A Deep Convolutional Spiking Neural Network for embedded applications

Deep neural networks (DNNs) have received a great deal of interest in solving everyday tasks in recent years. However, their computational and energy costs limit their use on mobile and edge devices. The neuromorphic computing approach called spiking neural networks (SNNs) represents a potential solution for bridging the gap between performance and computational expense. Despite the potential beneﬁts of energy efﬁciency, the current SNNs are being used with datasets such as MNIST, Fashion-MNIST, and CIFAR10, limiting their applications compared to DNNs. Therefore, the applicability of SNNs to real-world applications, such as scene classiﬁcation and forecasting epileptic seizures, must be demonstrated yet. This paper develops a deep convolutional spiking neural network (DCSNN) for embedded applications. We explore a convolutional architecture, Visual Geometry Group (VGG16), to implement deeper SNNs. To train a spiking model, we convert the pre-trained VGG16 into corresponding spiking equivalents with nearly comparable performance to the original one. The trained weights of VGG16 were then transferred to the equivalent SNN architecture while performing a proper weight–threshold balancing. The model is evaluated in two case studies: land use and land cover classiﬁcation, and epileptic seizure detection. Experimental results show a classiﬁcation accuracy of 94.88%, and seizure detection speciﬁcity of 99.45% and a sensitivity of 95.06%. It is conﬁrmed that conversion-based training SNNs are promising, and the beneﬁts of DNNs, such as solving complex and real-world problems, become available to


Introduction
Following the rapid advancement of the mobile Internet and the Internet of Things (IoTs), the amount and complexity of the data are increasing exponentially.Meantime, driven by large amounts of data, technologies like artificial intelligence (AI) and cloud computing are growing [1].A type of artificial neural network (ANN) model, named deep learning (DL), is gradually dominating the AI applications.Deep learning provides the state-of-the-art solutions for various applications, such as smart devices, IoT, autonomous vehicles, image classification, and object detection [2].
Despite the tremendous success of DNNs, a significant challenge of this technique is their requirement to a large amount of energy required when deployed on mobile and edge devices [3].Accordingly, it is believed that a paradigm shift towards alternative algorithms and hardware solutions is necessary to their lower energy costs.Spiking neural networks (SNNs) try to mimic the brain's impulses (spikes) and local learning rules [4,5].They are proposed as the third generation of neural networks for embedded AI applications.SNNs are biologically inspired neurons that interact with each other via a series of spikes.ANNs, on the other hand, have continuous values rather than biologically plausible spikes [6].Another distinction is the activation function.SNNs have discrete values and non-differentiable functions.Therefore, considering the event-driven computational and resource-consuming benefits of the spiking neuron model, SNNs are promising for low-power embedded applications

Energy Gap
Fig. 1 Difference between an ANN (top) and a SNN (bottom) in terms of computation unit and hardware implementation compared to conventional ANNs [7]. Figure 1 shows the differences between ANNs and SNNs.
In this work, we investigate the use of deep convolutional SNNs for two case studies: scene classification problems and epileptic seizure detection.The contributions made in this work are as follow: • We develop a deep convolutional spiking neural network (DCSNN) to real-word classification problems.• We evaluate the performance of DCSNN in two case studies: LULC classification (EuroSAT dataset) and epileptic seizure detection (CHB-MIT dataset).• We evaluate the computational complexity and energy consumption of our DCSNN and against DCNN.
The rest of the paper is structured as follows.Section 2 describes the background on the fundamental components of deep convolutional SNNs.Section 3 describes the method of conversion of a deep convolutional neural networks (CNN) to a SNN.Section 3 describes theory of CNN to SNN conversion.Sections 4 and 5 describe the implementation of the first and second case study, respectively.Section 6 presents experimental results and proposes future improvements while Sect.7 concludes this paper.

Convolutional Neural Networks
Convolutional neural network (CNN) is a special sort of ANNs that have fewer connections and parameters making their training easier while maintaining competent performances [34].Figure 2 shows a classic CNN, LeNet, which includes four types of layers: an input layer, convolutional layers, pooling layers, and fully connected layers [35].The capacity of the network can be controlled by varying its parameters such as the shape of the input (batch size, height, width, channels), the number of channels in the first and second convolution layers, the number of neurons in the hidden layer, and the kernel size for the convolution and pooling filters.

