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Equation (1) is the first-order differential equation of the LIF model, where 𝜏_𝑚=𝑅_𝑚 𝐶_𝑚 is the membrane time constant, 𝑈 is the membrane voltage, 𝐼 is the sum of the firing currents of each presynaptic neuron, 𝑈_𝑟𝑒𝑠𝑒𝑡 is the reset voltage, and 𝑈_𝑟𝑒𝑠𝑡 is the resting voltage. Figure 1(a) and Figure 1(b) shows the process of neuronal spike sequence input and firing.
We refer to the conventional leakage process as exponential leakage because the membrane voltage leakage term exists in an exponential form. The state update process of the conventional LIF model can be expressed as Equations (2) and (3), where 𝑈[𝑡] denotes the membrane voltage at the current moment, 𝑈[𝑡−1] represents the membrane voltage at the previous moment, 𝑒^((−1)/𝜏_𝑚 ) is the membrane voltage leakage term, 𝑂[𝑡] represents the pulse emission function and W is the weight. At the membrane potential 𝑈 does not reach the threshold voltage 𝑈_𝑡ℎ the spike signal accumulates in the time domain and decays according to the membrane time constant 𝜏_𝑚 with time step; once the membrane potential 𝑈 reaches the threshold voltage 𝑈_𝑡ℎ, the neuron immediately fires a spike signal and resets to 𝑈_𝑟𝑒𝑠𝑒𝑡.
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IEEE/ICACT20230030 Slide.09
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