Canonic Signed Spike Coding for Efficient Spiking Neural Networks

Thank you for your thorough review. Below, we address some key points of your concerns.

Reference Implementation in Hardware

Compared to traditional rate coding with IF neurons, our method introduces three additional components: 1. Membrane potential amplification, 2. Silent period control and 3. Handling input and output of negative spikes.

Silent period control is efficiently managed by a state register. When a neuron starts computing, the register outputs 0. After $P$ clock cycles (where $P$ is the silent period length), it switches to 1 and remains there until a reset. This control signal is shared across multiple neurons, resulting in minimal hardware overhead.

Membrane potential amplification is implemented using a simple shift operation. Since the shift amount is fixed, this can be achieved only by introducing a grounding line (logic 0) at the least significant bit (LSB) of the membrane potential input to the adder. Specifically, the [n-2:0] bits are hardwired to the adder's input [n-1:1], while the LSB of the input is tied to 0. By performing threshold comparison, the system ensures that the residual value does not exceed $2^{n-1}$, thus preventing overflow. As a result, there is no additional cost for the amplification operations.

Handling negative spikes is straightforward and requires a two’s complement addition, which can be efficiently performed by the adder. Specifically, the most significant bit (MSB) of the membrane potential is used to determine its polarity. If the MSB is 1, we take the two’s complement and compare it with the positive threshold in the comparator. This approach effectively compares the absolute value of the membrane potential with the threshold, maintaining a single comparator, which incurs minimal hardware overhead. Based on the comparison and the MSB value, we can determine both the presence and the polarity of the spike.

Thus, the only notable addition is the two’s complement unit. The silent period control and spike emission modules contribute negligible overhead. We provide an illustration of the reference design at this URL. The amplification operation incurs virtually no overhead and constitutes only a small proportion of the total operations. For details on the proportion, please refer to our response to Reviewer ujyj.

Based on our analysis and experimental results, our method is hardware-friendly and has minimal impact on energy consumption.

Our Main Contributions

First, we would like to clarify that we do not use LIF neurons ($\beta<1$); instead, we introduce the novel TSA neuron ($\beta>1$). The difference in $\beta$ leads to distinct weight patterns and using LIF neurons would cause significant conversion errors due to the residual membrane potential at the end. Additionally, we introduce a negative threshold mechanism to further reduce inference latency. For more details, please refer to our response to Reviewer cfNu.

Second, we highlight the differences between our work and that of Stöckl & Maass [1]. Their approach relies on complex neuron designs and increased computational latency to ensure conversion accuracy and support GeLU activation. In contrast, while our method does not support GeLU activation, it maintains network simplicity and significantly reduces inference latency. Moreover, ReLU activation remains the most widely adopted target for conversion. For additional experiments related to latency, please refer to our response to ujyj.

Lastly, we emphasize that our approach leverages stepwise weighting, which incurs minimal additional cost while delivering substantial benefits. Our method is also flexible, as it adheres to the standard ANN-SNN conversion framework, requiring only the replacement of IF neurons with TSA neurons. This enables our approach to be effectively applied to architectures such as Transformers and tasks like object detection, significantly reducing the required number of timesteps. For further details, we have provided additional experiments on these aspects in our response to pam4 for your reference.

[1] Optimized Spiking Neurons Classify Images with High Accuracy through Temporal Coding with Two Spike

If you have any further questions, we would be happy to address them.

Thank you for your thorough review. Below, we address some key points of your concerns.

First, we would like to emphasize that our core contribution lies in the innovation of the encoding method. Our work is not a continuation of Li et al. (2022) and Wang et al. (2022) because our core focus is on weighting the spikes, whereas they still rely on rate coding. Although both approaches use negative spikes, their roles are different, as we explained in Section 4.2.

By leveraging spike weighting, we enhance the encoding capacity of spike sequences. Compared to mainstream rate coding or TTFS coding, our approach significantly reduces the required timesteps. Our method follows the existing ANN-SNN conversion framework, making it straightforward to transition from rate coding to CSS coding. Since the core objective of ANN-SNN conversion is to accurately represent ANN activations using spike sequences, our approach is not limited to specific network architectures or tasks but rather provides a broadly applicable optimization.

