Minimal network partitions using average -hedra

Author(s):  
M. E. Glicksman ◽  
P. R. Rios
Author(s):  
Serkan Kiranyaz ◽  
Junaid Malik ◽  
Habib Ben Abdallah ◽  
Turker Ince ◽  
Alexandros Iosifidis ◽  
...  

AbstractThe recently proposed network model, Operational Neural Networks (ONNs), can generalize the conventional Convolutional Neural Networks (CNNs) that are homogenous only with a linear neuron model. As a heterogenous network model, ONNs are based on a generalized neuron model that can encapsulate any set of non-linear operators to boost diversity and to learn highly complex and multi-modal functions or spaces with minimal network complexity and training data. However, the default search method to find optimal operators in ONNs, the so-called Greedy Iterative Search (GIS) method, usually takes several training sessions to find a single operator set per layer. This is not only computationally demanding, also the network heterogeneity is limited since the same set of operators will then be used for all neurons in each layer. To address this deficiency and exploit a superior level of heterogeneity, in this study the focus is drawn on searching the best-possible operator set(s) for the hidden neurons of the network based on the “Synaptic Plasticity” paradigm that poses the essential learning theory in biological neurons. During training, each operator set in the library can be evaluated by their synaptic plasticity level, ranked from the worst to the best, and an “elite” ONN can then be configured using the top-ranked operator sets found at each hidden layer. Experimental results over highly challenging problems demonstrate that the elite ONNs even with few neurons and layers can achieve a superior learning performance than GIS-based ONNs and as a result, the performance gap over the CNNs further widens.


2018 ◽  
Vol 43 (3) ◽  
pp. 1-45 ◽  
Author(s):  
Orestis Polychroniou ◽  
Wangda Zhang ◽  
Kenneth A. Ross

1999 ◽  
Vol 81 (3) ◽  
pp. 1274-1283 ◽  
Author(s):  
F. K. Skinner ◽  
L. Zhang ◽  
J. L. Perez Velazquez ◽  
P. L. Carlen

Bursting in inhibitory interneuronal networks: a role for gap-junctional coupling. Much work now emphasizes the concept that interneuronal networks play critical roles in generating synchronized, oscillatory behavior. Experimental work has shown that functional inhibitory networks alone can produce synchronized activity, and theoretical work has demonstrated how synchrony could occur in mutually inhibitory networks. Even though gap junctions are known to exist between interneurons, their role is far from clear. We present a mechanism by which synchronized bursting can be produced in a minimal network of mutually inhibitory and gap-junctionally coupled neurons. The bursting relies on the presence of persistent sodium and slowly inactivating potassium currents in the individual neurons. Both GABAA inhibitory currents and gap-junctional coupling are required for stable bursting behavior to be obtained. Typically, the role of gap-junctional coupling is focused on synchronization mechanisms. However, these results suggest that a possible role of gap-junctional coupling may lie in the generation and stabilization of bursting oscillatory behavior.


2019 ◽  
Author(s):  
Mark Olenik ◽  
Conor Houghton

AbstractSynaptic plasticity is widely found in many areas of the central nervous system. In particular, it is believed that synaptic depression can act as a mechanism to allow simple networks to generate a range of different firing patterns. The simplicity of the locomotor circuit in hatchling Xenopus tadpoles provides an excellent place to understand such basic neuronal mechanisms. Depending on the nature of the external stimulus, tadpoles can generate two types of behaviours: swimming when touched and slower, stronger struggling movements when held. Struggling is associated with rhythmic bends of the body and is accompanied by anti-phase bursts in neurons on each side of the spinal cord. Bursting in struggling is thought to be governed by a short-term synaptic depression of inhibition. To better understand burst generation in struggling, we study a minimal network of two neurons coupled through depressing inhibitory synapses. Depending on the strength of the synaptic conductance between the two neurons, such a network can produce symmetric n - n anti-phase bursts, where neurons fire n spikes in alternation, with the period of such solutions increasing with the strength of the synaptic conductance. Using a fast/slow analysis, we reduce the multidimensional network equations to a scalar Poincaé burst map. This map tracks the state of synaptic depression from one burst to the next, and captures the complex bursting dynamics of the network. Fixed points of this map are associated with stable burst solutions of the full network model, and are created through fold bifurcations of maps. We prove that the map has an infinite number of stable fixed points for a finite coupling strength interval, suggesting that the full two-cell network also can produce n - n bursts for arbitrarily large n. Our findings further support the hypothesis that synaptic depression can enrich the variety of activity patterns a neuronal network generates.


2018 ◽  
Vol 28 (10) ◽  
pp. 1850123 ◽  
Author(s):  
Yo Horikawa ◽  
Hiroyuki Kitajima ◽  
Haruna Matsushita

Bifurcations and chaos in a network of three identical sigmoidal neurons are examined. The network consists of a two-neuron oscillator of the Wilson–Cowan type and an additional third neuron, which has a simpler structure than chaotic neural networks in the previous studies. A codimension-two fold-pitchfork bifurcation connecting two periodic solutions exists, which is accompanied by the Neimark–Sacker bifurcation. A stable quasiperiodic solution is generated and Arnold’s tongues emanate from the locus of the Neimark–Sacker bifurcation in a two-dimensional parameter space. The merging, splitting and crossing of the Arnold tongues are observed. Further, multiple chaotic attractors are generated through cascades of period-doubling bifurcations of periodic solutions in the Arnold tongues. The chaotic attractors grow and are destroyed through crises. Transient chaos and crisis-induced intermittency due to the crises are also observed. These quasiperiodic solutions and chaotic attractors are robust to small asymmetry in the output function of neurons.


2020 ◽  
Vol 138 ◽  
pp. 109951 ◽  
Author(s):  
S Yu Makovkin ◽  
I V Shkerin ◽  
S Yu Gordleeva ◽  
M V Ivanchenko
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