Neuronal Model of Decision Making

1
Neuronal Model of Decision Making

• How the noisy background activity of the brain
  influences the dynamics of simple decision making

2
Motivations/Overview

• Specific neurons involved in decisions. A
  benchmark decision task about moving dots,
  involving area LIP (Newsome and Shadlen, 2001 ).
• Accumulation of evidence threshold decision
  making (Smith and Ratcliff, 2004).
• Dynamical models of decision through mutual
  inhibition. (Wang, 2003, Amitt and Brunel, 1997).
• Low level background activity of the brain
  (Salinas, 2003).
• A complete story from sensory inputs to the
  movement that expresses the decision.
  (Merleau-Ponty, )
• Second order statistics Gentz, Feng.

3
Network Connectivity
Upwards detector
E X C I T A T I O N
E up
I N H I B I T I O N
I down
I up
Downwards detector
E down
Saccadic Eye Movement
Background Activity
Kinematogram Stimulus
4
Integrate and Fire Model

• Membrane model

• Diffusion Approximation with Poissonian synaptic
  inputs processes
• The Variance of ISI is equal to its mean
• Activities of neurons characterised by FR
• r is the ratio between excitatory and
  inhibitory inputs

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Global Direction Detectors
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Results of the Direction Detector
The Firing Rate of a directtion detector is a
linear function of the coherence of the
stimulus. Increasing r increases discrimination
accuracy. (Gaillard et al, 2005). Gaussian
distribution of ISIs Fits Biological data,
common approach in literature. (Wang, 2003).
7
LIP column where the decision takes place
Inh
E up
Background activity
Upwards detector
E down
Inh
Downwards detector
Inh
Exc
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Weights Matrix
9
Embedded decision Saccadic Eye Movement.
In order to express the decision, any living
being has to make a move. For example, in
Newsomes experiments on monkeys, the monkeys
indicate their decision by moving their eyes in
one direction or another. They use a Saccadic Eye
Movement.
K and l are parameters. Fup and Fdown are the
forces applied to eye by the muscles,
proportional to the Firing Rate of the decision
neurons. The tangent function expresses an
elastic force, that prevents the eye position
from diverging. Same decision criterion as
psychophysical experiments.
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Time course of a decision and working memory
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Illustrating Movie
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Simulations Results

• Influence of the FR (mean ISI) of the Background
  Activity on Reaction Time

13
Simulations Results

• Influence of the Standard Deviation of the
  Background Activity on Reaction Time

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Simulations Results

• The Influence of the standard deviation of the
  background activity on Error Rate

In the middle, there is the mean over all values
of the mean. Surrounded by two extreme cases.
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Prediction Error Rate as a function of Reaction
Time
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Partial conclusions

• Confirm that background activity controls RT, not
  a switch, a continuum.
• Not only the intensity of the background
  activity, but also the actual noise reduces
  Reaction Time. (And increases Error Rate).
• A Non invasive idea for biological research
  ERf(RT).
• Non monotonous behaviour. Interpretation?
• Second order statistics are essential to the
  system dynamics We cannot use the Poisson
  assumption.

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Propagation of Moments

• Usual Approximation Scheme for the Integrate and
  Fire model

• Homogenous case with r inhibitory synapses for
  one excitatory

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Propagation of Moments

• Expressions of the first and second moment

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Propagation of Moment

• Expression of the mapping

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System Study

• Homogenous case.
• Two stable attractors quiet and high activity.
• If Inhibition stronger than excitation (rgt1), low
  level activity attractor.
• Our case is heterogeneous. We study the
  generation of islands of higher activity within
  the stable sea of low level activity.
• Resort to simulations.

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The mapping
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No decision when small background variance.
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Time course of a decision
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Reaction Time depends on the moments of
background activity
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Conclusions

• MNN results contradict Poisson model Detrimental
  assumption.
• The intensity of the background activity seems to
  act like a switch, whilst the actual noise
  controls Reaction Time as a continuum. (And
  probably increases Error Rate).
• Non monotonous behaviour.
• How to measure ER?

26
Some References

• 1 E. Salinas. Background Synaptic Activity as a
  Switch Between Dynamical States in a Network.
  Neural Computation, 15 1349-1475, 2003.
• 2 N. Berglund and B. Gentz. Pathwise
  description of dynamic pitchfork bifurcation with
  additive noise. Probab. Theory Related Fields,
  122(3)341388, 2002.
• 5 M. N. Shadlen and W. T. Newsome. The Neural
  basis of a perceptual Decision in the Parietal
  Cortex (Area LIP) of the Rhesus Monkey. J.
  Neurophysiology, 86 1916-1935, 2001.
• 6 E. P. Simoncelli and D. J. Heeger. A model of
  neuronal responses in visual area MT. Vision
  Research, 38743761, 1998.
• 7 X. J. Wang. Probabilistic decision making by
  slow reverberation in cortical circuits. Neuron,
  36955968, 2002.
• 8 D. J. Amit and N. Brunel. Model of global
  spontaneous activity and local structured
  activity during delay periods in in the cerebral
  cortex. Cereb Cortex 7, 237-252, 1997.
• 10 P.L. Smith and R. Ratcliff. Psychology and
  neurobiology of simple decisions. Trends in
  Neuroscience 27(3), 161-168, march 2004.
• 11 B. Gaillard and J. Feng. Modelling a visual
  discrimination task. Neurocomputing,
  65-66203209, 2005.