A Design Method for Analog and Digital Silicon Neurons ???-Mathematical-Model-Based Method-

Kohno, Takashi; Aihara, Kazuyuki; Ricciardi, Luigi M.; Buonocore, Aniello; Pirozzi, Enrica

doi:10.1063/1.2965080

Cited by 8 publications

(5 citation statements)

References 20 publications

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“…9 In this method, we reconstruct the mathematical structure in the original model using the characteristic output curves of simple analog electronic circuits, which allows us to avoid using complex circuits to approximate the equations in the original model directly.…”

Section: Mathematical-structure-based Approachmentioning

confidence: 99%

A two-variable silicon neuron circuit based on the Izhikevich model

Mizoguchi

Nagamatsu

Aihara

et al. 2011

Artif Life Robotics

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A two-variable silicon neuron circuit based on the Izhikevich model which is diffi cult in simulations using digital computers. In addition, it can be compact if it is implemented into an analog very large-scale integrated (aVLSI) circuit. For those reasons, it is expected that the silicon neuron will be applied for real-time systems such as hybrid systems, medical devices, and robots.Silicon neurons have been developed by two different basic approaches. The fi rst is to reproduce only signifi cant neuronal behavior, which is called the phenomenological method. Silicon neuron circuits designed by this method 7 tend to be simple, but can only reproduce a few fi ring patterns because of their oversimplifi ed dynamics. The second approach is to reproduce the neuronal dynamics precisely by solving the ionic conductance model, which is called the conductance-based method. Silicon neurons designed by this method 8 can reproduce various fi ring patterns, but their circuitry is large and complex.Recently, Kohno and Aihara 9 proposed another method, the mathematical-structure-based approach, which allows us to design simple circuits with rich neuronal dynamics by reproducing the mathematical structure of the original models. By using this method, Nagamatsu et al. 10 proposed a silicon neuron circuit (in this article, we will call it the "previous circuit"), which reproduces the mathematical structure of the Izhikevich model. 11 This silicon neuron circuit reconstructs the dynamics of the Izhikevich model with a simple circuit whose average power consumption is about 15 nW. However, in the circuit that implements the jump of state in the Izhikevich model (we call this circuit the "reset circuit"), the voltage variation is relatively large in comparison to the other parts of the circuit operated in the sub-threshold region. Furthermore, the input current that triggers the spiking of the silicon neuron needs to be small, which is likely to be diffi cult to produce.Here, we propose an improved circuit with a new reset circuit in which the voltage variation is about 0.4 V, which is lower than that of the previous circuit by about 2.25 V. In addition, we scaled up the input current by altering part of the circuit. These modifi cations are expected to lower the diffi culty of aVLSI implementation in this circuit. AbstractThe silicon neuron is an analog electronic circuit that reproduces the dynamics of a neuron. It is a useful element for artifi cial neural networks that work in real time. Silicon neuron circuits have to be simple, and at the same time they must be able to realize rich neuronal dynamics in order to reproduce the various activities of neural networks with compact, low-power consumption, and an easy-toconfi gure circuit. We have been developing a silicon neuron circuit based on the Izhikevich model, which has rich dynamics in spite of its simplicity. In our previous work, we proposed a simple silicon neuron circuit with low power consumption by reconstructing the mathematical structure in the Izhikevich model usin...

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Section: Mathematical-structure-based Approachmentioning

confidence: 99%

A two-variable silicon neuron circuit based on the Izhikevich model

Mizoguchi

Nagamatsu

Aihara

et al. 2011

Artif Life Robotics

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“…In our previous works (Kohno and Aihara, 2005 , 2007 , 2008a ; Sekikawa et al, 2008 ; Kohno and Aihara, 2010 ; Li et al, 2012 ; Kohno and Aihara, 2014a ; Kohno et al, 2014b ), we proposed a qualitative-modeling-based design approach for SNs. In this approach, a qualitative neuronal model that reproduces the dynamical structure in a target neuronal model is constructed by combining the formulae for the characteristic curves of favorable elemental circuit blocks instead of polynomials.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, a model that supports the mathematical structures in different classes of neurons can be designed, and one of them is invoked by appropriately selecting the model parameters. We developed a configurable low-power analog SN circuit (Kohno and Aihara, 2008a , b ; Sekikawa et al, 2008 ; Kohno and Aihara, 2010 ) and a configurable simple digital SN circuit (Kohno and Aihara, 2007 ; Li et al, 2012 , 2013 ). Our analog SN supports five classes of neuronal activities, Class I and II in the Hodgkin's classification, regular spiking (RS), square-wave bursting, and elliptic bursting (Wang and Rinzel, 2003 ) by appropriately setting the parameter voltages, and our digital SN supports Class I and II and Class I * (Tadokoro et al, 2011 ) neuronal activities.…”

