Theoretical framework and advanced applications of spiking neural networks

Developed from traditional Artificial neural networks (ANN), the Spiking neural network (SNN) faithfully mimics the biological behaviours of natural neurons. SNNs transmit information through firing of spiking neurons only when the membrane potential reaches a certain threshold. Because of this property, SNNs are referred to as the most biologically plausible neural model. They are also evaluated as time-efficient and low power-consuming when dealing with complex computational tasks. In this paper, the differences between SNNs and ANNs are first identified. The theoretical framework of the SNN, including the biomedical background, classical spiking neuron models, neural coding mechanisms as well as the learning algorithm are then thoroughly introduced. From the theories, the SNN’s biological plausibility, working principles, strengths and limitations are discussed. Additionally, two applications in the medical & robotics field using the SNN’s pattern recognition and classification are described in detail, indicating its potential in more innovative studies. More imaginative uses of SNNs are in demand for its dominant role in future computational fields.


Introduction
Recent years have seen an ever-growing interest from researchers all around the world on the topic of brain-inspired technology.Among the studies, the neural network, or called the Artificial Neural Network (ANN) was created based on artificial neurons modeled from the natural neurons.It was developed, continuously evaluated over years, and practically applied in many computational fields.However, despite its success in problem-solving fields, its power-consumption and processing rate is gradually falling behind the exponentially growing demands.The Spiking Neural Network (SNN) is a variant developed from the ANN.However, it innovatively mimics the natural behaviors of neurons, making neural networks more biologically plausible.One of the important differences between ANNs and SNNs is the concept of time [1].Traditional ANNs have both the inputs and outputs in analog values, and they encode the information through the method of spike firing rate coding.SNNs use spiking neural models that encode information using the exact timing of spikes instead of the firing rate, which makes them more powerful tools in processing spatiotemporal information [2].
This paper gives a review of SNN studies and recent development.Firstly, the biological background of SNN is introduced for a comprehensive understanding of SNN's biological plausibility.Secondly, some classical spiking neuron models are explained focusing on how the property of "spikes" are mimicked in the network.Then, the idea of neural encoding was discussed by neural coding mechanisms.The learning strategies and algorithms are also reviewed for a big picture of how SNNs learn and how they are trained.Finally, some most recent real-world application examples of SNN are discussed, as well as its potential of being used in novel fields of studies.

Biological Background
A basic neuron structure consists of three main parts: the cell body (the soma), the dendrites and the axon.When there's no electrical signal sent across, the neuron is said to be "at rest".The difference between the intracellular and extracellular voltage is measured at about -70 mV, which is called the resting potential.This happens as a result of the relative concentration difference between sodium ions outside the cell and potassium ions inside the cell.If the intracellular voltage gets less electronegative, the neuron is said to be depolarized.On the contrary, if it becomes more electronegative than -70 mV, it is said to be hyperpolarized.When the neuron is depolarized to a certain threshold, an action potential is triggered and propagates along the axon.
The electrochemical signal transmission among neurons is achieved at the point of communication called synapse, as shown by figure 1.At the synapse, the firing of an action potential in the presynaptic neuron transmits an electrochemical signal to the postsynaptic neuron that either causes or inhibits the firing of its action potential.Specifically, the excitatory postsynaptic potential, or EPSP, causes depolarization of the cell membrane and hence makes the postsynaptic neuron more likely to generate an action potential.While the inhibitory postsynaptic potential, or IPSP, causes hyperpolarization of the cell membrane and hence makes the postsynaptic neuron less likely to generate an action potential.SNN as a neural network that faithfully mimics the signal transmitting, receiving, and processing in the nervous system, is also of the property that generates electrical signals only a threshold potential is reached on the neuronal membrane.Because of this property, SNN is more efficient in energy saving in both learning and training process.It is also capable of capturing dynamic neuronal signals in several dimensions such as time, frequency, and phase [3].Therefore, SNN is a promising technology that could offer strong support for future progress in artificial intelligence.