Our experimental design aims to verify the accuracy of the encoding and the effectiveness of the TSA design. We choose image classification as the primary task because it is the most common benchmark in SNN research. We adopt CNN architectures as they are still the most widely used in ANN-SNN conversion. Additionally, we compare with CNNs of the same structure to highlight the impact of the encoding method, thereby better demonstrating the value of our work. To address your concerns regarding applicability, we have further extended our method to ViTs and object detection tasks, with preliminary results provided below.

Extended Experiments

Conversion of Transformer architectures

To demonstrate that CSS can also encode activations in Transformers, we converted ViT-S and ViT-B for the ImageNet classification task. We used the pre-trained weights provided in SpikeZIP-TF [1], where "32Level" denotes the quantization precision. As shown, our encoding scheme significantly reduces the required timesteps under the same weights. Additionally, we provide the actual runtime for a more intuitive comparison.

Object detection tasks

To demonstrate that CSS can be applied to object detection tasks, we conducted experiments on the VOC2007 dataset using the same architecture and weights as in Fast-SNN [2]. The results are shown in the table below. As observed, our method not only reduces the required timesteps but also significantly lowers the conversion loss.

In addition, we have also included the experiment on the neuromorphic dataset in our response to Reviewer cfNu, which you may find useful for reference.

We would like to emphasize once again that our core contribution lies in the nonlinear encoding scheme, which has broad applicability. For existing rate-based ANN-SNN frameworks, one only needs to replace the IF neurons with TSA neurons, as we have done in the experiments above.

[1] SpikeZIP-TF: Conversion is All You Need for Transformer-based SNN [2] Fast-SNN: Fast Spiking Neural Network by Converting Quantized ANN

Energy Estimation

Our energy estimation is based on an open-source codebase, and we have carefully re-examined the code without identifying any issues. Although it may seem counterintuitive, it is entirely plausible that CSS exhibits lower energy consumption than TTFS. First, CSS operates with only three timesteps, meaning each neuron can fire at most three spikes. Second, the CSS encoding scheme applies a more aggressive quantization to ANN activations—many small activations in the ANN are encoded as zero. In contrast, TTFS utilizes more timesteps for fine-grained quantization, encoding a greater number of "less important" activations. As a result, although TSA neurons may fire multiple spikes, significantly fewer neurons are activated in CSS coding. This combined effect leads to CSS achieving lower overall energy consumption.

If you have any further questions, we would be happy to address them.

Thank you for your thorough review. Below, we address some key points of your concerns.

Energy Overhead of Spike Weighting

To achieve nonlinear encoding, we double the membrane potential at each time step. First, we would like to emphasize that this method enhances encoded information with almost no additional cost. In our design, the shift amount is fixed for each step, allowing it to be implemented purely through wiring. Specifically, the [n-2:0] bits are hardwired to the adder's input [n-1:1], while the LSB of the input is tied to 0. This eliminates the need for shift registers, and incurs negligible energy consumption. Furthermore, the amplification is performed independently for each neuron, whereas the majority of operations arises from inter-neuron connections (e.g., convolutional or fully connected layers). Therefore, even if all neurons perform a shift at every time step, the overall cost remains minimal.

We provide a breakdown of the amplification operation's contribution to total operation count in the table below. The experiment was conducted with ResNet-18 on CIFAR-10. It can be observed that the operations for weighting are also minimal in number (accounting for just 4% of AC operations). Overall, their impact can be considered negligible.

Additionally, we would like to clarify that our approach is indeed quite hardware-friendly. We have provided a detailed reference design in our response to Reviewer MkoZ, which we encourage you to check for further details. We also provide an illustration of the reference design at this URL.

Methodological Details

OFC Method

The goal of OFC is to control the residual membrane potential to reduce conversion loss. This is achieved by lowering the firing threshold (causing Over-Firing) and introducing negative spikes (to Correct the excess firing). This method is also applicable to rate coding, as residual membrane potential impacts conversion loss in that setting as well. We addresses the question of how much to lower the threshold by deriving an optimal threshold mathematically. Notably, we have already conducted ablation experiments on negative spikes in Section 5.3, and experimental validation of the optimal threshold is provided in Section 5.4.

