the Non-linear LCAi

Quasi-continuous, quasi-discrete

decision states

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PredictionsWe should be able to find signs of differences in decision states associated with correct and incorrect responses.We should be able to see signs of bifurcation even if we ask for a continuous response.

We should be able see evidence of rebound of suppressed alternatives if the input changes.

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PredictionsWe should be able to find signs of differences in ‘strength’ of decision states associated with correct and incorrect responses.

We should be able to see signs of bifurcation when we ask for a continuous response.

We should be able see evidence of recovery of suppressed alternatives if the input changes.

Slide22

v

v

Distribution of

winner’s activations

when incorrect

alternative wins

Distribution of

winner’s activations

when correct

alternative wins

Slide23

Gao, Tortell and McClelland

(in press) Experiment on Effect of Reward on Decision Dynamics

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Proportion of Choices toward Higher Reward

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Fits based on full LCAi*

*Reward affects the initial state of the accumulators,

before the stimulus starts to affect them.

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Relationship between

choice and RT for each

participant and combined

Data from Gao et al (2012)

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An Account:Two-Stage LCAi

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Response StageModel

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PredictionsWe should be able to find signs of differences in ‘strength’ of decision states associated with correct and incorrect responses.

We should be able to see signs of bifurcation even when we ask for a continuous response.

We should be able see evidence of recovery of suppressed alternatives if the input changes.

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Bifurcation in the LCAi

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Bimodality in Decision StatesLachter, Corrado, Johnston & McClelland (in progress)

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Results and Descriptive Model of Data from 1 Participant

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Experiment 2Used much finer scale, much more practice & data per participantFound evidence that some participants show a bifurcation while others show un-

imodal

responses

Mapping to response scale appears to be non-linear in many participants

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PredictionsWe should be able to find signs of differences in ‘strength’ of decision states associated with correct and incorrect responses.

We should be able to see signs of bifurcation even when we ask for a continuous response.

We should be able see evidence of recovery of suppressed alternatives if the input changes.

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Reversability in the LCAiIf activation of loser cannot go below 0, reversal of decision states can occur

This leads to a predicted interaction of timing by duration.

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ExperimentParticipants viewed random dot motion stimulus presentations of varying durationsThree types of trials:Constant evidence

fixed non-zero coherence throughout trial

Early evidence

non-zero coherence in first half, 0 in second half

Late evidence

0 coherence in first half, non-zero in second half

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Interaction of timing by durationin one participant

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PredictionsWe should be able to find signs of differences in ‘strength’ of decision states associated with correct and incorrect responses.

We should be able to see signs of bifurcation when we ask for a continuous response.

We should be able see evidence of recovery of suppressed alternatives.

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ConclusionsEvidence from several studies is consistent with the idea of quasi-continuous, quasi discrete, sometimes reversible, decision states, although, in general, data from only some of the participants plays a strong role in selection between models.

The

LCA

i

model provides a simple yet powerful framework in which such states arise.

Alternative models considered have difficulties addressing aspects of the data.

More work is needed to understand if the

LCAi will turn out to be fully adequate, and how the data might be addressed with other approaches.

Quasi-continuous, quasi-discrete

decision states