Spiking neuron models
In this section, representative models that are characteristic for three types of models are discussed, which are respectively 1) Biologically plausible model; 2) Integrate-and -fire model with fixed threshold; 3) Nonlinear spike-generation model.The schematic diagram of the H-H model is shown by figure 2. The semipermeable cell membrane, intracellular and extracellular liquid are translated into an equivalent RC electric circuit, where important components are treated as electrical elements.For example, voltage-gated ion channels for sodium and potassium ions are represented by electrical conductance (  for sodium ion channel and   for potassium ion channel), and the leakage channel for chloride ion is represented by linear conductance (  ).The lipid bilayer is modeled by a capacitance (  ), which also indicates the membrane ability to store electric charge.On the basis of the equivalent circuit model as well as extensive voltage clamp experiments, Hodgkin and Huxley summarized their findings into a set of four nonlinear differential equations: where the membrane potential is denoted by   .Notice that the equation ( 1) is derived from the conservation of electric current in the circuit, and other equations (2) (3) (4) describe the dynamics via specific ion channels.Overall, the H-H model firstly reproduces the characteristics of the neuron through mimicking real biological neuron behaviors, hence it shows better biological plausibility over other models.However, the intrinsic computational complexity of the 4-dimensional mathematical model means it's never computational cost-efficient, hence it can only be used to simulate small-scale of neurons [3,4].

Leaky Integrate-and-Fire Model.
The Leaky Integrate-and-Fire (LIF) Model is another one of the most widely used neuron models that was developed from the Integrate-and Fire (I&F) model.In 1907, Lapicque developed the I&F model even before the mechanisms underlying the generation of neuronal action potential were figured out.Lapicque modeled the neuron with a simple RC circuit consisting of a capacitor connected in parallel with a resistor, which represent the capacitance and leakage resistance.He postulated that when a driven current was applied and the membrane capacitance reached a certain threshold, a spike would be generated, and the capacitor would start discharging until the membrane voltage is restored to its resting potential.The I&F model was considered simple and useful enough given a lack of biophysical explanation on action potential in the early 1900s.However, because of its simplicity and poor biological plausibility, the I&F neurons failed in exhibiting the leakage, accumulation, and firing threshold that are considered as key features in neuronal action potential generation.where   () is the membrane potential,   is the membrane resistance, and   is the membrane capacitance.
By multiplying equation ( 5) by   , introducing the membrane time constant   =     as well as considering the membrane resting potential, the standard form is further derived as where   is the constant membrane resting potential.
From the equation ( 6), the relationship between the cell membrane potential and the driving current also reflects the property of the refractory period, which indicates that the model is more biologically realistic compared to the non-leaky I&F model.Overall, the LIF model as a one-dimensional model shows a relatively low computation cost in large-scale neural network application.
where  represents the neuronal membrane potential,  represents the injected DC current as a function of time, and  represents a membrane recovery variable that describes the activation or inactivation effect of ions on the membrane potential .Also, there's an auxiliary after-spike resetting that   ≥ 30 , ℎ {  ←   ←  + . ( With different choices of the dimensionless parameter , ,  and , the intrinsic firing patterns vary, which is shown by figure 4. The Izhikevich Model successfully used the bifurcation methodologies to simplify the H-H Model into two equations with only one nonlinear term.It is acknowledged as one of the simplest possible models that can achieve biologically realistic behavior and can be applied to large-scale simulation on spiking neurons with a resolution of 1 millisecond.

Neural Coding
Neurons are capable of propagating electrochemical signals rapidly through action potential.Different types of stimuli result in different patterns of action potential.This is done by neurons through changing the firing sequence of action potentials in various temporal patterns when subject to different types of external stimuli.The action potentials are then transmitted into and around the brain for processing.
Neural coding is mainly focused on the relationship between external stimuli and neural activities.In neural coding studies, an action potential sequence is characterized by a series of zeros and ones along the time axis.In this section, three hypothesized coding schemes will be introduced to show how stimuli are translated into characteristic action potential sequences.
2.3.1.Rate Coding.Rate coding as a concept was originally proposed by E.D. Adrian in 1926.They found that as the mass of the suspended object increased on a muscle, the neuron firing frequency also increased.The rate coding is a conventional coding model the states that the neuron firing rate is positively proportional to the stimulus intensity.Figure 5 shows an example rate coding scheme.Because the measurement of firing rate was relatively easy, this model was used as a standard tool for description of neural activities.Typically, the spike-count rate and the time-dependent firing rate are evaluated.However, since the approach only cares about rate but mostly neglects temporal information delivered by the exact happening timing of each spike, it performs poorly in efficiency, but is rather robust to noises [7].

