### Abstract

Since more than a decade ago, three statements about spiking neuron (SN) implementations have been widely accepted: 1) Hodgkin and Huxley (HH) model is computationally prohibitive, 2) Izhikevich (IZH) artificial neuron is as efficient as Leaky Integrate-and-Fire (LIF) model, and 3) IZH model is more efficient than HH model (Izhikevich, 2004). As suggested by Hodgkin and Huxley (1952), their model operates in two modes: by using the α’s and β’s rate functions directly (HH model) and by storing them into tables (HHT model) for computational cost reduction. Recently, it has been stated that: 1) HHT model (HH using tables) is not prohibitive, 2) IZH model is not efficient, and 3) both HHT and IZH models are comparable in computational cost (Skocik & Long, 2014). That controversy shows that there is no consensus concerning SN simulation capacities. Hence, in this work, we introduce a refined approach, based on the multiobjective optimization theory, describing the SN simulation capacities and ultimately choosing optimal simulation parameters. We have used normalized metrics to define the capacity levels of accuracy, computational cost, and efficiency. Normalized metrics allowed comparisons between SNs at the same level or scale. We conducted tests for balanced, lower, and upper boundary conditions under a regular spiking mode with constant and random current stimuli. We found optimal simulation parameters leading to a balance between computational cost and accuracy. Importantly, and, in general, we found that 1) HH model (without using tables) is the most accurate, computationally inexpensive, and efficient, 2) IZH model is the most expensive and inefficient, 3) both LIF and HHT models are the most inaccurate, 4) HHT model is more expensive and inaccurate than HH model due to α’s and β’s table discretization, and 5) HHT model is not comparable in computational cost to IZH model. These results refute the theory formulated over a decade ago (Izhikevich, 2004) and go more in-depth in the statements formulated by Skocik and Long (2014). Our statements imply that the number of dimensions or FLOPS in the SNs are theoretical but not practical indicators of the true computational cost. The metric we propose for the computational cost is more precise than FLOPS and was found to be invariant to computer architecture. Moreover, we found that the firing frequency used in previous works is a necessary but an insufficient metric to evaluate the simulation accuracy. We also show that our results are consistent with the theory of numerical methods and the theory of SN discontinuity. Discontinuous SNs, such LIF and IZH models, introduce a considerable error every time a spike is generated. In addition, compared to the constant input current, the random input current increases the computational cost and inaccuracy. Besides, we found that the search for optimal simulation parameters is problem-specific. That is important because most of the previous works have intended to find a general and unique optimal simulation. Here, we show that this solution could not exist because it is a multiobjective optimization problem that depends on several factors. This work sets up a renewed thesis concerning the SN simulation that is useful to several related research areas, including the emergent Deep Spiking Neural Networks.

Original language | English |
---|---|

Pages (from-to) | 196-217 |

Number of pages | 22 |

Journal | Neural Networks |

Volume | 122 |

DOIs | |

State | Published - Feb 2020 |

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### Keywords

- Accuracy
- Computational cost
- Numerical method
- Simulation
- Spiking neuron
- Time step

### Cite this

*Neural Networks*,

*122*, 196-217. https://doi.org/10.1016/j.neunet.2019.09.026

}

*Neural Networks*, vol. 122, pp. 196-217. https://doi.org/10.1016/j.neunet.2019.09.026

**On the accuracy and computational cost of spiking neuron implementation.** / Valadez-Godínez, Sergio; Sossa, Humberto; Santiago-Montero, Raúl.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the accuracy and computational cost of spiking neuron implementation

