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

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Yakov Kazanovich

Modeling brain cognitive functions by

• scillatory 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

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Abstract

• I’ll describe an oscillatory neural network

designed as a system of generalized phase

• scillators 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

• f various cognitive functions: consecutive

selection of objects in the image, visual search, and multiple object tracking.

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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.

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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.

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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.

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Photos (1)

• Christoph Wolf Alan
• von der Malsburg Singer Baddeley

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Photos (2)

• M.N. Livanov

O.S. Vinogradova P.K Anokhin

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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

• ptimally 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).

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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].

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Central Executive (Cowan, 1988, 2008)

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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).

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Models

• 1. Attention.
• 2. Consecutive selection of objects in the

image.

• 3. Visual search.
• 4. Multiple object tracking.

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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

• bject 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

• scillators is described as the process of phase locking.

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Phase Oscillator with an External Input

• θ current phase, dθ/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):

) t Ω ( a t d d       sin

       ) ( a Ω t d d , Ωt      sin

Ω d d Ω , Ω a a Ω             t

• t

      , , sin arc

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Kuramoto Systems

• Global (all-to-all) coupling

n ,..., i , ) ( f a d d

n j i j ij i i

1 t

1

   





   

• Local coupling

n ,..., i , ) ( f a d d

i

N j i j ij i i

1 t    





   

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

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A Network of Phase Oscillators with a Central Element

Dynamical equations Connection architecture





  

n j

• j

) ( f n a dt d

1

   

) ( g b dt d

i i i

       n ,..., i 1 



1



2



n



a1f a2f anf bg bg bg

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Partial Synchronization. Dynamics of the Current Frequencies of Oscillators.

• 4
• 2

2 4 6 8 10 12 14 16 1 2 3 4 5 6 7

Time Current frequencies

1 2 3

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Generalized Phase Oscillators Dynamics equations Interaction and resonance functions

g(x)=sin(x)





  

n i i j

) ( f a n dt d

1

1    

n , , i ), ( bg dt d

i i i

 1        

)) ( h c a ( dt da

i i i

        

         



 1

       dt d ) ( f a n dt d

n i i j

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“Winner-take-all”. Dynamics of Oscillator’s Amplitudes

10 2

, , a a 

10 2

, , a a 

10 2

, , a a 

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Dynamics of Phase Differences between the Central Oscillator and Peripheral Oscillators

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A Model of Attention

• Objects (stimuli) are represented by ensembles of
• scillators 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
• scillator.
• A stimulus is attended if the ensemble of the peripheral
• scillators that codes this stimulus works in the regime of

partial synchronization with the central oscillator.

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Dynamics Equations

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Different Types of Attention Focus Formation Depending on the Values of the Interaction Parameters

a b a b PSA –А is attended, PSВ –В is attended, GS – both A and B are included in the attention focus, NS –a stable focus of attention is not formed.

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Large-scale model for image processing

• The model

combines attention, feature binding and novelty detection.

4 3 2 1

Groups of oscillators (memory for novelty) Central executive Novelty detection layer Computation of invariant features Computation of local features Selection of

• bjects

Input image

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A Model of Consecutive Selection of Objects in the Visual Scene

A scheme for modeling consecutive selection of objects. Objects are coded by assemblies of locally connected oscillators. The selection of a particular object in the attention focus is realized by the WTA procedure in a system of generalized phase

• scillators with a central element. Gray

arrow shows assigning values to the natural frequencies of POs. Black filled arrow shows synchronizing connections that are used for object representation by a synchronous assembly of POs and for synchronization of the CO with an assembly of POs. Black hollow arrow shows desynchronizing connections that are used to prevent simultaneous synchronization of the CO with several assemblies of POs.

Центральный осциллятор Периферические осцилляторы Входное изображение

Central

• scillator

Peripheral

• scillators

Input image

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Dynamics of the Amplitudes of Oscillators that Represent the Pixels of the Letters in the Word HELLO

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Visual Search

• The tasks of visual

search of different difficulty

• Mean reaction times

(experimental data) (Wolfe et al., 2010)

Feature search Conjunction Spatial configuration search search

Feature search Conjunction Spatial configuration search search

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Simulation Results

• Simulation results for visual search: (a) probabilities (as functions of n) that a

target object will be selected in the attention focus during one attempt; (b) average number of attempts needed to select a target with return; (c) average number of attempts, needed to select a target without return.

(a) (b) (c)

1 2 3 4 5

n rn

5 4 3 2 1

n

1 n

M

5 4 3 2 1

2 n

M n

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Multiple Object Tracking

• The experiment takes place under covert attention. Targets are shortly

flashed before moving. The observer must identify the targets after the movement is stopped (5-7 s) using a computer mouse (Pylyshyn &

Annan, 2006).

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A Model of Multiple Object Tracking

• The probability of

errors during identification of target

• bjects. Experimental

and modeling results

• The architecture of

model connections in the case of three targets

Layer 3 Layer 2 Layer 1 CO 3 CO 1 CO 2

Synchronizing connection Desynchronizing connection

The number of target objects Probability of errors

Model Experiment

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Conclusions for Neuroscientists

• It is not easy to distinguish a system with global interactions

from a system with a central element. The debate about the existence of a central executive in the attention system is still

• ngoing.
• If the system is complex enough, hierarchical, has convergent

connections, and implements the winner-receive-all procedure, it is worth looking for whether it has a central element.

• It is nesessary to continue the search for oscillatory modes

and synchronization in various psychophysical experiments.

• The hypothesis of ​the Time Correlation Theory that binding

and attention are a result of synchronization of all neural activity related to one object in the general case, apparently, is not true. How it should be modified taking into account saccades remains the subject of future experimental and model studies.

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Conclusions for Computational Neuroscientists

• It is necessary to develop plausible and effective

models of long-term memory and recognition based on oscillatory principles.

• Cognitive function models based on multi-

frequency vibrations are needed.

• The use of phase oscillators in the case of

strong interactions is mathematically incorrect. It is necessary to discend to a more detailed level

• f representation of brain structures and their

interaction in the implementation of cognitive functions.

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References

• Kazanovich Y. Modeling brain cognitive

functions by oscillatory neural networks. Optical Memory & Neural Networks / Information Optics, 2019, 28(3), 175-184.

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Thank you for Attention!

Pushchino, view from above