Temporal Coding.
Temporal coding is another coding model that takes into account the information carried by exact firing timing and high-frequency firing-rate fluctuations, given the findings that the temporal resolution of the spike firing can be precise down to milliseconds [8].Temporal coding focuses more on the temporal structure of spikes rather than just the firing rate.For example, given a certain sequence of 0 and 1 to represent spike and no spike, even though they share the same mean firing rate, the permutation might vary.Different from rate coding, some significant features of the spike activity are captured by temporal coding, such as spike randomness and variability [9].However, as temporal coding entirely takes information along the spike train, it could also encode the irregularities such as noises.Therefore, it is less robust in dealing with high-frequency firing-rate fluctuations which could be noise or be useful information.encoded based on a cluster of cells [10].It performs faster than rate coding and is capable of reflecting changes in the stimulus conditions almost instantaneously.

Learning Strategies
In neuroscience, plasticity is defined as the adaptability of the brain to changes in environment or new information.Synaptic plasticity specifically refers to changes that occur at synapses, and it is acknowledged as the biological substrate of the study of memory and learning.In 1949, Donald Hebb made the first attempt to explain synaptic plasticity during the learning process.His theory, also called Hebbian theory or Hebb's rule, claimed that synaptic plasticity increases with constant and repeated stimulation from a presynaptic cell to a postsynaptic cell.
Many unsupervised learning approaches for SNN were inspired from Hebb's rule.As one of the three main types of learning strategies, unsupervised learning is a machine learning paradigm characterized by analyzing events or datasets without associated labels.Spike Timing Dependent Plasticity (STDP) is an example of a variant developed from Hebb's rule.A standard STDP learning time window shown by figure 7, where two cases are identified.If the presynaptic cell repeatedly spikes just before the postsynaptic cell, it is a causal activity, while the opposite order is an acausal activity.Causal activities result in long-term potentiation (LTP), and acausal activities result in long-term depression (LTD).The classical STDP form is considered to successfully create a unique neural mechanism for the identification of causality and non-causality on a millisecond timescale.This time dependent plasticity is also proved in modeling studies to be rate dependent and offer flexibility and computational power in building cortical circuits [11].Overall, STDP as a model of the spike plasticity has been proved to be a good choice for neural network learning algorithm and can be efficiently used for modeling of information processing in the brain.The main difference between supervised learning from unsupervised learning is it relies on labeled input and output training data.Recent years lots of studies have been conducted on supervised learning for SNNs.The existing learning algorithms can be classified into categories.Take the SNN architecture as an example, some characteristic supervised learning algorithms for single-layer SNNs include Perceptron-based algorithms, Synaptic plasticity algorithms, and Spike train convolution algorithms [2].For multilayer feed forward SNNs, Gradient descent algorithms are usually used, while Synaptic plasticity algorithms and Spike train convolution algorithms still remains applicable.
Reinforced learning is another basic machine learning paradigm, together with supervised learning and unsupervised learning.It is basically a reward-based algorithm that deals with the environment given sample data, and it usually works on dynamically achieving a balance between exploration and exploitation.Typical reinforcement learning models include the Markov decision process and the Q learning where dynamic programming techniques are usually used for learning optimal behaviors [12].

Applications
Recent years, SNNs have been frequently applied in fields such as computer vision, signal processing, and robotic control.In this section, two specific examples of SNN application regarding pattern recognition and classification will be introduced.

Hand Gesture Recognition
Pattern recognition is one of the popular research fields for SNN application, because of SNN's computational and power efficiency.One example of application on hand gesture recognition tasks was proposed in 2019 [13].In the paper, a new rapid spike firing time search algorithm was first introduced to address the existing limitations of the present SNN.Specifically, they started from the LIF model to realize SNN, and designed a new search algorithm for narrower search interval (hence faster in determining of the spike firing time) in the current SNN model.They also used a gradient descent algorithm to train a multilayer SNN rather than a single-layer structure to effectively improve the performance by accelerating the convergence and avoiding early training terminations.
The hand rehabilitation robot application of SNN was aimed for effective rehabilitation processes, through making the robots understand and capable of recognizing patients' hand motion intention for corresponding assistance.Before applying SNN, eight typical hand gestures were selected and recorded in surface electromyography (sEMG) signals from volunteers.Appropriate features of sEMG signals in the time and time-frequency domain were then selected for the proposed multilayer SNN, whose structure is shown by figure 8.The inputs from the input layer are connected to the spike neurons in the subnet layer, while each subnet layer includes spiking neurons that correspond with one certain feature.Neurons in the mixture layer are fully connected with those in the subnet layer.Eventually, the spiking neurons in the output layer give a spike sequence encoded using a modified population coding strategy.The experimental results shown that nearly 40% of iterations was reduced using the new search algorithm, which means the process was successfully accelerated.Also, there was a 0.9% increase in the recognition accuracy ratio compared with previous SNNs.