AU - Valadez-Godínez, Sergio

AU - Sossa, Humberto

AU - Santiago-Montero, Raúl

PY - 2020/2

Y1 - 2020/2

N2 - Since more than a decade ago, three statements about spiking neuron (SN) implementations have been widely accepted: 1) Hodgkin and Huxley (HH) model is computationally prohibitive, 2) Izhikevich (IZH) artificial neuron is as efficient as Leaky Integrate-and-Fire (LIF) model, and 3) IZH model is more efficient than HH model (Izhikevich, 2004). As suggested by Hodgkin and Huxley (1952), their model operates in two modes: by using the α’s and β’s rate functions directly (HH model) and by storing them into tables (HHT model) for computational cost reduction. Recently, it has been stated that: 1) HHT model (HH using tables) is not prohibitive, 2) IZH model is not efficient, and 3) both HHT and IZH models are comparable in computational cost (Skocik & Long, 2014). That controversy shows that there is no consensus concerning SN simulation capacities. Hence, in this work, we introduce a refined approach, based on the multiobjective optimization theory, describing the SN simulation capacities and ultimately choosing optimal simulation parameters. We have used normalized metrics to define the capacity levels of accuracy, computational cost, and efficiency. Normalized metrics allowed comparisons between SNs at the same level or scale. We conducted tests for balanced, lower, and upper boundary conditions under a regular spiking mode with constant and random current stimuli. We found optimal simulation parameters leading to a balance between computational cost and accuracy. Importantly, and, in general, we found that 1) HH model (without using tables) is the most accurate, computationally inexpensive, and efficient, 2) IZH model is the most expensive and inefficient, 3) both LIF and HHT models are the most inaccurate, 4) HHT model is more expensive and inaccurate than HH model due to α’s and β’s table discretization, and 5) HHT model is not comparable in computational cost to IZH model. These results refute the theory formulated over a decade ago (Izhikevich, 2004) and go more in-depth in the statements formulated by Skocik and Long (2014). Our statements imply that the number of dimensions or FLOPS in the SNs are theoretical but not practical indicators of the true computational cost. The metric we propose for the computational cost is more precise than FLOPS and was found to be invariant to computer architecture. Moreover, we found that the firing frequency used in previous works is a necessary but an insufficient metric to evaluate the simulation accuracy. We also show that our results are consistent with the theory of numerical methods and the theory of SN discontinuity. Discontinuous SNs, such LIF and IZH models, introduce a considerable error every time a spike is generated. In addition, compared to the constant input current, the random input current increases the computational cost and inaccuracy. Besides, we found that the search for optimal simulation parameters is problem-specific. That is important because most of the previous works have intended to find a general and unique optimal simulation. Here, we show that this solution could not exist because it is a multiobjective optimization problem that depends on several factors. This work sets up a renewed thesis concerning the SN simulation that is useful to several related research areas, including the emergent Deep Spiking Neural Networks.

AB - Since more than a decade ago, three statements about spiking neuron (SN) implementations have been widely accepted: 1) Hodgkin and Huxley (HH) model is computationally prohibitive, 2) Izhikevich (IZH) artificial neuron is as efficient as Leaky Integrate-and-Fire (LIF) model, and 3) IZH model is more efficient than HH model (Izhikevich, 2004). As suggested by Hodgkin and Huxley (1952), their model operates in two modes: by using the α’s and β’s rate functions directly (HH model) and by storing them into tables (HHT model) for computational cost reduction. Recently, it has been stated that: 1) HHT model (HH using tables) is not prohibitive, 2) IZH model is not efficient, and 3) both HHT and IZH models are comparable in computational cost (Skocik & Long, 2014). That controversy shows that there is no consensus concerning SN simulation capacities. Hence, in this work, we introduce a refined approach, based on the multiobjective optimization theory, describing the SN simulation capacities and ultimately choosing optimal simulation parameters. We have used normalized metrics to define the capacity levels of accuracy, computational cost, and efficiency. Normalized metrics allowed comparisons between SNs at the same level or scale. We conducted tests for balanced, lower, and upper boundary conditions under a regular spiking mode with constant and random current stimuli. We found optimal simulation parameters leading to a balance between computational cost and accuracy. Importantly, and, in general, we found that 1) HH model (without using tables) is the most accurate, computationally inexpensive, and efficient, 2) IZH model is the most expensive and inefficient, 3) both LIF and HHT models are the most inaccurate, 4) HHT model is more expensive and inaccurate than HH model due to α’s and β’s table discretization, and 5) HHT model is not comparable in computational cost to IZH model. These results refute the theory formulated over a decade ago (Izhikevich, 2004) and go more in-depth in the statements formulated by Skocik and Long (2014). Our statements imply that the number of dimensions or FLOPS in the SNs are theoretical but not practical indicators of the true computational cost. The metric we propose for the computational cost is more precise than FLOPS and was found to be invariant to computer architecture. Moreover, we found that the firing frequency used in previous works is a necessary but an insufficient metric to evaluate the simulation accuracy. We also show that our results are consistent with the theory of numerical methods and the theory of SN discontinuity. Discontinuous SNs, such LIF and IZH models, introduce a considerable error every time a spike is generated. In addition, compared to the constant input current, the random input current increases the computational cost and inaccuracy. Besides, we found that the search for optimal simulation parameters is problem-specific. That is important because most of the previous works have intended to find a general and unique optimal simulation. Here, we show that this solution could not exist because it is a multiobjective optimization problem that depends on several factors. This work sets up a renewed thesis concerning the SN simulation that is useful to several related research areas, including the emergent Deep Spiking Neural Networks.

KW - Accuracy

KW - Computational cost

KW - Numerical method

KW - Simulation

KW - Spiking neuron

KW - Time step

UR - http://www.scopus.com/inward/record.url?scp=85074273933&partnerID=8YFLogxK

U2 - 10.1016/j.neunet.2019.09.026

DO - 10.1016/j.neunet.2019.09.026

M3 - Artículo

C2 - 31689679

AN - SCOPUS:85074273933

VL - 122

SP - 196

EP - 217

JO - Neural Networks

JF - Neural Networks

SN - 0893-6080

ER -