## 2 Materials and Methods
### The Spiking Neuron Model  
PLIF [5] achieves high accuracy at low time steps with low computational cost by learning and pooling membrane potential parameters, while transforming average-pooling to max-pooling layers. This method demonstrates the heterogeneity of neurons and enhances the expressive ability of SNNs. The basic computational unit of SNNs is the spiking neuron. To accurately describe the precise relationship between input and output signals of biological neurons, neuron scientists have developed several models of spiking neurons. The LIF neuron achieves a balance between biological plausibility and computing cost.  
To assess the impact of synaptic weight and membrane time constants on neural dynamics, the pre-synaptic neuron \(z_{j}\) (Figure 3a) transmits a weighted input \(X(t)=wI(t)\) to the LIF neuron \(z_{i}\).  
The resting potential \(V_{\text{rest}}\) is set to zero. The membrane potential of the LIF neuron \(z_{i}\) varies with time when the input is constant, specifically, \(I(t)=I\); this behavior is illustrated by the blue curve in Figure 3b and is calculated using Equation (2). The \(w+\) and \(w-\) curves indicate that varying \(w\) causes the \(v=f(t)\) curve to extend in the \(V\) direction. Conversely, altering \(\tau\) extends the \(v=f(t)\) curve to lengthen in the \(t\) direction without affecting the steady-state voltage of the neuron \(z_{i}\), as \(V(+\infty)=w1\).  
The functions of various spiking neuron models are represented as \(f(\cdot)\). The following describes the role of \(f(\cdot)\) for LIF neurons [17]:  
\[H_{t}=V_{t-1}+\frac{1}{\tau}[-(V_{t-1}-V_{\text{reset}}\,)+X_{t}] \tag{2}\]  
where \(X_{t}\) is the neuron's input at time \(t\), \(V_{t}\) is the neuron's membrane potential at time \(\tau\), and \(\tau\) is the membrane time constant.  
Figure 2: The proposed AMSpiking-VGG for object detection, where use PLIF model combined with CBAM self-attention mechanism. The PLIF neuron model is used in each module of the framework, and the CBAM mechanism is incorporated in the backbone of the network, as shown in the purple module in the figure above.  
This limitation constrains the diversity of spiking neurons and the expressive power of SNNs. Parameterized spiking neurons [5] incorporate one or more learnable parameters related to membrane potential and adjust these parameters during the training process of SNNs. The network becomes less sensitive to initial values and accelerates the learning speed by introducing learnable membrane time constants.  
For PLIF neurons, directly optimizing the membrane time constant \(\tau\) in Equation (2) may lead to numerical instability when \(\tau\) is set as the denominator. Additionally, Equation (2) represents a discrete version of traditional neurons model, serving as an effective approximation only when the time step \(dt\) is shorter than \(\tau\), i.e., \(\tau>1\). To prevent these issues, PLIF neurons are reformulated using the following equation incorporating a trainable parameter \(a\):  
\[H_{t}=V_{t-1}+k(a)[-(V_{t-1}\text{-}V_{\text{reset}}\ )+X_{t}] \tag{3}\]  
where \(k(a)\) represents clamp function, \(k(a)\in(0,1)\), \(\tau=1+\exp(-a)=\frac{1}{k(a)}\in(1,\infty)\).  
The diversity of PLIF neuron enables the network effectively adapt to different input patterns, thereby enhancing the accuracy and robustness of feature extraction. Additionally, because PLIF neurons can learn membrane time constants, the network becomes more flexible and efficient in handling complex image features.  
Consequently, we integrate the PLIF neuron model into the core modules--EMS_Block, AM_Block and LCB block--of our AMS_YOLO and AMSpiking_VGG, as depicted in Figures 1 and 2.