Information coding
The initial phase of an SNN is to transform the original features into spikes to feed the spiking networks.The encoding strategy has a significant effect on network performance.Selecting the best coding strategy depends on the application, hardware limitations, and the neuron model [36].In general, three encoding mechanisms have been popularised with respect to input data.

Neuron model for ANN
An ANN consists of at least two fundamental components: processing units (neurons) and connections (weights).Each neuron receives an input, uses its transfer function to process it, and then produces an output according to its activation function, as shown in Fig. 3a.The transfer function T F J is the weighted sum of the inputs I 1→M with respect to the weights ω 1→M, J of the links connected to the neuron J .Accordingly [40]: The output y J of the J th neuron is expressed as y J AF J (net J ) where the activation function AF J is often the rectified linear units (ReLU) function.

Neuron model for SNN
The spiking neuron receives inputs from presynaptic neurons over multiple timesteps, while in ANNs, each neuron's state is updated periodically [41].The leaky integrate-andfire (LIF) is a first-order model and one of the simplest and most used neuron models, thanks to its computational efficiency.The basic concept of the LIF model is that the neuron has a membrane potential that evolves through time due to incoming excitatory or inhibitory currents and a leakage parameter [42].An output spike occurs whenever the membrane potential of a neuron crosses its threshold, and its membrane potential is then reset to its resting state, as shown in Fig. 3b.This behaviour is characterised as: where V (t) is the membrane potential, L is the leakage parameter, X (t) is the summation of all synaptic inputs at time t, V rest is the resting membrane potential, and V threshold is the membrane threshold.To propose a hardware friendly method, we use no leakage (L 0), which gives the integrateand-fire (IF) neuron model.

Modified leaky integrate-and-fire model
In this paper, we investigate a rate encoded SNNs, so the basic LIF model as presented in the previous section has an issue when used for rate-based computations that happen close to zero: the output result is dependent on the order of arriving spikes, which is not desirable in a rate-based context.Specific care should be given to low firing rates and low threshold values.To illustrate this, let us consider a LIF neuron J with two different inputs I i weighted by their respective weight w i .In addition, assume that the V resting is set to zero.Let us suppose w 1 a < 0 and w 2 b > 0. If I 1 spikes before I 2 , the output is y J b as y J (0−a)+b 0+b b.However, if the order is reversed, y J b − a.This simple example highlights the limitations of this model.We applied an adapted model to fix this issue: setting the lower bound threshold θ down threshold to a negative value, θ down threshold −θ up threshold while keeping v resting 0 and θ up threshold θ threshold .This modification mathematically solves the problem around zero.As a matter of fact, y J b − a in both cases now.Yet, the problem still exists around θ down threshold .V m could be reset to v resting without firing or simply kept at θ down threshold (selected in this work).
Once the spike is generated, the membrane potential is reset.We discuss next two types of resets: reset to zero presented by Diehl et al. [43], always sets the membrane potential back to a baseline, typically zero.Reset by subtraction, or "linear reset mode" presented by Diehl et al. (2016); Cassidy et al. (2013), subtracts the threshold V thr from the membrane potential at the time when it exceeds the threshold [44,45].Accordingly, the adapted model inspired by similar considerations of work in [46][47][48] is given in Eqs.(5)(6)(7)(8).
If V (t) ≥ θ threshold, Spike and reset by subtraction V (t) θ threshold , this model is equivalent to the basic LIF neuron model.In this work, the modified LIF model is used without leak, i.e.L 0. We choose F min 50 Hz and F max 200 Hz in this work.

Rate-based coding
To convert the original features into spikes to feed the spiking networks, rate strategies are used for encoding information in SNNs, which is based on spike firing rate.To simulate neuron behaviours, a Poisson process is often used to generate spike trains.SNNs receive a series of spikes as input and produce a series of spikes as the output, which is usually referred to as spike trains.It is a process where events are assumed to be statistically independent which gives a good approximation of stochastic neuronal firing.The Poisson process is often used to convert the pixel illumination into a spike train: it A black pixel will never produce a spike, while a white pixel corresponds to 100% of the spike produces on average a spiking rate proportional to the illumination of pixels while introducing noise [49].Figure 4 shows an example of the rate coding.