Section: Introductionmentioning

confidence: 99%

Qualitative-Modeling-Based Silicon Neurons and Their Networks

Kohno

Sekikawa

et al. 2016

Front. Neurosci.

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The ionic conductance models of neuronal cells can finely reproduce a wide variety of complex neuronal activities. However, the complexity of these models has prompted the development of qualitative neuron models. They are described by differential equations with a reduced number of variables and their low-dimensional polynomials, which retain the core mathematical structures. Such simple models form the foundation of a bottom-up approach in computational and theoretical neuroscience. We proposed a qualitative-modeling-based approach for designing silicon neuron circuits, in which the mathematical structures in the polynomial-based qualitative models are reproduced by differential equations with silicon-native expressions. This approach can realize low-power-consuming circuits that can be configured to realize various classes of neuronal cells. In this article, our qualitative-modeling-based silicon neuron circuits for analog and digital implementations are quickly reviewed. One of our CMOS analog silicon neuron circuits can realize a variety of neuronal activities with a power consumption less than 72 nW. The square-wave bursting mode of this circuit is explained. Another circuit can realize Class I and II neuronal activities with about 3 nW. Our digital silicon neuron circuit can also realize these classes. An auto-associative memory realized on an all-to-all connected network of these silicon neurons is also reviewed, in which the neuron class plays important roles in its performance.

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“…Rather, the digital program is substituted by the dynamics in non Euclidean space. We can program the CrossNet (Takashi Kohno, 2008), (Rinzel, 1998) electrical system as it was used by Snider to compute the parameters useful to generate the desired trajectories to solve problems. Geometric and physical description of the intentionality (Freeman, 1975) is beyond any algorithmic or digital computation.…”

Section: Introductionmentioning

confidence: 99%

Geometric Image of Neurodynamics

2012

Proceedings of the 4th International Joint Conference on Computational Intelligence

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We know that the brain is composed of simple neural units given by dendrites, soma, and axons. Every neural unit can be modelled by electrical circuits with capacitors and adaptive resistors. To study the neural dynamic we use special Ordinary Differential Equations (ODE) whose solutions give us the behaviour or trajectory of the neural states in time. The problem with ODE is in the definition of the parameters and in the complexity of the solutions that in many cases cannot be found. The key elements that we use are the multidimensional vector spaces of the electrical charges, currents and voltages. So currents and voltages are geometric references for states in the central neural system (CNS). Any neuro-biological architecture can be modelled by an adaptive electrical circuit or neuromorphic network that relates voltage with current by conductance matrix or on the contrary by impedance matrix. Given a straight line with a change of reference we reshape the straight line in a geodetic and in a new form for the distance. The change of the reference transforms a set of variables into another so this transformation is similar to a statement in the digital computer that we associate to the software. Every change of variables can be reproduced by a similar change of voltages (currents) into currents (voltages) by conductance (impedance) matrix. We use the CNS as a material support or hardware in the digital computer to realise the wanted transformation. In conclusion geometry fuses the digital computer structure with neuromorphic computing to give efficient computation where conceptual intention is the change of the reference space , while material intention is given by the neurodynamical processes modelled by the change of the electrical charge space where we define the metric geometry and distance.

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A Design Method for Analog and Digital Silicon Neurons ???-Mathematical-Model-Based Method-

Cited by 8 publications

References 20 publications

A two-variable silicon neuron circuit based on the Izhikevich model

A two-variable silicon neuron circuit based on the Izhikevich model

Qualitative-Modeling-Based Silicon Neurons and Their Networks

Geometric Image of Neurodynamics

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