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This paper explores the intrinsic relationship between linear leakage and pulse emissivity through the derivation of equations. As shown in Figure 2 and Figure 3, assume that a spike signal 𝑈_𝑚𝑒𝑚 is received at each time step in a single neuron, the membrane voltage 𝑈_([𝑡]) integrates each spike signal and linear decays by the leaky factor 𝜏_𝑚 at each time step. Linear leakage implies that the membrane voltage 𝑈_([𝑡]) decays a fixed value at each time step. In order to understand the leakage method more intuitively, Figure 3 shows the change trend of the LIF neuron membrane voltage signal under different leakage modes when no other signal is received. In terms of bionicity, linear leakage is somewhere between exponential leakage and no leakage.
At the time step 𝑇, the integrated membrane voltage 𝑈_([𝑡]) is equal to the threshold voltage 𝑈_𝑡ℎ. This paper uses the variable 𝑅_1 represents the rate of the threshold voltage 𝑈_𝑡ℎ and the spike signal 𝑈_𝑚𝑒𝑚, and the variable 𝑅_2 represents the rate of the leaky factor 𝜏_𝑚 and spike signal 𝑈_𝑚𝑒𝑚, then we can obtain the relationship between the spiking rate (1/𝑇), 𝑅_1 and 𝑅_2, which is shown in Equation (5).
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IEEE/ICACT20230030 Slide.13
[Big Slide]