Theory of CNN to SNN conversion
The idea behind the conversion approach is to use the traditional training algorithms on a continuous-valued architecture such that optimal weights can be obtained and then transferred to an equivalent SNNs architecture.The key distinctions among ANNs and SNNs are the type of input and activation unit.ANN's inputs and activations are analogue values with no concept of time, whereas SNNs work with binary spike trains over time.The basic idea behind converting ANNs into SNNs is to match the firing rates of SNN neurons with the activation of the original ANN neurons [43,50].To understand the conversion method, we begin with relation between firing rates of spiking neurons and the activations of rectified linear units (ReLUs) in network conversion.Firstly, the ReLU can be considered a firing rate approximation of an IF neuron with no refractory period, whereby the output of the ReLU is proportional to the number of spikes produced by an IF neuron within a given time window.ReLU neurons computationally cheaper and they bear functional equivalence to an IF spiking neuron without any leak and refractory period [51].This explains why this activation function is used to simulate an IF neuron, instead of the Tanh or the sigmoid functions, for instance.The inputs of an ANN are encoded as Poisson spike trains into the first hidden layer of a SNN.The approximation errors between the activation of ANN neurons and the firing rates of SNN neurons are the key source of performance loss during the conversion.CNN-to-SNN mapping has the following steps.Figure 5 shows the CNN-to-SNN mapping steps.The first step of the mapping approach is to convert the original CNN into a modified CNN.Some modifications are required to make the static network convertible to spiking neurons: • Bias neural units Typically, bias neural units are used for ANNs, which allows the classifier to translate its decision boundary by a fixed value.A bias-less neural units constraint is included in our paper.This is due to the fact that including bias in a SNN, leads to accuracy loss during the conversion procedure, expanding the parameter space exploration and affecting the threshold voltage.By including a zero bias in the training process of the CNN, we ensure that SNN neurons are only defined by their threshold function and the synaptic weights, which reduce the complexity of the design space.

• Dropout
We used dropout to assist the regulation process during training.This technique eliminates a specific number of inputs to avoid overfitting.

• Pooling operation
The pooling operations are commonly employed in CNNs to reduce the dimensionality convolution map.Average pooling and max pooling are two common choices for performing the pooling operation.Max pooling is a commonly used function in CNN to spatially down-sample feature maps.However, because SNNs use binary activations rather than analogue values, the max pooling cannot be implemented.This is due to the fact that using max pooling could result in a considerable loss of information for the next layer.So, we use the average pooling in our design.

• SoftMax
The SoftMax function is used in CNN outputs.It generates a probability distribution of the output belonging to a particular class.In terms of SNNs, there are two ways to predict the output class.Firstly, predicting the output class associated with the neuron that spiked most.This method, however, is inefficient if all neurons in the last layer receive negative inputs.The second way is to replicate the behaviour of Soft-Max in a spiking neuron.We used an external spike generator The second step is to train the modified CNN using the backpropagation method.The third and last step maps the weights from the ReLU network to a network of IF units and applies weight-threshold balancing to achieve faster convergence and less loss accuracy.The main challenge during the mapping approach is to avoid a substantial drop in classification accuracy after conversion.This loss comes from the following factors: 1.The input firing rates are too low such that the IF units do not cross their threshold, leading to a lower effective output.2. The input firing rate is so high that the IF units output too many spikes Therefore, an appropriate balancing between the firing threshold and the input weights is essential to ensure an accurate translation of continuous-valued neuron activations into firing rates of spiking neurons that makes the quality of the mapping greatly dependent on the ratio between the neuron threshold and the synaptic weights.The two common ways to achieve a proper rescaling are to use either a weight normalisation (WN) or threshold balancing (TB) proposed by Diehl et al. [43] and Sengupta et al. [52].The former is used to regulate the spiking rate to decrease accuracy loss, and the latter is used to assign an appropriate threshold to the spiking neurons.The firing rates of the spiking neurons are limited to the range (0, r max ) in SNNs simulation.On the other hand, ReLU activation has no such restrictions.To ensure that the firing rates are approximated by the activations, a weight normalisation approach is employed to normalise the ReLU activations from (0, a l max ) to (0, r max ) by rescaling the convolutional layers weights.The weight normalisation can be represented as follows: where λ l is the max activation of layer l.

