1. Stochastic Dynamics as a Principle of Brain Functions: Binary and Multiple Decision and Detection G. Deco, R. Romo and E. Rolls Universitat Pompeu Fabra/ICREA Barcelona UniversidadAutonoma de Mexico Mexico University of Oxford Oxford

2. Neural Mechanisms Underlying Probabilistic Behavior Single Cell Recordings in Awake Monkeys I.Decision-Making: Binary: Vibrotactile Discrimination Task Multiple: Moving Dots Discrimination I.Perceptual Detection: Detection of a Mechanical Vibration Romo et al.

3. Vibrotactile frequency discrimination After Romo and Salinas (2003) Nature Reviews Neuroscience

4. r(t)=a1(t).f1+a2(t).f2+c(t) Response of S1, S2, PFC, MPC Neurons

5. Response of VPC Neurons r(t)=a1(t).f1+a2(t).f2+c(t) Romo, Hernandez and Zainos (2004) Neuron

6. Spiking network for probabilistic decision-making P P P GABA P AMPA NMDA Background... Selective Input I Selective Input II Non-selective Spiking Neuron -> Integrate-and-Fire Model: Spikes Reset EPSP, IPSP Spike Synapses Synaptic Dynamics: Populations of Neurons

7. f1>f2 f1<f2 Nonspecific Neurons Inhibitory Pool Spiking network for probabilistic decision-making AMPA NMDA Background AMPA NMDA Background AMPA 1 1 1 W-W- W-W- W+W+ WIWI GABA f1 f1+ f1 f1- f2 f2+ f2 f2-

8. Attractors Design: Mean-Field Reduction f1>f2 f1<f2 Nonspecific Neurons Inhibitory Pool AMPA NMDA Background AMPA NMDA Background AMPA 1 1 1 W-W- W-W- W+W+ WIWI GABA Pool M Neurons Pool-Activity

9. Neurodynamical Mechanisms “Bifurcation Diagram” Stationary States (Attractors) Choice f1>f2 f1>f2 f1<f2 f1>f2 f1<f2 Bistability Choice f1<f2 S f1>f2 f1<f2 “Attractors Picture” Delta-f Fluctuations f1>f2 f1<f2

10. Simulations: Decision-Making in VPC Neurons

11. Weber’s law: The increase in a stimulus that is just noticeable (Delta-f, or f1-f2) is a constant proportion of the initial stimulus (f1) for any one sense, i.e. Delta-f / f = a constant Neuronal Variability vs. Probabilistic Behavior

12. To reach 85% correct Delta-f must be larger as f2 increases. Weber’s Law: Performance Simulations Weber’s Law is implemented by the increase of Delta-f that is needed to push the network into the correct attractor as f increases.

13. Deco et al. 2007, J. of Neuroscience Weber’s Law: Experimental Results in Humans

14. Stochastic Bifurcations: Role of Multistability/Fluctuations Deco and Romo, TINS 2008

15. Multiple choices 1.Most real-life decisions involve the need to select between multiple alternatives.  The first neurophysiological data for a four-alternative choice task has only been published last year. (Churchland et al., 2008)

16. Random-dot motion discrimination task During the choice process: 1.Sensory areas (e.g., motion area MT) provide noisy evidence supporting the alternatives. 2.Neurons in certain cortical regions (e.g., LIP) gradually increase their firing rates  “integrate” the evidence. 3.Choice is made when activity of the neuronal population representing one of the alternatives reaches a decision threshold.  Neurophysiology with primates (Shadlen group, e.g. Churchland et al., 2008) Neurophysiology of decision making

17. Spiking neuron model: Structure All network parameters are independent on the number of alternatives!!! Albantakis and Deco, PNAS 2009

18. Results: Psychometric function Experimental Data adapted with permission from Churchland et al., 2008 Albantakis and Deco, PNAS 2009

19. Results: firing-rates Churchland et al., 2008 Albantakis and Deco, 2009  Same threshold regardless of number of alternatives  Integration process starts at lower value for 4 choices than for 2 possible choices

