Artificial Neural Networks (ANNs), while achieving impressive results in various tasks, suffer from high energy consumption. Spiking Neural Networks (SNNs), inspired by the brain's energy-efficient communication via sparse binary spikes, offer a potential solution. However, training deep SNNs to match the performance of ANNs has been a significant hurdle. This paper addresses this challenge by focusing on Time-to-First-Spike (TTFS) coding, where each neuron fires at most one spike, maximizing energy efficiency. The research investigates the learning dynamics of TTFS networks theoretically and through simulations, aiming to understand and overcome the limitations that prevent deep SNNs from reaching the performance levels of their ANN counterparts. The study's importance lies in bridging the performance gap between SNNs and ANNs, paving the way for energy-efficient AI implementations in resource-constrained environments such as edge devices. The specific research question is how to overcome the instability issues observed during the training of deep TTFS networks and achieve performance comparable to deep ANNs.

Several methods have been proposed to train SNN parameters. Traditional approaches used biological plasticity rules, but gradient-descent optimization (backpropagation) has proven more effective. Successful paradigms treat spiking neurons as discrete-time recurrent units with binary activation, using surrogate gradients during backpropagation. Other approaches translate ANN activations into SNN spike counts or utilize temporal coding with many spikes, compromising energy efficiency. In contrast, TTFS coding, focusing on the timing of the first spike, offers energy efficiency. Recent microelectronics research has also independently shown benefits of leveraging temporal coding. While an approximation-free conversion from ANNs with ReLUs to TTFS networks is possible, training or fine-tuning deep SNNs with gradient descent in the TTFS setting has remained difficult, suggesting underlying issues during spike-time optimization. Previous attempts at training deep TTFS networks with exact gradients have been limited to shallow architectures or employed gradient approximations, failing to achieve high performance in deeper networks.

The study uses deep SNNs with TTFS coding, where neurons communicate via spikes, and earlier spikes encode more salient information. The network architecture consists of fully connected or convolutional layers. Inputs are encoded into spiking times, with high intensity leading to early spikes. The neuron's membrane potential follows integrate-and-fire dynamics with linear post-synaptic potentials. Two key models are explored: the α-model (from prior work) and the B1-model (a novel model introduced in this paper). The paper presents an exact reverse mapping between the TTFS network and an equivalent ReLU network. This mapping is essential for theoretical analysis and training. The study uses exact backpropagation to compute gradients with respect to spiking times and parameters. The vanishing-or-exploding gradient problem is analyzed, showing how the choice of parameters affects the stability of the training. The identity mapping (B1-model), where the slope of the membrane potential at threshold is constant, is key to ensuring equivalent training trajectories between SNNs and ReLUs. The methodology involves training the B1-model on MNIST and Fashion-MNIST datasets and fine-tuning on larger datasets like CIFAR10, CIFAR100, and PLACES365. The impact of L1 regularization on spiking sparsity is also investigated. Finally, fine-tuning is performed to address hardware constraints such as noise, quantization, and latency.

The paper's key findings include: 1) Analytical identification of a vanishing-or-exploding gradient problem in deep TTFS networks when using naive ANN parameter initialization. 2) The B1-model (identity mapping), with a constant slope of the membrane potential at threshold, guarantees equivalent training trajectories between SNNs and ReLUs, solving the instability issue. 3) Successful training of deep TTFS networks on MNIST and Fashion-MNIST, achieving accuracy comparable to ReLU networks. 4) Fine-tuning on larger datasets (CIFAR10, CIFAR100, PLACES365) with the B1-model, surpassing previous SNN performance, while maintaining high spiking sparsity (less than 0.3 spikes per neuron). 5) Demonstration that fine-tuning compensates for hardware constraints such as noise, quantization, and latency, recovering high accuracy even with significant constraints. The high performance (accuracy comparable to ReLU networks) combined with high spiking sparsity (average of 0.2-0.3 spikes per neuron) makes this a significant finding for energy-efficient implementations. Table 1 shows the superior performance of the proposed approach on different network architectures compared to existing SNN methods. Table 2 shows high accuracy and spiking sparsity on larger benchmark datasets, demonstrating the efficacy of the approach for practical applications. Figure 2 illustrates the eigenvalue distribution of the SNN Jacobian for different models, demonstrating the B1-model's stability. Figure 3 compares the learning curves of the B1-model and α1-model highlighting the superior stability and performance of the B1-model. Figure 4 depicts the conversion and fine-tuning process for VGG16 network. Figure 5 demonstrates the robustness and efficiency after fine-tuning for different hardware constraints, showcasing the practical utility of the proposed model.

The results demonstrate the successful training of high-performance, energy-efficient deep SNNs using TTFS coding. The identity mapping (B1-model) is crucial for solving the instability during training caused by the vanishing-or-exploding gradient problem. This work bridges the performance gap between SNNs and ANNs, offering a practical solution for energy-efficient AI. The finding of high spiking sparsity (below 0.3 spikes/neuron) is particularly significant, as this directly translates to lower energy consumption in hardware implementations. The robustness to hardware constraints further enhances the practicality of the proposed method for real-world applications. The model's ability to achieve high performance even with significant hardware limitations indicates its potential for deployment on resource-constrained devices. This study contributes significantly to the field by providing a practical and robust method for training deep SNNs that can match or exceed the performance of ANNs, opening doors for more energy-efficient and sustainable AI systems. The biological interpretation of TTFS coding, as an abstraction of neural activity with strong adaptation or balanced inhibition, provides further insights into biological neural processing.

This paper presents a novel method for training high-performance deep spiking neural networks using time-to-first-spike coding, achieving accuracy comparable to ANNs with significantly reduced energy consumption. The identity mapping in the B1-model is key to achieving this result by ensuring training stability. Future research directions include extending the approach to handle skip connections, incorporating batch normalization, and adapting the TTFS network for temporal data processing such as video analysis. The potential for on-chip training or hardware-in-the-loop training could further optimize SNN performance for specific hardware.

The current study focuses on feed-forward networks. Generalizing the approach to recurrent networks and handling asynchronous spiking activity remains a challenge for future work. While the model addresses some hardware constraints, further research is needed to explore a wider range of hardware imperfections and limitations. Additionally, the study mainly focuses on image classification datasets; exploring other applications and data types would further validate the proposed method's general applicability.