First case study: land use and land cover classification
Remote sensing (RS) technology has made rapid progress over the last decade.An unprecedented volume of data is available, and access to information is more straightforward.All of this gives us an understanding of the constant changes in the earth's surface, as well as the socio-ecological interactions that accompany them.Land use and land cover (LULC) data is critical for a wide range of geospatial applications, including city planning, local administration, and environmental management.Significant efforts have been made to study the possibility of applying AI, especially DNNs, on Earth Observation (EO) satellites.However, the limited energy budget of DNNs on hardware is one of the problems restricting the application of DNN models.This fact has motivated the study of energy efficiency networks such as SNNs to solve remote sensing tasks.

Methods
In this research, we initiated the experiments with one of the standard deep learning models-Visual Geometry Group (VGG16) network [53].Figure 6 shows the conversion of the VGG16-based ANN convolutional block to an SNN convolutional block.Some changes are needed to be able to transfer the VGG16 network to spiking neurons.We eliminate the bias and batch normalisation, as they lead to accuracy loss during the conversion process.We also swap the max pooling with average pooling in our design.The second step is to train the VGG16 network using the backpropagation method in order to have a robust and accurate trained model.We apply data augmentation techniques including resizing, rotation, horizontal flip, and vertical flip.

Dataset
The EuroSAT is a dataset for LULC classification taken from the Sentinel-2 satellite [54]

Performance
After training the deep convolutional model, we convert it into an SNN model by replacing the ReLU functions with spiking activations.Finally, we transfer the trained weights to a network of IF units and apply the weight-threshold balancing technique.The best overall model, which uses all 13 bands, accurately classified 94.88% of the testing set over T 400 timesteps.Figure 9 shows the results of VGG16 (training and validation).Tables 1 and 2 show the corrected prediction result for each class and accuracy of Deep CNN and Deep CSNN models, respectively.
The training stopped at the 57th epoch due to an early stopping strategy.This method prevented the model from overfitting and saved computational time.Based on Table 1, the sea/lake, river, industrial, and forest classes showed the best performance above 96% accuracy on test dataset.

Second case study: epileptic seizure detection
One of the most common neurological disorders in the world is epilepsy, which affects people of all ages [55].Thus, it is critical to suggest a highly precise and energy-efficient method of predicting seizure onsets.Electroencephalography (EEG) is a technique used to record electrical activity in the brain.An epileptic patient's EEG recordings can be classified into four states: interictal (between seizures), preictal (pre-seizures), ictal (during seizures), and postictal (postseizures).The predictive task's goal is to distinguish the pre-seizure state from the other three states.However, this is a time-consuming and costly task even for a single patient.For this reason, recent research focuses on machine learning techniques for EEG signal processing such as CNN.However, CNNs are known to be computationally intensive, which makes them difficult to implement on wearable medical devices.Alternatively, SNN is an energy-efficient candidate for choice for embedded hardware.This section aims to deploy a deep convolutional SNN for epileptic seizure detection using a conversion method.

Methods
In this research, we propose a deep convolutional SNNs to make epileptic seizure predictions from the EGG samples.
The proposed approach consists of the same procedure discussed in Sect. 4. Firstly, a number of modifications have been done to make the VGG16 model transferable to spiking model.After training the model with the ReLU activations function and getting the weights, the model transformed into a spiking domain by replacing the ReLU units with IF units.We also applied a weight-threshold balancing technique to ensure an accurate translation of continuous-valued neuron activations into the firing rates of a spiking neuron.Because the SNN layers only received binary spikes as inputs, the numerical EEG signals must be represented as spikes.We employ rate coding, which encodes each signal value normalised to (0, 1) as a spike train of length T .Figure 10 shows the conversion process of the Deep CNN to Deep SCNN for epileptic seizure prediction.

Dataset
We used the EEG recordings provided by the children's Hospital of Boston-Massachusetts Institute of Technology (CHB-MIT) to train and test the model for seizure prediction [56].It includes 23 individuals and 969 h of scalp EEG recordings.The EEG recordings are divided into 24 sets and were recorded with a 16-bit resolution.Table 3 shows the details of the CHB-MIT EEG dataset.Each patient's data is divided into 70/15/15 ratios for training, validation, and test, respectively.We need to mention the   raw recorded signals used in this work, as they need less computational resources from a hardware implementation point of view.

Data pre-processing
Imbalance number of sample in each class is one of the common problems in most classification datasets.This problem can also be found in the CHB-MIT, where only 198 seizures are available, suffering from class imbalances and few positive samples.To address this issue, we divided the EEG records into overlapping time windows with 50% overlap and 4-s window size.To get more samples from the seizure class, we increase the number of windows.

