1. Modeling working memory and decision making using generic neural microcircuits
Prashant Joshi,
Institute for Theoretical Computer Science,
Technische Universität Graz,
Austria
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2. Synopsis
Decision making is a recurring event in our day to day lives, and involves three phases:
L – Initial loading of stimulus into working memory (WM),
M – Maintaining the stimulus in WM for a couple of seconds,
D – Making a binary decision on the arrival of second stimulus
A neurocomputational model using generic neural microcircuits with feedback can integrate these three phases into a single unified framework!

3. Outline Background & Methods Interval discrimination tasks
Computational principles
Generic neural microcircuits
What is a liquid state and who are the “neural users”?
Interval discrimination tasks
Two-interval discrimination (TID)
Delayed match-to-sample (DMS)
A glimpse of biology – the role of pre-frontal cortex in decision making
Modeling Results
Additional Results
Conclusions

4. Computational Principles
Dilemma – Analog fading memory has an upper limit on the order of tens of msec whereas working memory holds information on the order of seconds
New theoretical results [Maass, Joshi, Sontag, 2005] imply that generic neural microcircuit with feedback has unexpected computational capabilities:
It can emulate any dynamical system, in particular any analog computer
Induces multiple co-existing “partial-attractor” states in the circuit dynamics
This work demonstrates that even in presence of feedback noise, such “partial attractor” states can be held by generic neural microcircuits on the time-scales of several seconds, which is obviously a requirement for tasks involving working memory

5. Generic Cortical Microcircuits
Neurons – leaky integrate-and-fire neurons, 20% of them inhibitory, neuron a is connected to neuron b with probability C.exp(-D2(a,b)/λ2)
Synapses – dynamic synapses with fixed parameters w, U, D, F chosen from distributions based on empirical data from Henry Markram’s lab

6. What is a liquid state and who are the “neural users”?
Each readout neuron receives as input a vector x(t), which has as many components as it has the pre-synaptic neurons in the circuit
The ith component of x(t) results from the spike-train of the ith pre-synaptic neuron by applying a low-pass filter, which models the low-pass filtering properties of receptors and membrane of the readout neuron
We assume that a readout neuron has at time t a firing rate proportional to w.x(t)
Remark: Experimental results from the labs of Nicolelis and Poggio show that such weighted sums (from neurons in visual or motor cortex) contain behavior-relevant information

7. Interval Discrimination Task
Classical experimental paradigm to study working memory and decision making
Subject has to compare two stimuli (tactile, visual, auditory etc.)
The experiment starts with presentation of the first stimulus
Second stimulus is presented after a temporal delay
Subject needs to make a binary (yes/no) decision after the presentation of the second stimuli, usually by pressing a corresponding switch

8. Two-Interval-Discrimination
Subject receives two frequencies f1 and f2 and has to decide if f1 > f2?

9. Delayed-Match-to-Sample
Cue stimulus (a color) is presented initially on the screen
Subsequently two probe stimuli (one identical to cue stimulus) are presented
Subject has to decide which probe stimuli has the same color as the cue stimulus

10. A glimpse of biology – the role of pre-frontal cortex in decision making
f1 > f2?
Two kinds of neurons (+ and “-”) have been observed in PFC which show opposite activities is response to the above question
The “+” neurons show an increase in their activity during the decision phase when the answer to the above question is “yes”
The “– “neurons show an increase when this answer is “no”
Figure from Machens et. Al. Science, 307:

11. Modeling Results
The generic neural microcircuit is used as a model for PFC
Inputs are fed to the circuit with a simple form of spatial coding (moving Gaussian window)
Each input is fed to a layer of 100 neurons in the circuit
At each time step t, a signal-dependent noise was added to the input signal ( ρ . f(t))
ρ is a random number drawn from a Gaussian distribution with mean 0 and SD 1
f(t) is the current value of the input signal
Simple linear readouts trained by linear regression are used to model the “+” or “-” neurons, and send feedback of their activity to the neural circuit

