1. Mechanisms of Simple Perceptual Decision Making Processes
Xueying Wang
SAMSI/NCSU
CMMSC, NCTU, December 30, 2009

2. Outline History of two-alternative decision making research
Drift-diffusion models (DDMs)
The reduced two-variable models (RTVM)‏
Analytical study on DDMs
Theoretical reduction of the RTVM to a DDM
Numerical investigation on the RTVM
Experimental data fitting
Summary and discussion

5. DDMs

6. DDMs
Free response tasks
Force response tasks

7. Directional Discrimination Tasks
Mazurek et al. ,Cereb Cortex 13, 2003

8. Biological background
MT (middle temporal area)‏
LIP (lateral intraparietal area)‏

9. Decision processes
Mazurek et al., Cereb. Cortex 13, 2003

10. The spiking neuronal network model
Wang, X.J., Neuron,36,2002

11. The RTVM
Wong and Wang, J. Neurosci. 26, 2006

12. The RTVM

13. Analysis of DDMs on the force response tasks

14. Analysis of DDMs on the force response tasks
Drift rate and diffusion coefficient are only functions of time
Drift rate and diffusion coefficient are only functions of the spatial variable

15. Analysis of DDMs on the free response tasks
Case I: Drift rate and diffusion coefficient are only functions of time

16. Analysis of DDMs on the free response tasks
Case I: Drift rate and diffusion coefficient are only functions of time

17. Analysis of DDMs on the free response tasks
Case II: Drift rate and diffusion coefficient are only spatially dependent.

18. Simulation of binary decision making process by the RTVM

19. Dynamics of this model

20. Dynamics of this model with weak noise

21. The features of the dynamics of this model
We show that the stochastic solution and the deterministic counterpart remain close when the amplitude of noise is weak enough.

22. The analysis on the RTVM

23. Reduction to a 1-dimensional DDM

24. The original model vs. the simplified model
the correct response probability
Mean reaction time
black dots -- monte carlo simulation of the original model over 50,000 trials
red curves – the analytical results of the simplified model

25. Reduction to a 1-dimensional DDM

26. Effect of the starting point and the coherence level on the performance

27. Accuracy

28. Mean reaction time

29. Numerical investigation on the RTVM
The transition pdf
coh=0
coh=30

30. Numerical investigation on the RTVM
The correct response probability (CP)‏
coh
noise
decision threshold

31. Numerical investigation on the RTVM
Mean reaction time
coh
noise
decision threshold

32. Experimental data fitting
Quantile probability plot

33. Experimental data fitting33

34. Summary
We uncovered mechanisms underlying the simple perceptual decision making processes by investigating DDMs and the RTVM.
We gave a detailed analysis of DDMs.
Force response tasks
Free response tasks
We found precise conditions on parameters for when the biophysical-based two-dimensional model can be rigorously reduced to a one-dimensional DDM.
We provided precise estimates on the parameter values so that the biophysical-based model can be controlled to reproduce the psychological experimental data.

35. Discussion and future research
Apply asymptotic analysis to study the RTVM in the case of weak noise, which may characterize the stochastic dynamics of the whole system without the reduction to the unstable manifold.
The dynamics of neural activity governed by the properties of the individual neurons, network architecture and synaptic plasticity
The mechanisms of multiple-choice decision making processes

36. Thanks
Questions?