Performance
To evaluate the performance of Deep CSNN classifier, we used two well-known metrics, namely sensitivity and specificity.Sensitivity is the probability of seizure samples that the model correctly classifies as a seizure.Specificity is the proportion of non-seizure samples that the model correctly classifies as non-seizure.
The patient-specific Deep CNN algorithm was evaluated on the CHB-MIT database.Our results reveal that the sensitivity is 96.4% and the specificity is 99.66%.After converting Deep CNN to Deep CSNN, model was evaluated on test dataset.Our results reveal that the sensitivity is 95.06% and the specificity is 99.45% with T 200. Figure 11 shows the sensitivity and specificity of the Deep CSNN model on test dataset.Table 4 shows the average sensitivity and specificity of Deep CNN and Deep CSNN models.

Discussion
In the first case study, deep convolutional SNNs were used to tackle the problem of LULC classification.For this task, a well-known learning architecture, namely, VGG16 was employed on the EuroSAT dataset.After training the VGG16 model, we transform it into an SNN by replacing the ReLU units with IF units.We transfer the trained weights to a network of IF units and apply weight-threshold balancing technique.The best overall model was able to accurately predict the classification for 94.88% of the testing set.The performance of the introduced model compared with different existing methods is presented in Table 5. Dewangkoro and Arymurthy [57] combined CNN with Channel Squeeze & Spatial Excitation (sSE) block for LULC classification.The sSE block is used in their design to recalibrate the CNN function.They also used support vector machine (SVM) and Twin SVM (TWSVM) instead of the SoftMax classifier.Their three models (ResNet50, Incep-tionV3, and VGG19) accurately predicted the classification for 64.32%, 80.36%, and 94.57% of the testing set, respectively.Sonune [58] tackled the problem of land use and land cover classification with two models, namely random forest and ResNet-50.The authors achieved an accuracy of 94.25% and 61.46% using a ResNet50 and random forest model, respectively.In another work, Chen et al. [60] applied the knowledge distillation training approach for remote sensing scene classification on the EuroSAT dataset.Their experimental results showed overall an accuracy of 94.74%.For the second case study, we have presented a deep convolutional SNNs for seizure detection.We used the overlapping windows method to address the problem of imbalanced datasets.As it is shown in Table 6, our model performance is comparable to state-of-the-art methods, with a sensitivity of 95.06% and a specificity of 99.45%.In the spiking domain, Tian et al. [61] proposed a Spiking-CNN to make seizure prediction.Their experiments only consider lead seizures that occur at least 4 h after the previous seizure, which means seven subjects in the CHB-MIT dataset.According to their experimental results, the sensitivity and specificity of 95.1% and 99.2% are achieved.Zhao et al. [62] proposed an FT-VGG16 classifier to classify seizure and non-seizure EEG signals.Their experimental results reveal the sensitivity and specificity of 98.75% and 98.18%, respectively.Several researchers applied SVM methods for epilepsy classification [63].For example, Song et al. [64] used SVM and the weighted-permutation entropy method.They achieved an epilepsy detection accuracy of 91.62 for six different cases.
Considering the event-driven computational and resourceconsuming benefits of the spiking neuron model, SNNs are promising for low-power embedded applications compared to conventional ANNs.To verify the energy consumption of our developed DCSNN, a neuromorphic hardware, like Loihi [66] or SpiNNaker [67], is needed as it has non-von Neumann architecture.Here, however, we provide an insight into energy consumption by evaluating the computational complexity of our DCSNN and against DCNN.
We employ the multiply-and-accumulate (MAC) operation to determine the computational complexity.Due to the use of different neuron models, the number of operations for the DCSNN and the DCNN is calculated differently.The computation cost of the DCNN is generally defined by the MAC procedure in Eq. (1), Sect.2.2.Whereas in the DCSNN, data transferred between layers is a binary spike, and it performs asynchronous accumulate (AC) operations to update the state of each neuron in Eq. (2), Sect.2.3.
We need to mention that the integration is event-driven in spiking neurons, indicating no computation occurs, if there is no spike delivered.The computation cost can be calculated C SNN C add (11) where C add is the computation cost of additions and C mul is the computation cost for multiplications.
Although the DCSNN is required to evaluate over timesteps, its computation cost is lower than the DCNN, because the AC operations cost less than MAC operations.According to the findings in [66], an energy cost for a 32bit AC operation is 5.1× more energy-efficient than a MAC operation.AC operation needs 0.9 pJ, whereas a MAC operation needs 4.6 pJ for 32-bit floating-point computation (45nm CMOS technology).
We have calculated the number of AC and MAC operations and energy consumption in 45nm technology, proposed by Horowitz [68].Tables 7 and 8 compare the DCNN and DCSNN for patient-specific seizure detection, and LULC classification in terms of their energy cost with 50 timesteps, respectively.
We can see that the DCSNN has more addition operation than the DCNN, because of the rate coding time window.On the other hand, removing costly multiplication operations is helpful for energy reduction.According to calculations of energy consumption, the ratio of SNN energy to ANN energy for patient-specific seizure detection is 1.88 lower and the ratio for LULC classification is 1.86.
An important characteristic of SNNs is the time required to generate output.If the number of timesteps is too few, the SNN will not get enough information for training or inference.By contrast, a large number of timesteps results in an increase in prediction latency.Another observation is that a longer time window can result in improved accuracy but increases computing costs and energy consumption.As an example, Fig. 12 illustrates the comparison of LULC classification accuracy with different timesteps and its associated energy consumption.
As we expected, higher timestep leads to higher accuracy.However, this causes higher energy consumption.The timestep of 400 is sufficient to achieve 94.88 accuracy, while the lowest accuracy is obtained with a timestep of 50.Hence, having a trade-off between accuracy, inference latency, and energy remains a significant challenge in neuromorphic computing.One of the main reasons for this issue is the difficulty in determining proper hyperparameter values for the SNNs.
Future works will include applying a multi-objective optimization method to produce high-accuracy and low-latency inference.Moreover, we plan to continue this work by deploying the models on neuromorphic hardware, such as Loihi or SpiNNaker, enabling us to perform more accurate measurements and checking of the actual energy consumption of the SNNs.

