Modeling brain cognitive functions by oscillatory neural networks - PowerPoint PPT Presentation

Yakov Kazanovich Modeling brain cognitive functions by oscillatory neural networks Institute of Mathematical Problems of Biology RAS – A branch of Keldysh Institute of Applied Mathematics RAS Theoretical Physics and Mathematics of the Brain December 4, 2019, Moscow State University 1

Abstract • I’ll describe an oscillatory neural network designed as a system of generalized phase oscillators with a central element. It is shown that a winner-take-all principle can be realized in this system in terms of the competition of peripheral oscillators for the synchronization with a central oscillator. Several examples illustrate how this network can be used for the simulation of various cognitive functions: consecutive selection of objects in the image, visual search, and multiple object tracking. 2

Brain Rhythms • In the electrical activity of the brain there are a variety of rhythmic components manifested in different frequency ranges. These ocsillations correlate with external influences and the psychological state of the organism under study. Sustained patterns of rhythmic activity were found in various brain structures at the level of individual neurons, neural populations, and brain structures. Such experimental data were obtained in the primary zones of the visual and olfactory cortex, sensorimotor cortex, in the thalamus, in the hippocampus and in other structures. 3

Oscillations, Why Does the Brain Need Them? • Periodic movements: breathing, heart beating, walking, swimming. • Pathological activity related to Parkinson disease or epilepsy. • Brain cognitive functions: feature binding, attention, novelty detection, memory formation and recall, perception, consciousness. 4

Theoretical Concepts • Temporal Correlation Theory (Malsburg, Singer, Gray). Individual objects are represented in the brain by ensembles of synchronously working neurons. There is no synchronization between ensembles. This is a mechanism for feature binding (the integration of different properties of objects in accordance with their belonging to these objects ). • The Theory of a Central Executive of the attention system (Baddeley, Cowan). Attention is a result of the interaction of the central executive (a neural network located in the prefrontal cortex) with a neural ensemble that codes the features of a particular object that is currently included in the attention focus. 5

Photos (1) • Christoph Wolf Alan • von der Malsburg Singer Baddeley 6

Photos (2) • M.N. Livanov O.S. Vinogradova P.K Anokhin 7

Oscillatory Activity in the Visual Cortex Multiunit activity and local field potential responses recorded from area 17 in an adult eat to the presentation of an optimally oriented light bar moving across the receptive field of the recorded cells. Oscilloscope records of a single trial showing the response to the preferred direction of movement. In the upper two traces, at a slow time scale, the onset of the response is associated with an increase in high frequency activity in the local field potential. The lower two traces display the activity at an expanded time scale. Note the presence of rhythmic oscillations in the local field potential and the multiunit activity that are correlated in phase (Gray, 1994). 8

Synchronization and Binding Interareal synchronization is sensitive to global stimulus features. A. Position of the recording electrodes. A17, area 17; LAT, lateral sulcus; SUPS, suprasylvian sulcus; R posterior; L, lateral B(1-3). Plots of the receptive fields of the PMLS and area 17 recordings. The diagrams depict the three stimulus conditions tested. The circle indicates the visual field center. C(1-3). Peristimulus-time histograms for the three stimulus conditions. The vertical lines indicate 1-see windows for which auto-correlograms and cross- correlograms were computed. D(1- 3). Comparison of the auto- correlograms computed for the three stimulus conditions. E(1-3). Cross-correlograms computed for the three stimulus conditions (Gray, 1994]. 9

Central Executive (Cowan, 1988, 2008) 10

Synchronization and Attention • Attentional enhancement of synchronization. C. Coherence between spikes in FEF and LFPs in V4. (E) LFP-LFP coherence between FEF and V4 sites. Attention on stimulus - red lines, no attention - blue lines. The highest coherence is at the frequency about 50 Hz. There is no coherence in the theta and beta frequency ranges (Gregoriou et al., 2009). 11

Models • 1. Attention. • 2. Consecutive selection of objects in the image. • 3. Visual search. • 4. Multiple object tracking. 12

Mathematical Principles of Modeling Phase oscillators (or generalized phase oscillators) are used as the elements of neural networks. Phase oscillators represent ensembles of biological neurons (cortical columns) that code object features. LFP recording of such ensembles have the form of continuous curves . The dynamics of phase oscillators are described by a single variable, oscillation phase. The interaction between phase oscillators is described as the process of phase locking. 13

Phase Oscillator with an External Input  d      Ω a sin ( t ) d t • θ current phase, d θ /dt current frequency of oscillations, • ω natural frequency , • Ω frequency of the external input, • sin interaction function, • a interaction parameter (the interaction strength). Synchronization condition (stable state):  d            Ωt Ω , a sin ( ) 0 d t      Ω d t -           Ω Ω Ω  arc sin , a , , t   a d 14

Kuramoto Systems • Global (all-to-all) coupling  n d         i a f ( ) , i 1 ,..., n i ij j i d t  j 1 • Local coupling  d         i a f ( ) , i 1 ,..., n i ij j i d t  j N i 15

Yoshiki Kuramoto talks about the Kuramoto model: https://www.youtube.com/watch?v=lac4TxWyBOg 16

A Network of Phase Oscillators with a Central Element Dynamical equations Connection architecture  n d a        0 f ( ) 0 j o dt n   j 1 0  d a n f a 1 f       i a 2 f b g ( ) i 0 i dt bg bg bg     1 2 n i 1 ,..., n 17

Partial Synchronization. Dynamics of the Current Frequencies of Oscillators. 16 14 12 Current frequencies 10 8 1 2 6 3 4 2 0 0 1 2 3 4 5 6 7 -2 -4 Time 18

Generalized Phase Oscillators Interaction and resonance functions Dynamics equations g(x)= sin (x)  n d 1        0 a f ( ) 0 j i 0 dt n  i 1  d        i  bg ( ), i 1 , , n i 0 i dt      n d d          0  0  a f ( ) j i 0 0   dt n dt  i 1 da          i ( a c h ( )) i i 0 dt 19

  a a , , , , a a 2 2 10 10 “Winner -take- all”. Dynamics of Oscillator’s Amplitudes  , , a a 2 10 20

Dynamics of Phase Differences between the Central Oscillator and Peripheral Oscillators 21

A Model of Attention • Objects (stimuli) are represented by ensembles of oscillators with similar (but not identical) natural frequencies. The case of two stimuli ( А and В ) is considered. These stimuli compete for the attraction of attention. The parameters of the interaction a and b are interpreted as the saliency of stimuli. • The central executive is represented by the central oscillator. • A stimulus is attended if the ensemble of the peripheral oscillators that codes this stimulus works in the regime of partial synchronization with the central oscillator. 22

Dynamics Equations 23

Different Types of Attention Focus Formation Depending on the Values of the Interaction Parameters a a b b PS A – А is attended, PS В – В is attended, GS – both A and B are included in the attention focus, NS – a stable focus of attention is not formed. 24

Large-scale model for image processing Groups of oscillators (memory for novelty) • The model Novelty detection layer combines Computation of attention, feature 4 invariant 3 2 features 1 binding and Computation of local features novelty detection. Central executive Selection of objects Input image 25