# Autonomous Driving with Spiking Neural Networks

Rui-Jie Zhu1, Ziqing Wang2∗, Leilani Gilpin1, Jason K. Eshraghian1

1University of California, Santa Cruz, USA
2Northwestern University, USA Equal contributionCorresponding author,
<EMAIL_ADDRESS>
###### Abstract

Autonomous driving demands an integrated approach that encompasses perception,
prediction, and planning, all while operating under strict energy constraints
to enhance scalability and environmental sustainability. We present Spiking
Autonomous Driving (SAD), the first unified Spiking Neural Network (SNN) to
address the energy challenges faced by autonomous driving systems through its
event-driven and energy-efficient nature. SAD is trained end-to-end and
consists of three main modules: perception, which processes inputs from multi-
view cameras to construct a spatiotemporal bird’s eye view; prediction, which
utilizes a novel dual-pathway with spiking neurons to forecast future states;
and planning, which generates safe trajectories considering predicted
occupancy, traffic rules, and ride comfort. Evaluated on the nuScenes dataset,
SAD achieves competitive performance in perception, prediction, and planning
tasks, while drawing upon the energy efficiency of SNNs. This work highlights
the potential of neuromorphic computing to be applied to energy-efficient
autonomous driving, a critical step toward sustainable and safety-critical
automotive technology. Our code is available at
https://github.com/ridgerchu/SAD.

##  1 Introduction

Autonomous driving, often considered the ‘holy grail’ of computer vision,
integrates complex processes such as perception, prediction, and planning to
achieve higher levels of vehicle automation as classified by the SAE J3016
standard SAE2014 . Many new vehicles now feature Level 2 autonomy, with
transitions to Level 3 marking notable advancements. However, these systems
must adhere to energy constraints of 50-60 W/h powerbudget  and face
increasing environmental concerns. Sudhakar et al. highlight the need for
hardware efficiency to double every 1.1 years to maintain 2050 emissions from
autonomous vehicles below those of 2018 data center levels sudhakar2022data .

Spiking Neural Networks (SNNs) offer a promising solution for energy-efficient
intelligence by using sparse, event-driven, single-bit spiking activations for
inter-neuron communication, mimicking biological neurons roy2019towards ;
eshraghian2023training ; li2023brain ; maass1997networks . Such workloads can
be accelerated for low latency and low energy, when processed on neuromorphic
hardware that utilizes asynchronous, fine-grain processing to efficiently
handle spiking signals and parallel operations davies2018loihi . Much like in
the brain, spikes are thought to encode information over time, and have shown
improvements in the energy efficiency of sequence-based computer vision tasks
by several orders of magnitude in a variety of workloads azghadi2020hardware ;
frenkel2019morphic ; ottati2023spike .

In the past several years, SNNs have rapidly improved in performance across
various tasks, including image classification Fang_2021_ICCV ; yao2024spike ;
zhou2022spikformer ; zhu2022tcja ; wang2023masked ; wang2024autost ;
qiu2024gated ; deng2024tensor ; shan2023or , object detection su2023yolo ;
kim2020spikingyolo ; yao2023spikev2 , semantic segmentation
kim2022segmentation , low-level image reconstruction qiu2023vtsnn ;
kamata2022vae ; zhan2023esvae ; qiu2023taid ; cao2024spiking , and language
modeling zhu2023spikegpt ; lv2023spikebert ; bal2024spikingbert , with most of
these works focused on computer vision. These advancements have brought SNN
performance closer to that of Artificial Neural Networks (ANNs) in fundamental
computer vision tasks. Despite this progress, SNNs have not yet proven
effective in complex real-world computer vision applications that involve
multiple subtasks.

We introduce the first SNN designed for end-to-end autonomous driving,
integrating perception, prediction, and planning into a single model.
Achieving this milestone for SNNs involved spatiotemporal fusion of visual
embeddings for enhanced perception, probabilistic future modeling for accurate
prediction, and and a high performance temporal mixing spiking recurrent unit
that effectively incorporates safety and comfort considerations into high-
level planning decisions. By leveraging the event-driven and energy-efficient
properties of SNNs, our model processes visual inputs, forecasts future
states, and calculates the final trajectory for autonomous vehicles.
Previously, GRUs or 3D convolutions were used in spatiotemporal visual tasks,
though these operators have been entirely replaced with spiking neurons for
time-mixing. This work marks a significant advancement in neuromorphic
computing, demonstrating the potential of SNNs to handle the complex
requirements of low-power autonomous driving. Our experiments show that this
SNN-based system performs competitively with traditional deep learning
approaches, while offering improved energy efficiency and reduced latency.

Figure 1: How SAD enables autonomous driving from vision to planning: The
system processes inputs from six cameras across multiple frames. The
perception module encodes feature information related to the present input
frame ($T=n$), the prediction module predicts feature information of the next
frame using sequential information ($T=n+1$), and the model output generates a
steering and acceleration plan. This process creates a bird’s eye view (BEV)
and trajectory plan for navigation.