Conclusion
This study presents an investigation on developing a deep convolutional spiking neural network for energy-efficient land cover and land use classification and epileptic seizure prediction.We convert pre-trained VGG16 into corresponding spiking equivalents with nearly comparable performance to the original one.We have tested the model datasets: EuroSAT dataset and CHB-MIT dataset.Experimental results show a classification accuracy of 94.88%, and seizure detection specificity of 99.45% and a sensitivity of 95.06%.Deep convolutional SNN training with a conversion method is promising and confirms that the benefits of DNNs are available for SNNs.

Fig. 2 A
Fig. 2 A typical CNN architecture, consisting convolutional, pooling, and fully connected layers

Fig. 3
Fig.3 An overview of ANN and SNN operation, a inputs, outputs, and processing unit of ReLU neuron b inputs, outputs, procedure of integrating, fire, and reset of LIF neuron

Fig. 4
Fig.4 Rate coded input pixel and spiking correspond to the pixel value.A black pixel will never produce a spike, while a white pixel corresponds to 100% of the spike

•
Step 1: Modifying CNNs • Step 2: Training CNN using Tensorflow-Keras • Step 3: Transferring weights from the modified CNN to the equivalent SNN architecture while performing a proper weight-threshold balancing.

Fig. 7 Fig. 8 Fig. 9
Fig. 7 Conversion process of the Deep CNN to Deep CSNN for LULC classification

Fig. 10
Fig. 10 Conversion process of the Deep CNN to Deep CSNN for epileptic seizure prediction

Fig. 11
Fig. 11 Specificity and sensitivity of the Deep CSNN

Table 1
Performance of the deep convolutional SNN on the EuroSAT dataset

Table 3
Specifications of the CHB-MIT datasets

Table 4
Sensitivity and specificity of Deep CNN and Deep CSNN models

Table 5
Performance of the introduced model compared to different methods

Table 6
Performance

Table 7
The energy consumption comparison between DCNN and DCSNN for patient-specific seizure detection

Table 8
The energy consumption comparison between DCNN and DCSNN for LULC classification The trade-off between accuracy, power consumption, and inference timesteps.The x-axis is SNN inference latency, the y-axis on the left measures the SNN inference accuracy, and the data label is estimated energy consumption based on 45 nm CMOS technology