## 4 Results
### Relation between Sliding Windows and Time Constants  
Second experiment setup: We performed experiments to understand the correlation between sliding windows and neuronal processing speed. The membrane time constant \(\tau_{mem}\) and synaptic time constant \(\tau_{syn}\) were varied with different window sizes and hop sizes to obtain results for the accuracy and onset latency for the siren prediction task. We further investigated the impact of windowing without any overlap for different time constants to obtain an optimal window size and to understand the impact of individual neuronal leakages. Figure 4: **Sliding windows with different sample size impacts performance. ** Evaluation of Spike-SireNet for sliding window with mel channel variation on the anomaly detection task with membrane and synaptic time constants set to 2 s. **(a)** Introduction of hop length improves the prediction accuracy (**b**) Onset latency reduces for overlapping windows. From **(a–f)**, the mel channel variation is seen from M = 32, 64 and 128 respectively. SpikeSireNet is trained on [18] for this set of experiments. We explored the relation between neuronal time constants of charge-based LIF and their impact on the performance with sliding windows. To garner results in this direction, we performed experiments with a variation in the overlap ratios for a window size of 4096 with different \(\tau_{mem}\) and \(\tau_{syn}\) ranging from 1 s to 100 s. From Figure 5, a clear trend indicates the accuracy was best for neuronal time constants ranging between 2-4 s. With larger time constants, the neurons decayed at a much slower rate, and this effect led to a slight degradation in accuracy for overlapping windows. An accuracy drop of nearly 5% occurred for higher time constants because fast responses or the high sensitivity of neurons with a slower membrane decay led to missing crucial information within overlapping windows. However, for smaller time constants, this was reflected as a benefit in terms of modest deviation in accuracy. The results from the onset latency plots in Figure 5 suggest that there is a linear trend with time constants. Smaller time constants led to higher accuracy and a nearly 4\(\times\) processing speed with the addition of overlapping windows for a fixed window size of 4096. In order to understand the impact of neuronal time constants on the spiking activity of the neurons and extrapolate these results for acoustic siren sounds, we performed a grid search method on Siren dataset [18] on SpikeSireNet for tuning of different time constant values and quantify in terms of performance metrics like accuracy. We expanded our experiments to accommodate individual variables for each set of membrane and synaptic time constants as shown in Table 2.  
We varied time constants with a variable window size of 4096, \(\ldots\), 512 and without overlap to analyze the correlation between neuronal decays for windowing. The case of no overlaps was considered to constrain the experiment space and direct the focus towards understanding the statistical relation between the time constants for this particular task. The accuracy was higher for window sizes ranging between 85-50 ms with time constants in the range of 2-4 s. Smaller windows meant coarse features, and with no overlap, there was a chance of spectral leakage. In the window size range of 5-10 ms, having a time membrane and synaptic time constants in the range of 10-100 s, meant the decay was faster for both the time constants. This implied a higher firing rate and missing of information, leading to a slight degradation in performance. With both time constants in the higher bracket, the spikes retained were constrained to the specific window, which may have been the reason for the slight performance reduction. From Table 2, it is evident that the best performance was achieved for smaller neuronal time constants with an optimal window between 85.33-42.66 ms.  
Figure 5: **Smaller time constants result in higher performance.