12. Modeling Two-interval-discrimination
400 neurons, arranged of a 20 x 5 x 4 grid
Circuit receives two external inputs (f1 and f2), and feedback from the readouts modeling the “+” and “-” neurons
Total simulation time for one trial = 3.5 sec
Simulation time-step = 10 msec
10 pairs of input frequencies
f1 and f2 are presented for 0.5 sec each, during the L and D phases respectively

13. Results - TID
f1 = 18 Hz, f2 = 26 Hz
Readouts perform exceptionally well even in the presence of feedback noise (correlation of 0.9 and above)
Robustness – Setup is robust to synaptic pruning – control values (no pruning) for 10 validation runs, mean = , SD =
Interesting as traditional models of attractor based neural computation fail to demonstrate robustness

14. Additional Results
Decision making followed by action selection is one of the most challenging events of our daily lives
Involves 4 phases – 3 for decision making (L,M, and D), and one for acting on the decision (called the A phase)
Neurocomputational models of working memory (including this talk till now) fail to address how the decisions made by neurons in PFC are converted into motor commands, which are executed by the sensori-motor system?
Similarly, models for computational motor control ignore the first three phases (L, M and D)
A neurocomputational architecture is proposed that integrates the four phases (LMDA) involved in the process of action selection in presence of a decision
Essentially this model integrates two different cortical modalities – decision making carried on by PFC, and subsequent action selection carried out by sensori-motor system
A spiking neural network model is presented for the DMS task followed by an arm movement to the decided goal position

15. Modeling DMS followed by arm movement
PFC Circuit:
500 neurons, arranged of a 20 x 5 x 5 grid
Circuit receives three external inputs (Csample, Cleft, and Cright), and feedback from the readouts modeling the “left” and “right” neurons
M1 Circuit:
1000 neurons (20 x 5 x 10)
4 external inputs (The x and y coordinates of the center of left and right probe regions)
the output of the “left” and “right” readouts from PFC circuit
feedback from readouts that predict joint angles
feedback from readouts that compute joint torques
Arm Model:
Standard model of a 2-joint robot arm
Trajectory followed by the tip of the arm is generated using the minimum jerk model
Simulation:
Total simulation time for one trial = 2.5 sec
Simulation time-step = 10 msec
5 triplets of input colors
Csample is presented for 0.32 seconds during the L phase, and Cleft, and Cright are presented simultaneously for 0.6 seconds, during the D phase

16. Results – DMS + Arm Movement
Movement occurs during the A phase (last 500 msec)
Biologically realistic bell-shaped velocity profile observed
Performance – tested over 100 validation runs:
Left – mean = , SD =
Right – mean = , SD =
τ1 – mean = , SD =
τ2 – mean = , SD =
θ1 – mean = , SD =
θ2 – mean = , SD =

17. Results – DMS + Arm Movement

18. Conclusions
A new neurocomputational paradigm is described that uses synaptic learning mechanisms and is able to integrate the L,M,D and A phases involved in decision making followed by action selection
Task independent and biologically realistic
Demonstrates the ability of generic neural microcircuit models to hold “partial attractor” states
Robustness to factors such as synaptic pruning and feedback noise
Works for significant long time-scales in presence of noise because:
Generic neural microcircuits are inherently endowed with fading memory
Feedback enhances this
Adding noise to teacher-feedback helps in making the target an attractor
Reflects the “internal model” hypothesis

19. References
Machens , C.K., Romo, R., and Brody, C.D., 2005, Flexible control of mutual inhibition: a neural model of two-interval discrimination, Science, 307:
W. Maass, P. Joshi, and E. D. Sontag. Computational aspects of feedback in neural circuits. submitted for publication, (PDF, 1154 KB)
W. Maass, P. Joshi, and E. D. Sontag. Principles of real-time computing with feedback applied to cortical microcircuit models. In Advances in Neural Information Processing Systems, volume 18. MIT Press, in press. (PDF, 806 KB)
P.Joshi. Modeling working memory and decision making using generic neural microcircuits. In Proc. of the International Conference on Artificial Neural Networks, ICANN, in press
P. Joshi. From memory based decisions to decision based movements: A model of interval discrimination followed by action selection. submitted for publication, 2006