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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

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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.

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

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

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

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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

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f1>f2 f1

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Attractors Design: Mean-Field Reduction f1>f2 f1

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Neurodynamical Mechanisms “Bifurcation Diagram” Stationary States (Attractors) Choice f1>f2 f1>f2 f1

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Simulations: Decision-Making in VPC Neurons

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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

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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.

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

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

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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)

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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

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

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

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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

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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

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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

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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

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

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Experimental Results: Yes and No-Neurons

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- 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

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

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

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

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Stochastic Bifurcations: Role of Fluctuations Shift of the Bifurcation

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

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Stochastic Bifurcations: Role of Multistability/Fluctuations Finite-size Noise: Fluctuations

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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

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Time course of the probabilistic settling into a decision attractor

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Neurodynamical Mechanisms “Attractors Picture” S 11 22 22 11 A2 A1 S “Phase Space” f1>f2 f1

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Neurodynamical Mechanisms: Flow Diagram Rate Pool f1>f2 Rate Pool f1

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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.

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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)

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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.)

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