Intelligent skin cancer detection
Application of SNNs on pattern classification is showing its positive influence in the field of medical studies.In a study of SNN application on skin cancer detection, skin tumor classification was done by dividing tumor cells into two classes: benign and malignant [14].Detection of skin cancer was realized with a proposed deep learning model which successfully combines the autoencoder, spiking, and convolutional neural networks.In this study, a SNN based on the LIF model was mainly used for supporting the MobileNetV2 model for training and classification.It was considered to be an innovative approach to use spiking networks and the deep learning model at the same time.
As shown by figure 9, 1000 features from the original dataset and 1000 features from a structured dataset are combined on the input side.The dataset with 2000 features was then trained by the SNN, with the following classification process done with SWAT method on the last layer of the neural network.
As a result, the involvement of SNN enhanced the performance of the MobileNetV2 with a success ratio increased from 86.53% to 95.27%.The study successfully indicates the potential of applying SNN in medical fields, e.g., identifying different disease types.

Conclusions
In this paper, differences between SNNs and traditional ANNs was first identified.Focusing on the faithfulness of SNN to natural neurons, the biological background was then reviewed, indicating the importance of spikes in SNN signal transmitting, receiving, and processing.It also emphasized the property that spikes are generated only when a threshold potential is reached on the neuronal membrane.Then, three classical spiking neuron models are critically explained using theories and mathematical formulas with the pros and cons of each one clearly discussed.The section of neural coding gives the idea of how external stimuli are translated into spike signals, followed by the network learning strategy section where the importance of synaptic plasticity was identified.Additionally, the application of SNNs based on the LIF model were described in robotics and medical-related studies.Overall, the lower power consumption as well as excellence in computation indicate the SNN's unlimited potential in problem solving fields.Although in some articles the SNN's absolute advantages are still not as outstanding as expected, more imaginative uses of SNNs are in demand for a fully replacement over traditional ANNs as the dominant network computational tool [15].

Figure 1 .
Figure 1.The structure of the synapse.

2. 2 . 1 .
Hodgkin-Huxley model.The Hodgkin-Huxley model (also called H-H model) is a classic conductance-based model that describes the electrical characteristics of cell membranes.In 1952, based on extensive studies on the giant axon of the squid, Hodgkin and Huxley discovered the biophysical mechanism underlying the initiation and propagation of action potential generated by multi-ion exchange on the neuron cell membrane.

Figure 2 .
Figure 2. The schematic diagram of the Hodgkin-Huxley Model.

Figure 3 .
Figure 3.The equivalent circuit diagram of the LIF Model.The LIF model as an improvement of the original non-leaky I&F model faithfully takes into account the leak term which reflects the diffusion of ions down their concentration gradient through the cell membrane [5].As shown by figure 3, the input current () is represented as () =   ()   +     ()

Figure 4 .
Figure 4. Dynamics of the Izhikevich simple model with different parameters a, b, c and d.

2. 3 . 3 .
Population Coding.Population coding is an encoding strategy where information is encoded based on joint activities from populations of neuron cells.When subject to certain external stimuli, each neuron has a certain response distribution, and responses of a cluster of cells are combined to give a general indication of the input.Typical population coding involves spike responses in the form of a Gaussian tuning curve which vary linearly with stimulus intensity and reach the maximum (indicating the strongest response to a stimulus) around the mean.An example scheme of population coding is shown by figure 6.Some models based on population coding include Correlation Coding, Independentspike Coding and Position Coding.

Figure 6 .
Figure 6.Population coding scheme with a set of overlapping Gaussian functions.Population coding is considered as a mathematically well-organized coding strategy.It demonstrates the key features of neuron coding with a simplicity in mathematical analysis.Another important property of population coding is its robustness.Uncertainty due to variability among cells, as well as damage to a single cell would not introduce a catastrophic effect on the encoded representation, as information is

Figure 7 .
Figure 7.A standard STDP learning time window.

Figure 8 .
Figure 8. Structure of the SNN applied in this application.

Figure 9 .
Figure 9. Classification step performed in the study using the proposed approach.