Inference Procedure of TSA

We provide the pseudocode for TSA’s forward propagation in Algo. 1, where the input spans all timesteps for clarity. However, our actual implementation employs a pipelined inference process: TSA processes spikes at each timestep, adjusting its behavior based on its local phase (e.g., silent periods).

Due to the pipelined processing, while the total delay from input to output is $P\times L$, each image only occupies $T+P$ timesteps per layer, where $T$ timesteps are used for primary neural computation. We report $T$ in tables as it represents the actual encoding steps per input. This standard is also applied when comparing TTFS coding and [1], with a similar approach found in [2].

To further illustrate efficiency, we report actual runtime below. Although measured on standard GPUs, these results still reflect the pipeline design in inference. We implemented rate coding as a baseline, setting $P=T$ to simulate [1]. Using four 2080Ti GPUs, we validated 50,000 images on ImageNet with VGG-16. Additionally, we processed 2,000 images one by one and averaged the latency to obtain the inference latency per image (LPI).

[1] Optimized Spiking Neurons Classify Images with High Accuracy through Temporal Coding with Two Spike [2] Bridging the Gap between ANNs and SNNs by Calibrating Offset Spikes

Related Work

The two works you mentioned focus on implementing TTFS coding. Although both approaches involve accumulating information over time, we would like to emphasize that TTFS accumulates information in a linear manner [3], whereas our approach follows a nonlinear accumulation process. This key difference allows us to accumulate information more quickly, thereby reducing the required timesteps.

In our paper, we acknowledge that the silent period concept has been used in TTFS coding and [1]. However, we do not claim a contribution to the silent period itself; rather, we aim to minimize it to reduce inference latency. By incorporating the OFC method, we reduce $P$ to 1, whereas in [3,5], $P=T$.

[3] Temporal-Coded Spiking Neural Networks with Dynamic Firing Threshold: Learning with Event-Driven Backpropagation

If you have any further questions, we would be happy to address them.

Thank you for your thorough review. Below, we address some key points of your concerns.

Comparison with LIF

The neuron dynamics of TSA and LIF can both given by the following equation:

$u_{i}^{l}[t]=\beta u_{i}^{l}[t-1]+z_{i}^{l}[t]-S_{i}^{l}[t]$

Apart from the difference in handling negative spikes, the key distinction between TSA and LIF lies in the choice of $\beta$. While both mechanisms serve to weight the input, TSA sets $\beta>1$, resulting in a weight pattern that decreases over time. This design is primarily motivated by two factors:

1. Enabling rapid transmission of most information.
2. Reducing the weight of the final residual information, which is crucial for conversion accuracy.

For comparison, we set $\beta = 0.5$ in the table below and observed a significant increase in conversion error. We conducted experiments using VGG-16 on the CIFAR-10 dataset. It can be observed that when using (Ternary) LIF neurons, it is necessary to extend the length of the silent period to reduce conversion loss, which significantly impacts output latency. This further highlights the importance of adopting a decreasing weight pattern.

Additional Experiments

Our main contribution is compressing the timesteps for conversion through a stepwise weighting mechanism, which is both convenient and flexible: it still follows the standard ANN-SNN conversion framework, requiring only the replacement of IF neurons with TSA neurons. Therefore, our method is applicable to a wide range of network architectures, datasets, and tasks. We have included additional experimental results on CIFAR-100 in the table below. The experiments were conducted based on the full-precision VGG-16.

Moreover, we have conducted experiments on object detection tasks and applied our encoding method to Transformer architectures. The results of these experiments can be found in our response to Reviewer pam4.

Regarding neuromorphic datasets, as you pointed out, one of the challenges of applying our method is the absence of an ANN counterpart, which is also a general limitation of ANN-SNN conversion. A possible solution [1] is to integrate temporal information into static features and then train an ANN for classification. We conducted experiments using ResNet18 on the DVS128Gesture dataset, with the results shown in the table below. For comparison, we implemented a simple rate coding as the baseline.

[1] Masked Spiking Transformer

If you have any further questions, we would be happy to address them.