Transient sequences in adaptive spiking networks: hypernetworks and - - PowerPoint PPT Presentation

Transient sequences in adaptive spiking networks: hypernetworks and spatiotemporal processing

V.I. Nekorkin Institute of Applied Physics RAS Nizhny Novgorod

Plan

1) Transient sequential dynamics in neural networks; 2) Cognitive dynamics are competitive and transient — stable heteroclinic channel; 3) Hypernetworks for describing transient sequential dynamics; 4) Example of model implementation; 5) Map-based model of neurons and links; 6) Hypersimplexes and hypernetwork; 7) Spatiotemporal processing; 8) Biological neural networks and hypernetworks; 9) Conclusion; 10) Topical problems and publications.

Examples of sequential neural activity ✓ olfactory system ✓ gustatory cortex ✓ vocal tract of songbirds

• M. Wehr, G. Laurent, Odor encoding by temporal sequences
• f firing in oscillating neural assemblies, Nature, 1996.

The responses of two simultaneously recorded projection neurons (PN) to the odor cherry (21 trials). Transient patterns in the olfactory system of locust

Spatiotemporal sequential activity in neural networks

Many neurophysiologic experiments have indicated that some neural processes (for example, processes related with performing

• f

different cognitive tasks

• memory,

attention, psychomotor coordination and so on) are accompanied only by transient activity on the level

• f individual neurons or small enough groups of neurons. In the result of such processes a

certain sequence of transitional activity phases appears in neural network. It is clear that such activity of neural networks cannot be understood within the framework of classical models of nonlinear dynamics which are based on concept of attractor because here the main effect is achieved long before the system reaches its neighborhood.

Transient dynamics for odor encoding

Buonomano, D. V., & Maass, W. (2009). State-dependent computations: spatiotemporal processing in cortical networks. Nature Reviews Neuroscience, 10(2), 113. Broome, B. M., Jayaraman, V., & Laurent, G. (2006). Encoding and decoding of overlapping

• dor sequences. Neuron, 51(4), 467-482.

Responses of locust projection neurons to 2 different olfactory stimuli. Three-dimensional graphs were obtained from an analysis of the activity of 87 neurons using dimension reduction methods (including local embedding).

Cognitive dynamics are competitive and transient — stable heteroclinic channel

Winnerless competition is the dynamial origin of a stable heteroclinic chain — sequence of metastable states

Hypersimplexes and hypernetworks

Hypersimplexes are ordered sets of vertices with an explicit n-ary relation.

Hypernetworks are sets of hypersimplexes.

• J. Johnson. Hypernetworks in the science of complex systems. World Scientific, 2013.

Model for transient dynamics: traffic in hypernetwork

Maslennikov, O. V., Shchapin, D. S., & Nekorkin, V. I. (2017). Transient sequences in a hypernetwork generated by an adaptive network of spiking neurons. Phil. Trans. R. Soc. A, 375(2096), 20160288. Stimulus Artificial neural network Family of hypersimplixes: possible activity configurations Hypernetwork: structured set of hypersimplices Spatiotemporal processing in a hypernetwork: transient sequences in response to stimuli

Map-based model of neural activity

В.И. Некоркин, Л.В. Вдовин. Изв. вузов ПНД. 2007; M.Courbage, V.I. Nekorkin, L.V. Vdovin. Chaos. 2007.

x – membrane potential of the neuron; y –outward ionic currents (recovery variable); J – controls the level of depolarization; ε – time scale of the recovery variable; β, d – control threshold properties of bursting oscillations; a – controls shape of neural impulses.

Slow-fast dynamics

For fixed y there are two different regimes depending on y:

Fast dynamics (y is constant) Slow dynamics

   − + = = + − − −

+

), ( , ) ( ) (

1

J x y y I y d x H x F

n n n n n n

 

Gallery of dynamical regimes in map-based model

Regular regimes Chaotic regimes

When stimulated by rectangular impulse, the system generates a burst.

System`s response to stimulus

Interneuron links

Inhibitory coupling: ν = -0.5, θ = 0.2, and g=0.15. where g defines the coupling strength, ν is the reversal potential, and θ is the threshold parameter. if the j-th node affects the i-th node at the moment of n

• therwise

Adjacency matrix As a result, the network with a constant topology generates a cyclic sequence of clusters, the so-called cluster state

Chaotic oscillatory dynamics

a=0.1, β=0.3, d=0.45, ε=0.001 a=0.1, β=0, d=0.45, ε=0.01

Operator of connection rewiring

xi(n) — activity of neuron i E(n) — external stimulus T=T(xi, E, n) —

• perator of links

update due to plastisity G=(Gij) — matrix of interneuron links G(n+1) = TG(n) – update of links resulting in activation

• f a new hypersimplex

Hypersimplex: activity and structure configurations

Hypernetwork

Hypernetwork consisting of 30 hypersimplexes describing three- cluster states in the adaptive 5-node spiking network.

Spatial processing

Stimulus A Stimulus B

time

• No. oscillator

time

• No. oscillator

Spatiotemporal processing

Sequence of activity states Sk time

• No. oscillator

Spatiotemporal processing

Sequence of activity states Sk time

• No. oscillator

Biological neural networks and hypernetworks

Courtesy of J. Soriano (University of Barcelona)

Fluorescence imaging

1 1 1 ... ...

Sequence of activity states

... ... 1 ... ... 1 1 1 ... ...

... Sequence of hypersimplexes

Biological neural networks and hypernetworks

Homogeneous network

Data: neuron dynamics in vitro Spike rastrogram Sequence of hypersimplexes

Number of hypersimplexes

• bserved

Clustered network

Data: neuron dynamics in vitro Spike rastrogram Sequence of hypersimplexes

Number of hypersimplexes

• bserved

• A model was proposed for a spiking neuron network that

generates two-level

• dynamics. At

the first level, transient sequences of activity clusters are formed; at the second one — at the hypernetwork — paths of activations between different hypersimplexes are created.

• The approach was applied to analysing neurobiological in vitro

data and based

• n

the network spiking dynamics, the hypersimplexes were found and the activation paths in the hypernetwork were obtained.

Conclusion

Thank you for attention