20. Somatosensory Detection 1. PD:Stimulator on the fingertip 2. KD: Left hand on immobile key 3. Prestimulus period (1.5s to 3.5s)‏ 4. Stimulus period 5. Delay period (3s)‏ 6. MT:Response (''yes'' o ''no'')‏ 7. Reward: Hits and Correct rejections Lafuente & Romo (2005) Nature Neuroscience

21. Experimental results Proportion “Yes” ResponsesAverage Rate over Hits S1 neurons related to stimulus strength MPC neurons related to perceptual decisions Lafuente & Romo (2005) Nature Neuroscience

22. Detection as a Decision-Making Model CYNN (Competition Yes/No Neurons) NCY (No Competition Yes Neurons) YES NO Nonspecific Neurons Inhibitory Pool AMPA NMDA Background AMPA NMDA Background AMPA 1 1 1 W-W- W-W- W+W+ GABA YES Nonspecific Neurons Inhibitory Pool AMPA NMDA Background AMPA NMDA Background AMPA 1 1 1 W-W- WIWI GABA Stimulus Intensity Default- No spontaneous Yes-high No-high Yes-high

23. Model Simulations Proportion of “Yes” responses Mean Rate activity over hits NCYN CYNN Exp.

24. Experimental Results: Yes and No-Neurons

25. - Neuronal activity shows high variability. - We hypothesized that these fluctuations can have a functional role. - Neuronal and behavioral correlates of decision-making and perceptual detection are consistent with a scenario of fluctuation-driven computation that cause transitions between multistable states. Conclusions

26. Results:Mean field analysis NCYN (No Competition Yes Neurons)‏ CYNN (Competition Yes/No Neurons)‏

27. Average Rate Activity Temporal Evolution: Simulations NCYN CYNN NO - response Yes - Response

28. Stochastic Bifurcations: Role of Fluctuations Moments Method First & Second Order Moments Taylor Expansion

29. Stochastic Bifurcations: Role of Fluctuations Shift of the Bifurcation

30. Stochastic Bifurcations: Role of Fluctuations Neurodynamical Mechanisms: Stability of Decision-Making

31. Stochastic Bifurcations: Role of Multistability/Fluctuations Finite-size Noise:  Fluctuations

32. The final firing rate of the neurons in the attractor that wins is independent of Delta-f and of f: Weber’s Law is not implemented in the final firing rates. Simulations: Firing Rate of VPC Neurons

33. Time course of the probabilistic settling into a decision attractor

34. Neurodynamical Mechanisms “Attractors Picture” S 11 22 22 11 A2 A1 S “Phase Space” f1>f2 f1<f2 f1>f2 f1<f2 Delta-f Fluctuations

35. Neurodynamical Mechanisms: Flow Diagram Rate Pool f1>f2 Rate Pool f1<f2 11 22

36. Parameter-range of decision making Albantakis and Deco, 2009 4 different initial conditions: Black: all four pools 0 Hz Red: one 120 Hz, rest 0 Hz Green: two 30 Hz, rest 0 Hz Blue: all 30 Hz Yellow Region: Decision region, one pool fires at high rate, rest close to 0 Hz.

37. The coding level Albantakis and Deco, 2009 Coding level = fraction of excitatory neurons encoding one decision alternative (selective population) (0.2 in all network simulation)

38. Comparison to other models Furman and Wang, 2008: + continuous (ring of neurons, directionally tuned) - No mean-field analysis possible - 90°-case is identical to standard 2 choice case - 8 choices: in 49% of the trials no decision - top-down stimulus necessary to adjust input for different numbers of alternatives Beck et al., 2008: Probabilistic instead of biophysically realistic  mathematical approach (Bayesian Inference) + continuous + Log-odds (neurons also encode uncertainty?!?) - different decision thresholds for 2 and 4 choices - not aimed at modeling all neurophysiological aspects (target phase etc.)