Chapter 3. Stochastic Dynamics in the Brain and Probabilistic Decision-Making in Creating Brain-Like Intelligence, Sendhoff et al. Course: Robots Learning from Humans Lee, Tae-Min Computing and Memory Architecture Laboratory Dept. of Computer Science and Engineering Seoul National University

The Noisy Brain Stochastic Dynamics as a Principle of Brain Function Creativity is an output of stochastic nature of the brain

Contents Introduction Weber’s law Preliminaries Attractor network Integrate-and-Fire (IF) neuron Probabilistic decision-making network A probabilistic attractor network Spiking dynamics Properties & applications Conclusion

Experiment Setup Macaca Mulatta Vibration generator 5 ~ 50Hz f1>f2 f2>f1 (( f1 )) 0.5s (( f2 )) 0.5s delay 3s Ventral premotor cortex (VPC) acts 1) the remembered sensory stimuli, 2) their comparison and 3) motor response.

Weber’s Law The ratio of the difference-threshold to the background intensity is a constant

Weber’s Law The ratio of the difference-threshold to the background intensity is a constant Delta value Difference threshold 85% correct performance level

Preliminary Attractor network A recurrent dynamical network that evolves toward a stable pattern over time Single point attractor Multiple point attractor

Preliminary Attractor network A recurrent dynamical network that evolves toward a stable pattern over time Line attractorCycle attractor Chaotic attractor 1.Time-dependent function 2.Attraction states

Preliminary Integrate-and-Fire (IF) Neuron One of the earliest model of biological neuron models (i.e. spiking) Functional behavior Input is applied Voltage increases (proportional to C m ) Delta function firing if V > Vth (constant threshold V th ) Reset voltage Capacitance model Firing frequency Poisson-like spiking

Contents Introduction Weber’s law Preliminaries Attractor network Integrate-and-Fire (IF) neuron Probabilistic decision-making network A probabilistic attractor network Spiking dynamics Properties & applications Conclusion

Probabilistic Decision-Making Network A probabilistic attractor network Spiking dynamics Spontaneous background activity N ext = 800, 3Hz each

Probabilistic Decision-Making Network Dynamical evolution of VPC the comparison period The case of (f1= 30Hz, f2 = 20Hz )

Probabilistic Decision-Making Network Probability of correct discrimination w.r.t delta frequency The cases are f2=17.5Hz, 20Hz, 25Hz and 30Hz f2=17.5Hz f2=20Hz f2=25Hz f2=30Hz

Probabilistic Decision-Making Network Larger network -> higher accuracy Larger network -> slower convergence Larger network -> smaller standard deviation The effects of altering N, the number of neurons in the network The case of (f1=30Hz, f2=22Hz) 1.Time (t) dependency (>200ms) 2.Weber’s law 3.Network size (N) dependency

Properties of Biased Attractor Model Non-stationary full spiking simulation The decisions are taken probabilistically Statistical fluctuations <- finite size noise ~ sqrt(f_rate / # neurons) Psychophysical law e.g., weber’s is based on the synaptic connectivity The NMDA receptor accumulate evidence over several 100ms The operations of the brain is inherently noisy i.e. Poisson-like However the consequence is settling to a attraction state Hypothesis, comparisons with other models … etc. Read book

Applications of Decision-Making Model Model the brain function (hypothesis) Memory recall – recall cue – noise relation Hick’s Law: Reaction time increases linearly with log 2 (alternatives) Necker cube: switching bet. multi-stable states <- statistical fluctuations Probabilistic decision task Matching Law Noise as an adaptiveness Deterministic system become deadlocked Evolution Creativity

Conclusion To model the brain function, probabilistic decision-making network is proposed A probabilistic attractor network Spiking dynamics That shows good interpretations of Time dependency Weber’s law Network size dependency Further works: hypothesis to be proven, applications …