##  2 Related Works

Spiking Neural Networks in Autonomous Systems are particularly effective for
low-power, edge intelligence applications, leveraging deep learning and
neuroscience principles to boost operational efficiency li2023brain ;
roy2019towards ; henkes2022spiking ; hu2021spikingresnet ; schmidgall2023brain
. Many neuromorphic autonomous systems use SNNs as a Proportional Derivative-
Integral (PID) controller to adapt to changing conditions, such as different
payloads in unmanned aerial vehicles vitale2021event ; glatz2019adaptive ;
stagsted2020event ; stagsted2020towards , or to prevent drift in non-neutral
buoyancy blimps burgers2023evolving . Much of this work successfully deployed
SNNs as PID controllers in real-world systems on neuromorphic hardware,
highlighting the potential for low-power autonomous control. Moving from the
sky to the ground, SNN-based PID controllers have been used for lane-keeping
tasks in simulated environments with reference trajectories provided by the
lane bing2018end ; halaly2023autonomous ; kaiser2016towards , as well as with
LiDAR for collision avoidance in simulated environments shalumov2021lidar .
These tasks all show successful use of SNNs in adaptive control, though the
objective of a PID controller is to maintain a desired setpoint which is often
a well-defined and simpler goal than end-to-end autonomous driving in the face
of complex and noisy environments. We push the frontier of what SNNs are
capable of in this paper.

End-to-end Autonomous Driving directly maps sensory inputs to vehicle control
outputs using a single, fully differentiable model. Existing approaches can be
broadly classified into two categories: imitation learning and reinforcement
learning paradigms chen2023end . Imitation learning methods, such as behavior
cloning chen2020learning ; bojarski2016end ; codevilla2018end ; hawke2020urban
; codevilla2019exploring  and inverse optimal control zeng2019end ;
sadat2020perceive ; wang2021end ; hu2021safe ; khurana2022differentiable ,
learn a driving policy by mimicking expert demonstrations. On the other hand,
reinforcement learning techniques kendall2019learning ; liang2018cirl ;
toromanoff2020end ; chekroun2021gri  enable the driving agent to learn through
interaction with the environment by optimizing a reward function. Recent
advancements, such as multi-modal sensor fusion prakash2021multi ;
chitta2022transfuser ; shao2022safety ; jia2023think ; jaeger2023hidden ,
attention mechanisms prakash2021multi ; chitta2021neat ; chitta2022transfuser
, and policy distillation chen2020learning ; chen2021learning ; zhang2021end ;
wu2022trajectory ; zhang2023coaching  have significantly improved the
performance of end-to-end driving systems.

Figure 2: Overview of SAD. The multi-view features from the perception
encoder, including a spiking ResNet with inverted bottleneck and spiking
DeepLab head, are fed into a prediction module using spiking neurons. The
perception decoder then generates lane divider, pedestrian, vehicle and
drivable area predictions. Finally, the planning module models the scene and
generates future predictions to inform rule-based command decisions for
turning, stopping, and goal-directed navigation.

##  3 Method

This section presents the Spiking Autonomous Driving (SAD) method, an end-to-
end framework that integrates perception, prediction, and planning using SNNs
(Fig. 2). SAD’s biologically-inspired architecture enables efficient
spatiotemporal processing for autonomous driving, with the spiking neuron
layer at its core. This layer incorporates spatiotemporal information and
enables spike-driven computing, making it well-suited for the dynamic nature
of autonomous driving tasks.

The perception module is the first stage of the SAD framework. It constructs a
bird’s eye view (BEV) representation from multi-view camera inputs, providing
a human-interpretable understanding of the environment. This representation
serves as the foundation for the subsequent prediction and planning modules.
The prediction module uses the BEV to forecast future states using a ‘dual
pathway’, which allows data to flow through two separate paths, providing a
pair of alternative data embeddings. One pathway focuses on encoding
information from the past, while the other pathway specializes in predicting
future information. Subsequently, the embeddings from these two pathways are
fused together, integrating the past and future information to facilitate
temporal mixing. This enables the anticipation of dynamic changes in the
environment, which is crucial for safe and efficient autonomous driving.
Leveraging the perception and prediction outcomes, the planning module
generates safe trajectories by considering predicted occupancy of space around
the vehicle, traffic rules, and ride comfort. To optimize the entire pipeline,
SAD is trained end-to-end using a composite loss that combines objectives from
perception, prediction, and planning. The following subsections describe each
module in detail.

###  3.1 Spiking Neuron Layer

All modules consist of spiking neurons rather than artificial neurons, and so
a formal definition of spiking neurons is provided below. Spiking neuron
layers integrate spatio-temporal information into the hidden state of each
neuron (membrane potential) which are converted into binary spikes emitted to
the next layer. Spiking neurons can be represented as recurrent neurons with
binarized activations and a diagonal recurrent weight matrix such that the
hidden state of a neuron is isolated from all other neurons (see
eshraghian2023training  for a derivation). We adopt the standard Leaky
Integrate-and-Fire (LIF) maass1997networks  model, whose dynamics are
described by the following equations:

$\displaystyle U[t]=H[t-1]+X[t],$ (1) $\displaystyle
S[t]=\Theta\left(U[t]-u_{th}\right),$ (2) $\displaystyle H[t]=U_{\rm
reset}S[t]+\left(\beta U[t]\right)\left(1-S[t]\right),$ (3)

where $X[t]$ is the input to the neuron at time-step $t$, and is typically
generated by convolutional or dense operators. $U[t]$ denotes the membrane
potential of the neuron, and integrates $X[t]$ with the temporal input
component $H[t-1]$. $\Theta(\cdot)$ is the Heaviside step function, which is 1
for $x\geq 0$ and 0 otherwise. If $U[t]$ exceeds the firing threshold
$u_{th}$, the spiking neuron emits a spike $S[t]=1$ as its activation, and the
temporal output $H[t]$ is reset to $V_{\rm reset}$. Otherwise, no spike is
emitted ($S[t]=0$) and $U[t]$ decays to $H[t]$ with a decay factor $\beta<1$.
For brevity, we refer to Eq. 2 as ${\mathcal{SN}}(\cdot)$, where the input $U$
is a tensor of membrane potential values fed into multiple spiking neurons,
and the output $S$ is an identically-shaped tensor of spikes.

