Spiking Neural Networks (SNNs) have been widely studied as a computational model due to their sparse spiking patterns, asynchronous behavior, and event-oriented processing style. It enables energy-efficient and low-latency processing ideal for real-time tasks, edge computing, and neuromorphic hardware implementations.

However, efficient training of deep SNNs remains a significant challenge, as spikes can easily vanish or lead to an explosion in deep layers if the membrane potentials or the network weights are not properly initialized. The problem of deriving effective initial weights is addressed for deep, feedforward Artificial Neural Networks (ANNs), but still remains underexplored for SNNs. Though the existing ANN-based methods show some benefits for SNNs, the unique computational dynamics of SNNs are often neglected.

Recent studies suggest that the recurrent SNN is a dynamical system that exhibits a critical state, where spikes propagate across multiple time steps, leading to rich information representations, and is believed to be beneficial for neural computation.
Building upon this perspective, this thesis proposes a novel, bio-inspired, criticality-driven initialization method tailored for deep feed-forward SNNs.
We demonstrate the presence of a phase transition in our models, shifting from subcritical to supercritical dynamics.

Moreover, we apply a Hamming distance-based method to assess the network's ability to discriminate between different inputs. The results show that the system effectively maps distinct inputs to corresponding distinct outputs over very deep layer depth at criticality, as indicated by the minimized normalized mean square error (NMSE) between the input and output Hamming distance matrices. Furthermore, we demonstrate that while subcritical and supercritical regimes result in spike vanishing and explosion, respectively, operating at criticality allows spikes to propagate stably throughout the network.

To evaluate the proposed initialization method empirically, we conduct experiments using feedforward SNNs on standard benchmarks such as MNIST and Fashion-MNIST, and further extend the framework to convolutional SNNs for the more complex CIFAR-10 dataset. The results show that, for all datasets, our criticality-based initialization enables higher accuracy and faster convergence in low-latency settings compared to other baseline initialization methods.