Efficient ANN-SNN Conversion with Error Compensation Learning

We appreciate the reviewer’s insightful comments and constructive feedback. Below, we address the concerns raised and clarify the contributions of our work.

Response to Weaknesses

1. Fixed Hyperparameter Choices

While our method uses empirically determined hyperparameters (e.g., negative threshold $\theta'$ =-1e-3, membrane potential initialized at $\frac{\theta}{2}$), these choices are rigorously validated through ablation studies (Tables 3, 5, and 7). For instance, initializing $v^l(0)=\frac{\theta^l}{2}$ minimizes the expected conversion error (Eq. 8). We acknowledge the potential benefits of adaptive mechanisms. Future work will explore data-driven tuning (e.g., layer-wise threshold learning) to further enhance flexibility.

2. Scalability to Deeper Architectures

Our experiments focus on widely adopted networks (VGG-16, ResNet-18/20/34) for fair comparison with previous work. We further validate our method on ResNet-50 architecture (on CIFAR-10 and CIFAR-100 datasets). The results are shown in the following Table. On the CIFAR-10 dataset, our method achieves an accuracy of 96.05% when T=4. While on the CIFAR-100 dataset, when the time step is only 4, our method achieves an accuracy of 80.51%, which is similar to the accuracy of the source ANN. This demonstrates that our framework is robust even in deeper architectures. Moreover, the optimal membrane potential initialization and error compensation in the theoretical foundation (Section 3.4) also ensure consistent performance across network depths.

Table 1. Accuracy of ResNet-50 on CIFAR-10 and CIFAR-100 datasets

3. Applications Beyond Image Classification

Although our current experiments focus on VGG and ResNet architectures, the error compensation learning principles of adaptive threshold and dual threshold neurons are generalizable and adaptable. Adaptive threshold and dual threshold neurons can also be applied to event-driven tasks (e.g., video recognition, neuromorphic perception). We will explore dynamic data applications in subsequent work.

Response to Questions for Authors

1. Impact of Negative Threshold Selection

The negative threshold $\theta^{\prime}$=-1e-3 balances activation symmetry and stability. A smaller $\theta^{\prime}$ (e.g., -1e-4) reduces sensitivity to minor fluctuations, while a larger $\theta^{\prime}$ (e.g., -0.1) risks over-activation. Our experiments (Figure 3, Table 3) show $\theta^{\prime}$=-1e-3 optimally mitigates uneven error without destabilizing training.

2. Membrane Potential Initialization at half the threshold

This choice stems from minimizing the expected conversion error (Eq. 8). Mathematically, initializing $v^l(0)=\frac{\theta^l}{2}$ achieves the least squares fit between ANN activations and SNN firing rates. Empirical results (Table 1, T=2) suggest that it reduces quantization error by 19.31% in ResNet-18.

We appreciate the reviewer’s insightful comments and constructive feedback. Below, we address the concerns raised and clarify the contributions of our work.

1. Difference Between Dual-Threshold Neurons and Spiking Models in [1, 2]

Thanks for your feedback. Our design is fundamentally different from the spiking models in [1, 2]. While these approaches adjust the firing threshold or employ additional bias terms to mitigate transition errors, our dual-threshold neuron explicitly distinguishes between over-release at positive membrane potentials and under-utilization at negative membrane potentials. As discussed in Sections 3.3 and 4.2, this design not only compensates for quantization errors but also addresses the problem of non-uniform errors, a challenge that becomes critical at ultra-low latency (e.g., 2 time steps). Our dual-threshold neuron is theoretically demonstrated in Section 3.3 and empirically validated in Tables 3 and 5, showing significant accuracy improvements (e.g., 19.31% improvement over ResNet-18 at T=2 on CIFAR-10), highlighting the effectiveness of our approach compared to previous models.

2. Difference Between Learnable Threshold Clipping and QCFS [3]

The learnable threshold clipping function in our work (augmented with an optimal membrane potential initialization strategy) is significantly different from the QCFS function [3]. QCFS focuses on reducing the translation error by optimizing the activation quantization process. However, our approach employs the learnable threshold that maps directly to the SNN firing threshold. This ensures that the clipping error is minimized in a unified framework, and importantly, our initialization (as derived in Section 3.4) minimizes the expected squared translation error by setting the initial membrane potential to half the threshold. QCFS does not address this joint consideration of clipping, quantization, and non-uniform errors. Our approach achieves superior performance (e.g., 94.75% accuracy at T=2, compared to 75.44% for QCFS in Table 1). This adaptability is critical for ultra-low latency SNNs, as shown in Section 4.1.