###  3.2 Perception: Distinct Temporal Strategies for Encoder and Decoder

Fig. 3 illustrates the overall architecture of the perception module. The
perception stage constructs a spatiotemporal BEV representation from multi-
view camera inputs over $t$ time-steps through spatial and temporal fusion of
features extracted from the cameras. It consists of an encoder, which
processes each camera input to generate features and depth estimations, and a
decoder, which generates BEV segmentation and instructs the planning module. A
future prediction module is depicted between the encoder and decoder in Fig.
3. It is not used in the first stage where the perception module is trained
alone, but it is included in the second stage once the prediction module is
included.

The temporal dimension processing in the Encoder/Decoder architecture is a
crucial design consideration, as both SNNs and autonomous driving data
inherently possess a temporal structure. There are two approaches to handle
this:

  * •

Sequential Alignment (SA): sequential input data is passed to the SNN step-by-
step by aligning the time-varying dimension of the input data with the model

  * •

Sequence Repetition (SR): sequential input data is aligned with the batch
dimension for better parallelism during training, and individual frames are
repeated $T$ times over the model sequence, so as to create virtual timesteps.
SR is commonly used for pre-training sequence-based models on static image
datasets.

Given these two encoding options, we test all four combinations of these
options applied to both the encoder and decoder of the perception block. Based
on our experiments (detailed in Sec. 4.3.1), the best performing approach is
using SR for the encoder and SA for the decoder. The encoder is also pre-
trained on ImageNet-1K which requires the use of repeated images to create
virtual timesteps. Further details regarding the pre-training of the encoder
can be found in Appendix B.1. Conversely, the decoder is trained from scratch,
which naturally assumes a temporal-mixing role, making the alignment of
sequential data with the model sequence a more effective approach.

The training process involves first training the encoder-decoder, followed by
the prediction module. This approach integrates spatial and temporal
information for comprehensive BEV representation in autonomous vehicle
perception and planning.

##### Encoder: Spiking Token Mixer with Sequence Repetition

The encoder module can be thought of as a spiking token mixer (STM). The STM
consists of 12-layers of spiking CNN pre-trained on ImageNet-1K
deng2009imagenet  to generate vision patch embeddings, which is effectively a
deeper version of the ‘spiking patch embedding’ from Ref. yao2024spike ;
zhou2022spikformer . Across these 12 layers, the number of channels in each
layer is designed to first increase and then decrease so as to act as an
inverted bottleneck. While SPS layers are usually terminated by self-
attention, we replaced this with dense layers instead, which both reduces
computational resources and leads to improved performance. In doing so, we
achieved a 72.1% ImageNet top-1 classification accuracy with only 12M
parameters. In contrast, the previous spiking vision transformers that employs
self-attention reached 70.2% with the same number of parameters yao2024spike .

Figure 3: The perception module. The encoder takes multi-camera input data,
passes it through a spiking ResNet with inverted bottleneck to generate
feature representations, each of which has its own depth estimation. These are
fused and passed to the decoder, which generates predictions for lane
dividers, pedestrians, vehicles and drivable areas.

The encoder extracts feature embeddings and depth estimations while squeezing
the image into a smaller latent space. The overall workflow of the encoder can
be summarized as follows:

$\displaystyle X=\text{STM}(I),$ $\displaystyle I\in\mathbb{R}^{N\times
C_{in}\times T\times L\times H\times W},\quad X\in\mathbb{R}^{C\times T\times
L\times H\times W}$ $\displaystyle\mathcal{F}=\text{Head}_{\rm feature}(X),$
$\displaystyle X\in\mathbb{R}^{C\times T\times L\times H\times
W},\quad\mathcal{F}\in\mathbb{R}^{C_{f}\times L\times H\times W},$
$\displaystyle\mathcal{D}=\text{Head}_{\rm depth}(X),$ $\displaystyle
X\in\mathbb{R}^{C\times T\times L\times H\times
W},\quad\mathcal{D}\in\mathbb{R}^{C_{d}\times L\times H\times W}$
$\displaystyle Y=\mathcal{F}\otimes\mathcal{D},$ $\displaystyle
Y\in\mathbb{R}^{C_{f}\times C_{d}\times T\times L\times H\times W}$

The STM encoder described above is used to extract feature embeddings and
depth estimates from each camera frame $I_{t}\in\mathbb{R}^{N\times
C_{in}\times H\times W}$, where $N=6$ is the number of cameras, $C_{in}=3$
refers to the number of input channels (RGB), and $H\times W$ refers to the
video resolution. Note that the use of sequence repetition means that $T$ is
the number of times the same frame is repeated over the sequence, while $L$ is
the number of frames in a continuous camera recording. As such, the dimensions
$N\times L$ are stacked so as to speed up processing.

