## 3 Materials and Methods
### Network Architecture  
We adopted the model architecture from our previous work in [7; 28] to achieve predictions using a recurrent spiking neural network, as shown in Figure 2. Recurrent networks were chosen as they exhibit excellent ability to handle time-series data much better than feed-forward networks. Recurrences aid to excelling in tasks that need to uncover the realms of contextual understanding such as audio processing. The SpikeSireNet model  
Figure 1: Sliding window method in the processing pipeline. Block diagram highlights the sliding windows on acoustic anomaly sequences used as input features in the spiking architecture. Different window sizes (with and without overlaps) are provided in the form of time slices as an input to FFT; mel features are extracted to inject as current input to the recurrent SNN.  
comprised a hidden layer with 100 spiking leaky-integrate-and-fire (LIF) neurons with recurrent connections. For our experiments with sliding-window variation and time constants, we adopted a homogeneous network structure with parameters specifically from our research work on designing a model to detect siren sounds in [7]. With the aim to understand the impact of dataset augmentation, we further slightly modified the design of the SNNs in terms of input features and neuronal time constants of the hidden layer. The network in Figure 2 comprises a hidden spiking layer and a single readout for predicting siren or not. The information processing in the hidden layer of SpikeSireNet is in terms of spikes. LIF neurons are analogous to biological neuronal processing. When the input stimulus crosses the threshold voltage, neuronal firing occurs. We aimed to understand the effect of sliding windows and neuronal processing on network predictions with a great focus on the spectral feature components. Therefore, we conducted experiments with various membrane (\(\tau_{mem}\)) and synaptic (\(\tau_{syn}\)) time constants of the neurons to evaluate the impact of different windows on the task performance.  
The design parameters and the hyper parameters set for the evaluation of the anomaly detection task are described in Table 1. A surrogate gradient based method was used to approximate the derivative of the LIF recurrent cell [29]. We employed a Leaky-integrator (LI) cell as a readout neuron, which had a continuous-valued output. The SNNs used in this work were built using the Norse [30] framework, an extension of PyTorch [31]. The differential equations and dynamics of the current-based LIF neuron are extensively discussed and presented in Equations (1)-(3) in [26]. Neurons have a membrane potential that decays with a membrane time constant \(\tau_{mem}\). Synaptic currents follow specific temporal dynamics. The exponentially decaying current triggered by the pre-synaptic input leads to the second dynamics of LIF neurons. This exponential decay of synapses is termed as synaptic time constant \(\tau_{syn}\). The specific dynamics of CUTrent BAsed (CUBA)- LIF neurons for the exponential decay of synaptic currents and membrane potential are presented in [26] in Equations (3) and (4).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Design Parameters** & **Values** & **Hyper Parameters** & **Values** \\ \hline Network structure & M 1-100-1 & Learning rate & \(1\times 10^{-3}\) \\ Threshold voltage & 1 V & Batch size & 16 \\ Reset potential & 0 mV & Optimizer & Adamax \\ Membrane time constant & 2 s & & \\ Synaptic time constant & 2 s & & \\ \hline \hline \end{tabular}  
* M indicates mel channels.  
\end{table}
Table 1: Design parameters of SNN architecture and hyperparameters.  
Figure 2: **SpikeSireNet: Overview of the recurrent SNN used in this work is highlighted. The features extracted are given as M input channels (where M = number of mel bins) to the SNN. The spiking architecture comprises 100 hidden neurons with recurrent connections and a single readout neuron for siren predictions.**