3. Applicability to Transformer-Based SNNs

While our current experiments focus on VGG and ResNet architectures, the principles of error compensation learning of adaptive thresholds and dual-threshold dynamics are generalizable and adaptable. Because the adaptive thresholds and dual-threshold dynamics also could be applied to the spiking neuron models in the Transformer-Based SNNs. We acknowledge that transformer-based SNNs pose unique challenges (e.g., attention mechanisms) and would explore this direction in future work.

We appreciate the reviewer’s insightful comments and constructive feedback. Below, we address the concerns raised and clarify the contributions of our work

Response to Weaknesses

1. Computational Overhead of Dual-Threshold Neurons

Thanks for your feedback. We find that the additional threshold brings little computations cost per neuron due to the event-driven nature of SNNs. As shown in Table 1, we evaluated the computational cost in terms of energy consumption and synaptic operations (SOPs) to show the Computational Overhead of Dual-Threshold Neurons. The results show that the Dual-Threshold Neurons almost introduce no extra energy consumption especially in small time steps (T =2 and 4). And other large time steps only introduce limited energy consumption. Therefore, our method significantly reduces energy consumption compared to standard ANNs while maintaining competitive accuracy at ultra-low latency.

Table 1. Computational Overhead of Dual-Threshold Neurons using VGG-16 on CIFAR-100 dataset

2. Generalization Beyond Image Classification

We appreciate the suggestion to discuss how our method extends beyond static image classification tasks. Our conversion approach is designed to be broadly applicable, and the learnable threshold clipping function, dual-threshold neurons, and optimized membrane potential initialization can benefit event-driven data processing tasks, such as neuromorphic vision processing, speech recognition, and reinforcement learning. Although this work focuses on image classification benchmarks for fair comparison with prior ANN-SNN conversion methods, our approach can be extended to other spatiotemporal data. Specifically, the dual-threshold mechanism helps mitigate quantization errors in temporally sparse spike sequences, which is beneficial for event-driven data processing. We will explore these applications in subsequent work.

3. Reference Formatting

We acknowledge the oversight regarding outdated references and have updated the bibliography to reflect officially published versions of cited works where applicable in the revision.

Response to Questions for Authors

1. How does the learnable threshold clipping function adapt across different network depths?

Thanks for your feedback. The learnable threshold clipping function is trained alongside ANNs’ weights and adjust dynamically per layer. During training, it learns to match the optimal activation statistics of each layer, ensuring smooth ANN-to-SNN conversion. For deeper networks, the function effectively scales the thresholds based on the range of activation distributions, which helps mitigate conversion errors. Empirical results demonstrate that this adaptation enables high accuracy even for deeper models like ResNet-34 on ImageNet (e.g., For VGG-16, when T=16, our method achieves 74.15% accuracy, which is 23.18% higher than QCFS. For ResNet-34, we achieve 72.37% accuracy with only 16 time steps.)

2. How does the clipping function compare to other activation function alternatives, such as threshold scaling techniques?

Thanks for your feedback. Our learnable threshold clipping function provides a more flexible and data-driven alternative to static threshold scaling. Unlike predefined threshold adjustments (e.g., RMP, Opt), our function dynamically learns the optimal threshold mappings, reducing reliance on manual heuristics. We conducted additional experiments comparing our method with existing threshold scaling approaches, such as RTS and QCFS. Using the ResNet-18 model on the CIFAR-10 dataset, our method achieves an accuracy of 94.75% with only two time steps, 19.31% higher than QCFS, while RTS achieves an accuracy of 84.06% at T=32. The results show that our approach consistently outperforms prior methods across different datasets and network architectures while maintaining ultra-low latency.

3. Does the dual-threshold neuron introduce additional computational overhead during inference?

As mentioned earlier, the dual-threshold mechanism slightly increases per-neuron computation. However, since SNNs are event-driven and avoid redundant computations, the overall increase is negligible compared to conventional ANN operations. We measured the impact on inference latency and found that our method achieves faster convergence with fewer time steps (e.g., T=2 on CIFAR-10 with ResNet-18 at 94.75% accuracy). This efficiency gain compensates for the minor computational overhead. Additionally, the power consumption analysis (Table 1) suggest that our method maintains a highly efficient energy profile.