The encoder consists of 12 layers, each containing a 2D convolution layer,
batch normalization, and spiking neuron. The output of the encoder is a
feature map $\mathcal{F}\in\mathbb{R}^{C_{f}\times L\times H\times W}$ and a
depth estimation $\mathcal{D}\in\mathbb{R}^{C_{d}\times L\times H\times W}$,
where $C_{f}$ is the number of feature channels, $C_{d}$ is the number of
channels, each of which has a depth associated with it, and $(H,W)$ is the
spatial size. Formally, given an image sequence ${{I}}$:

$\displaystyle X={\mathcal{SN}}({\rm{BN}}({\rm{Conv2d}}(I))),$ (4)

where Conv2d represents a 2D convolutional layer (stride: 1, $3\times 3$
kernel size), $BN$ is batch normalization, and $\mathcal{MP}$ is a max-pooling
operator. The feature map $\mathcal{F}$ and depth estimation $\mathcal{D}$ are
then averaged over the sequence $T$ and combined using an outer product to
obtain a camera feature frustum:

$Y=\mathcal{F}\otimes\mathcal{D},Y\in\mathbb{R}^{C_{f}\times C_{d}\times
T\times L\times H\times W}$ (5)

The frustums from all cameras are transformed into a global 3D coordinate
system centered at the ego-vehicle’s inertial center at time $i$. Previous BEV
feature maps are merged with the current BEV by applying a discount factor
$\alpha$ to integrate these layers efficiently.

$\tilde{x}_{t}=b_{t}+\sum_{i=1}^{t-1}\alpha^{i}\times\tilde{x}_{t-i}$ (6)

where $\tilde{x}_{t}$ is the BEV at time $t$ which has an initial condition of
$\tilde{x}_{1}=b_{1}$, and the discount factor is $\alpha=0.5$. We then
average across the $T$ dimension to eliminate the repeated temporal dimension
and obtain the average firing rate. The resulting feature map is then be
passed to the decoder.

##### Decoder: Sequential Alignment with Streaming Feature Maps

The recurrent decoder aligns feature maps sequentially, introducing a new
instance of data at each time-step, contrasting with the encoder’s repeated
inputs. Using SA rather than SR for the decoder improves performance for two
reason: 1) the decoder does not need to be pre-trained on static, repeated
data, and 2) the decoder acts as a temporal mixer. In this architecture, time-
mixing is achieved using LIF neurons and allows them to take on the role of
self-attention without the same computational burden. The LIF neurons are
composed as a shared backbone as a set of layers used to extract features from
data before being passed to various specialized heads, each dedicated to a
specific task. The high-level dataflow summarized as follows:

$\displaystyle X=\text{SharedBackbone}(I_{D}),$ $\displaystyle
I\in\mathbb{R}^{C_{in}\times L\times H\times W},\quad
X\in\mathbb{R}^{C_{med}\times T\times L\times H\times W}$ $\displaystyle
Y_{k}=\text{Head}_{k}(X),$ $\displaystyle Y_{k}\in\mathbb{R}^{C_{out}\times
L\times H\times W},\quad k\in\\{\text{seg, ped, map, inst}\\}$

where $I_{D}$ is the input tensor to the decoder with dimensions
$(C_{in},L,H,W)$, $X$ is the output of the shared backbone with dimensions
$(C_{med},T,L,H,W)$,$Y_{k}$ is the output of the $k$-th head with dimensions
$(C_{out},L,H,W)$, and $k$ indexes into the heads of the different tasks:
vehicle segmentation (seg), pedestrian (ped), HD map (map), and future
instance (inst). The shared backbone is implemented using the first three
layers of MS-ResNet18 hu2024advancing  followed by three upsampling layers
with a factor of 2 and skip connections. More details about MS-ResNet can be
found in Appendix A. The resulting features have 64 channels and are then
passed to different heads according to the task requirements. Each head
consists of a spiking convolutional layer.

###  3.3 Prediction: Fusing Parallel Spike Streams

Predicting future agent behavior is crucial for an autonomous vehicle to be
reactive and make informed decisions in real-time. In our approach, we
accumulate historical BEV features and predict the next few timesteps using
purely LIF neurons. However, the stochastic nature of interactions among
agents, traffic elements and road conditions, makes it challenging to
accurately predict future trajectories. To address this, we model future
uncertainty with a conditional Gaussian distribution.

To accomplish this, two layers of LIF neurons are used. The first parallel
layer takes the present and prior output BEV feature maps from the encoder of
the perception model $(x_{1},\dots,x_{t})$ as inputs. The first BEV $x_{1}$ is
also used as the initial membrane potential for this LIF layer. The second
parallel layer accounts for the uncertainty distribution of future BEV
predictions. The uncertainty distribution is generated by passing the present
feature $x_{t}$ through 4 spiking MS-ResNet blocks, average pooling, and
another 2D spiking convolution with a kernel size of $(1,1)$ to transform the
channel depth to double the output of the first parallel layer. Another
averaging pooling operator compresses the feature map down to a vector. The
vector is split in two sub-vectors representing mean $\mu\in\mathbb{R}^{L}$
and variance $\sigma\in\mathbb{R}^{L}$, and these values populate a diagonal
Gaussian distribution of the latent feature map. Using the $\mu$ and standard
deviation $\sigma$, we can construct the Gaussian distribution at timestep
$t$, denoted as $\eta_{t}$. This distribution, represented by the parameters
$\mu$ and $\sigma$, can then be concatenated with the input at the current
timestep $x_{t}$.

Simultaneously, all prior spiking outputs are concatenated to the present
input $x_{t}$, denoted below $x_{0:t}$. The predicted BEV feature for the next
timestep is calculated below:

$\hat{x}_{t+1}=\mathrm{LIF}({\rm{BN}}({\rm{Conv2d}}(\text{concatenate}(x_{t},\eta_{t})))\oplus\mathrm{LIF}({\rm{BN}}({\rm{Conv2d}}((x_{0:t}))),$
(7)

where $\hat{x}_{t+1}$ represents the predicted BEV features for the next
timestep, $\mathrm{LIF}(\cdot)$ denotes the LIF neuron layer,
$\text{concatenate}(\cdot)$ represents the concatenation operation, and
$\oplus$ denotes element-wise addition of the outputs from the two LIF layers,
and the inner $\mathrm{Conv2d}(\cdot)$ and $\mathrm{BN}(\cdot)$ layers are
used to ensure consistency in the output dimensions of the first and second
LIF layers.

Figure 4: Dual pathway modeling for prediction. Neuron $a$ captures future
multi-modality by incorporating uncertainty distribution. Neuron $b$
compensates for information gaps using past variations. Inputs $x_{1}$ and
$x_{t}$ from both pathways are used for the next prediction step.

The mixture prediction serves as the basis for the subsequent prediction
steps. By recursively applying this dual-pathway prediction method, we obtain
the predicted future states $(\hat{x}_{t+1},\dots,\hat{x}_{t+n})$. The overall
datapath is illustrated in Fig. 4. Following the dual-pathway prediction, all
the features are fed into a Spiking ResNet using SA for additional temporal
mixing. The historical features $(x_{1},\dots,x_{t})$ and the predicted future
features $(\hat{x}_{t+1},\dots,\hat{x}_{t+n})$ are then passed to the
perception decoder, which consists of multiple output heads to generate
various interpretable intermediate representations.

###  3.4 Planning: Temporal Spiking Temporal for Trajectory Refinement

The primary objective of the SAD system is to plan a trajectory that is both
safe and comfortable, aiming towards a designated target. This is accomplished
through a planning pipeline that integrates predicted occupancy grids $o$, map
representations $m$, and temporal dynamics of environmental elements like
pedestrians.

Motion Planning. Initially, our motion planner generates a diverse set of
potential trajectories using the bicycle model polack2017kinematic . Among
these, the trajectory that minimizes a predefined cost function is selected.
This function integrates various factors including learned occupancy
probabilities (from segmentation maps generated in the Prediction section) and
compliance with traffic regulations to ensure the selected trajectory
optimizes for safety and smoothness.

Cost Function. The cost function $f$ employed is a multi-component function,
where:

$f(\tau,o,m;w)=f_{o}(\tau,o,m;w_{o})+f_{v}(\tau;w_{v})+f_{r}(\tau;w_{r})$ (8)

where $w=(w_{o},w_{v},w_{r})$ represents the learnable parameters associated
with each cost component, and $\tau$ denotes a set of trajectory candidates.
Specifically, $f_{o}$ evaluates trajectory compliance with static and dynamic
obstacles, $f_{v}$ is derived from the prediction decoder assessing future
states, and $f_{r}$ addresses metrics of ride comfort and progress towards the
goal. The aim is to select the optimal set of trajectories $\tau^{*}$ that
minimize this cost function. This cost function is adapted from Hu et al.
hu2022st  and is detailed in Appendix D.

Additionally, trajectories are filtered based on high-level commands (e.g., go
forward, turn left, turn right) which tailor the trajectory selection to the
immediate navigational intent.

Optimization with Spiking Gated Recurrent Unit. Following the initial
selection, the "best" trajectory $\tau^{*}$ undergoes further refinement using
a Spiking Gated Recurrent Unit (SGRU), as inspired by lotfi2020long . In this
optimization phase, the hidden state $h_{t}$ of the SGRU incorporates features
derived from the front camera’s encoder. The input state $x_{t}$ is formulated
by concatenating the vehicle’s current position, the corresponding position
from the selected trajectory $\tau^{*}$, and the designated target point.

The SGRU model processes inputs as follows:

$\displaystyle r_{t}$
$\displaystyle=\Theta(W_{ir}x_{t}+b_{ir}+W_{hr}h_{t-1}+b_{hr})$ (9)
$\displaystyle z_{t}$
$\displaystyle=\Theta(W_{iz}x_{t}+b_{iz}+W_{hz}h_{t-1}+b_{hz})$ (10)
$\displaystyle n_{t}$
$\displaystyle=\Theta(W_{in}x_{t}+b_{in}+r_{t}\odot(W_{hn}h_{t-1}+b_{hn}))$
(11) $\displaystyle h_{t}$ $\displaystyle=(1-z_{t})\odot n_{t}+z_{t}\odot
h_{t-1}$ (12)

where $h_{t}$ denotes the hidden state at time $t$, $x_{t}$ represents the
input, and $r_{t}$, $z_{t}$, $n_{t}$ are the reset, update, and new candidate
state gates respectively. The Heaviside function $\Theta$ ensures sparse and
binarized operations in the state of the SGRU, thus preserving the advantages
of SNNs.

This optimization step enhances trajectory reliability by mitigating
uncertainties inherent in perceptual and predictive analyses, and by
integrating dynamic traffic light information directly into the trajectory
planning process.

###  3.5 Overall Loss for End-to-End Learning

Our model integrates perception, prediction, and planning into a unified
framework optimized end-to-end using a composite loss function:

$\mathcal{L}=\mathcal{L}_{per}+\alpha\mathcal{L}_{pre}+\beta\mathcal{L}_{pla}$
(13)

where $\alpha$ and $\beta$ are learnable weights. These parameters dynamically
adjust to scale the contributions of each task based on the gradients from the
respective task losses.

Perception Loss. This component is multi-faceted, covering segmentation for
current and previous frames, mapping, and auxiliary depth estimation. For
semantic segmentation, a top-k cross-entropy loss is employed to effectively
handle the large amount of background, non-salient content in the BEV images,
following the approach in hu2021fiery . Instance segmentation utilizes an
$l_{2}$ loss for centerness supervision and an $l_{1}$ loss for offsets and
flows. Lane and drivable area predictions are evaluated using a cross-entropy
loss.

Prediction Loss. Our prediction module extends the perception task by
forecasting future semantic and instance segmentation. It adopts the same
top-k cross-entropy loss used in perception but applies an exponential
discount to future timestamps to account for increasing uncertainty in
predictions.

Planning Loss. The planning module begins by selecting the initial best
trajectory $\tau^{*}$ from a set of sampled trajectories as defined in Eq. 8.
This trajectory is then refined using an SGRU-based network to produce the
final trajectory output $\tau_{o}^{*}$. The planning loss comprises two parts:
a max-margin loss that differentiates between the expert behavior $\tau_{h}$
(treated as a positive example) and other sampled trajectories (treated as
negatives), and an $l_{1}$ distance loss that minimizes the deviation between
the refined trajectory and the expert trajectory.

Further details on these loss components and the training are provided in the
Appendix B.2.

Table 1: Perception results. We report the BEV segmentation IoU (%) of intermediate representations and their mean value. Method |  Spike |  Drivable Area |  Lane |  Vehicle |  Pedestrian |  Avg.
---|---|---|---|---|---|---
VED lu2019monocular RAL |  ✗ |  60.82 |  16.74 |  23.28 |  11.93 |  28.19
VPN pan2020cross RAL |  ✗ |  65.97 |  17.05 |  28.17 |  10.26 |  30.36
PON roddick2020predicting CVPR |  ✗ |  63.05 |  17.19 |  27.91 |  13.93 |  30.52
Lift-Splat philion2020lift ECCV |  ✗ |  72.23 |  19.98 |  31.22 |  15.02 |  34.61
IVMP wang2021learning ICRA |  ✗ |  74.70 |  20.94 |  34.03 |  17.38 |  36.76
FIERY hu2021fiery ICCV |  ✗ |  71.97 |  33.58 |  38.00 |  17.15 |  40.18
ST-P3 hu2022st ECCV |  ✗ |  75.97 |  33.85 |  38.00 |  17.15 |  42.69
SAD (Ours) |  ✓ |  64.74 |  27.78 |  34.82 |  15.12 |  35.62

##  4 Experiments

We evaluate the proposed model using the nuScenes dataset caesar2020nuscenes
with 20 epochs with SpikingJelly fang2023spikingjelly  framework. For our
experiments, we consider $1.0s$ of historical context and predict $2.0s$ into
the future, which corresponds to processing 3 past frames and predicting 4
future frames. Additional experimental details are elaborated in the Appendix.

###  4.1 Experimental Results on nuScenes

Perception. Our evaluation focuses on the model’s ability to interpret map
representations and perform semantic segmentation. For map representation, we
specifically assess the identification of drivable areas and lanes, which are
critical for safe navigation as they dictate where the Self-Driving Vehicle
(SDV) can travel and help maintain the vehicle’s position within the lanes.
Semantic segmentation tests the model’s ability to recognize dynamic objects,
such as vehicles and pedestrians, which are pivotal in urban driving
scenarios.

We employ the Intersection-over-Union (IoU) metric to quantify the accuracy of
our BEV segmentation tasks. The results, as summarized in Tab. 1, show that
our SAD method, which is fully implemented with spiking neural networks
(SNNs), competes favorably against state-of-the-art, non-spiking artificial
neural networks (ANNs). Notably, our model achieves a superior mean IoU on the
nuScenes dataset compared to existing leading methods such as VED
lu2019monocular , VPN pan2020cross , PON roddick2020predicting , and Lift-
Splat philion2020lift . Specifically, our SAD method outperforms the VED
lu2019monocular  model by 7.43% in mean IoU. This enhancement is significant,
considering that our network utilizes spiking neurons across all layers, which
contributes to greater computational efficiency. Despite the inherent
challenges of using SNNs, such as the binary nature of spikes and potential
information loss compared to traditional ANNs, our results demonstrate that
SAD is capable of delivering competitive perception accuracy in autonomous
driving scenarios.

Table 2: Prediction results. We report semantic segmentation IoU (%) and instance segmentation metrics from the video prediction area. The static method assumes all obstacles static in the prediction horizon. Method |  Spike |  Future Semantic Seg. | Future Instance Seg.
---|---|---|---
|  IoU $\uparrow$ |  PQ $\uparrow$ |  SQ $\uparrow$ |  RQ $\uparrow$
Static |  ✗ |  32.20 |  27.64 |  70.05 |  39.08
FIERY hu2021fiery ICCV |  ✗ |  37.00 |  30.20 |  70.20 |  42.90
ST-P3 hu2022st ECCV |  ✗ |  38.63 |  31.72 |  70.15 |  45.22
SAD (Ours) |  ✓ |  32.74 |  20.00 |  68.74 |  29.39
Table 3: Planning results. Method |  Spike | L2 ($m$) $\downarrow$ | Collision (%) $\downarrow$ |  Energy (mJ)
---|---|---|---|---
|  1s |  2s |  3s |  1s |  2s |  3s |
NMP zeng2019end CVPR |  ✗ |  0.61 |  1.44 |  3.18 |  0.66 |  0.90 |  2.34 |  -
Freespace hu2021safe CVPR |  ✗ |  0.56 |  1.27 |  3.08 |  0.65 |  0.86 |  1.64 |  344.11
ST-P3 hu2022st ECCV |  ✗ |  1.33 |  2.11 |  2.90 |  0.23 |  0.62 |  1.27 |  3520.40
SAD (Ours) |  ✓ |  1.53 |  2.35 |  3.21 |  0.62 |  1.26 |  2.38 |  46.92

Prediction. We assess the predictive capabilities of our model using multiple
metrics tailored for video prediction, specifically IoU, existing Panoptic
Quality (PQ), Recognition Quality (RQ), and Segmentation Quality (SQ) for
evaluating our prediction quality. The definition of these metrics can be
found in Appendix. C.2. The results, presented in Tab. 2, demonstrate that
while our model does not employ an additional temporal module, the inherent
temporal dynamics of spiking neurons facilitate effective information
processing. However, our SAD model still shows a gap in performance when
compared with state-of-the-art ANN methods.

Planning. In the planning domain, we evaluate our model using two primary
metrics: L2 error and collision rate. To ensure fairness, the planning horizon
is adjusted to $3.0s$. The L2 error measures the deviation between the SDV’s
planned trajectory and the human driver’s actual trajectory, providing a
quantitative measure of planning accuracy. The collision rate assesses the
model’s ability to safely navigate the driving environment without incidents.
Results, detailed in Tab. 3, reveal that our SAD method achieves an L2 error
and collision rate comparable to those of the state-of-the-art ANN-based
methods, underscoring the safety and reliability of our planning approach.

Energy Efficiency. Neuromorphic hardware is able to take advantage of small
activation bit-widths and dynamical sparsity davies2018loihi , and as such,
SNNs are able to significantly reduce energy consumption during inference $-$
provided there are sufficiently sparse activation patterns amongst spiking
neurons. As detailed in Table 3, we present an estimation of the energy usage
of each SOTA model based on dynamical sparsity (detailed calculation methods
described in Appendix E). Owing to the utilization of spiking neurons, our
model achieves substantial energy reductions: 7.33 $\times$ less than the
Freespace model hu2021safe  and 75.03 $\times$ lower compared to the ST-P3
model hu2022st . This exceptional energy efficiency makes our model highly
suitable for real-world applications.

Table 4: Ablation study on different timestep alignment strategies for the encoder and decoder on perception tasks. ‘SR’ denotes repeating the timestep input, ‘SA’ indicates aligning the timestep with the model’s inherent temporal dimension, and ’w/o T’ means eliminating the decoder’s inherent timestep association, resulting in no hidden state connections between timesteps. Our final model adopts the configuration of repeating the timestep in the encoder and aligning the timestep in the decoder. Encoder | Decoder | Results
---|---|---
SR | SA | SR | SA | w/o T | Drivable | Lane | Vehicle | Pedestrian | Avg.
| ✓ |  | ✓ |  | 43.84 | 15.25 | 4.41 | 1.62 | 16.28
✓ |  | ✓ |  |  | 0.00 | 0.00 | 0.00 | 0.42 | 0.11
✓ |  |  |  | ✓ | 61.80 | 20.92 | 31.78 | 13.46 | 31.99
✓ |  |  | ✓ |  | 61.81 | 25.31 | 33.89 | 15.24 | 34.06

###  4.2 Visualization

To evaluate the effectiveness of our SAD model in a more interpretable manner,
we provide qualitative results using the nuScenes dataset. Fig. 5 illustrates
the outputs of our model. The SAD model effectively generates a safe
trajectory that enables straight-ahead motion while avoiding collisions with
curbsides and the vehicle ahead. Additionally, we conducted a comparative
analysis with the ANN model, which demonstrated that our SAD model can achieve
comparable performance, ensuring accurate and reliable planning outcomes.More
visual results can be found in the Appendix C.3.

Figure 5: Qualitative Results of the SAD Model on the nuScenes Dataset. (a)
displays six camera view inputs utilized by the model. (b) illustrates the
planning result of the ANN model, and (c) presents the planning results of our
SAD model. The comparison shows that our SAD model can achieve performance
comparable to that of the ANN model and successfully generate a safe
trajectory.

###  4.3 Ablation Study

####  4.3.1 Timestep Strategy

The large space of architecture design decisions came with a large number of
ablation studies before determining the best performing model. We conducted an
ablation study to examine the effects of different timestep alignment
strategies on the performance of the encoder and decoder in perception tasks.
The strategies include ‘SR’ for the repetition of vision inputs over
timesteps, ‘SA’ where sequential inputs are aligned with the model’s inherent
temporal dimension, and ’w/o T’ where recurrent dynamics in the decoder are
removed, thus disconnecting the hidden states between timesteps. The results
are summarized in Tab. 4. The last row is the baseline configuration of our
model that serves as a reference point for these experiments. All ablation
experiments are run for 5 epochs.

Impact of Timestep Repetition in Encoder. (Row 1) When repeating timesteps in
the encoder which was pre-trained on the ImageNet-1K dataset for
classification tasks, we notice a substantial benefit. This approach leverages
the encoder’s ability to capture spatial information through repeated images,
a technique effective during its pre-training phase. Adopting this strategy in
the SAD model enhances perception performance by maintaining consistency with
the pre-training approach.

Impact of Timestep Alignment in Decoder. (Row 2) In contrast to the encoder,
the decoder, which is trained from scratch, benefits from aligning timesteps
with the model’s inherent temporal dimension (‘SA’). This strategy leverages
the decoder’s capacity to mix temporal information, improving performance over
the repeat strategy (‘SR’), which fails to show any performance gains.

Single Timestep Input. (Row 3) The purpose of this experiment was to study how
well spiking neurons perform as temporal mixers. In this setup, all inputs are
processed in one timestep without inter-frame connections, leading to a slight
performance decrease compared to our baseline. Therefore, it confirms that
spiking neurons inherently possess temporal processing capabilities.

####  4.3.2 Effectiveness of Different Modules

Tab. 5 outlines the results of an ablation study that assesses the impact of
various structural modifications to the encoder and decoder on planning tasks.
The study differentiates between ‘MS’ for MS-ResNet structure hu2024advancing
, ‘SEW’ for SEW-ResNet structure fang2021deep , ‘SP’ for single pathway model,
and ‘DP’ for dual pathway model. We analyze the planning performance of each
configuration. The last row represents the configuration of our final model,
which we use as the baseline for comparison.

Decoder Structure Evaluation. (Row 1) This part of the study compares the MS-
ResNet and SEW-ResNet structures in their roles as decoders. Each structure
possesses unique firing patterns, which are discussed in detail in the
Appendix A. Our results indicate that the MS-ResNet structure is more
effective for planning tasks in autonomous driving, likely due to its enhanced
capability to handle the spatial-temporal dynamics required in this context.

Pathway Model Comparison. (Row 2) Here, we explore the performance difference
between single and dual pathway prediction models. The dual pathway model
integrates information through two distinct processing streams. Our
experimental results show that the dual pathway model significantly
outperforms the single pathway model in planning tasks.

Table 5: Ablation Study on different modules for the encoder and the decoder on Planning tasks. ‘MS’ denotes the MS-ResNet structure, SEW denotes the SEW-ResNet structure, ‘SP’ means the single pathway model, and ‘DP’ means the dual pathway model. Decoder | Prediction | Results
---|---|---
MS | SEW | SP | DP | PQ | SQ | RQ
| ✓ |  | ✓ | 59.28 | 0.75 | 0.44
✓ |  | ✓ |  | 67.55 | 13.35 | 19.77
✓ |  |  | ✓ | 68.16 | 16.57 | 24.11

##  5 Conclusion

In this work, we presented Spiking Autonomous Driving (SAD), the first end-to-
end spiking neural network designed for autonomous driving. By integrating
perception, prediction, and planning into a unified neuromorphic framework,
SAD demonstrates competitive performance on the nuScenes dataset while
exhibiting exceptional energy efficiency compared to state-of-the-art ANN-
based methods. The perception module effectively constructs interpretable
bird’s eye view representations, the prediction module accurately forecasts
future states using a novel dual-pathway architecture with spiking neurons,
and the planning module generates safe and comfortable trajectories.
Crucially, SAD showcases the immense potential of SNNs in complex real-world
applications, marking a significant step towards realizing low-power,
intelligent systems for safety-critical domains like autonomous vehicles.
Moving forward, we believe this work will inspire further research into
neuromorphic computing for sustainable and robust autonomous driving
solutions.

## Acknowledgements

This work was supported in part by National Science Foundation (NSF) awards
CNS-1730158, ACI-1540112, ACI-1541349, OAC-1826967, OAC-2112167, CNS-2100237,
CNS-2120019, the University of California Office of the President, and the
University of California San Diego’s California Institute for
Telecommunications and Information Technology/Qualcomm Institute. Thanks to
CENIC for the 100Gbps networks. This project was also supported in-part by the
National Science Foundation RCN-SC 2332166.

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## APPENDIX

##  Appendix A Spiking ResNet Architecture

MS-ResNet [71] and SEW-ResNet [83] are two directly trained residual learning
methods for SNNs, primarily aiming to overcome the degradation of spiking
activity in training deep SNNs. In classic CNNs, ResNet achieves "very deep"
neural networks by attaching an identity mapping skip connection throughout
the entire network. However, directly copying the classic residual structure
to SNNs causes the training loss increases as the network deepens. The
underlying reason is that CNNs generate continuous valued activations, while
SNNs generate discrete spikes.

To address this issue, SEW-ResNet and MS-ResNet establish shortcut connections
between spikes or membrane potentials of different layers, respectively. SEW-
ResNet builds shortcuts between the output spikes of different layers, thereby
obtaining an identity mapping. On the other hand, MS-ResNet constructs
shortcuts between the membrane potentials of spiking neurons in different
layers. Fig. 6 illustrates the differences between these two methods. By
building residual learning on membrane potentials, MS-ResNet achieves higher
accuracy than SEW-ResNet.

##  Appendix B Training

###  B.1 Pretraining on Spiking Token Mixer (STM)

In STM, the architecture is similar to Spiking Transformers, consisting of a
Spiking Patch Embedding (SPS) layer followed by a Transformer-like
architecture. However, unlike Spiking Transformers, the SPS layer in STM is
not followed by a self-attention layer. We pre-train the STM on ImageNet-1K
for 300 epochs, aligning with other SNNs that are pre-trained on ImageNet. The
input size is set to 224 × 224, and the batch size is set to 128 or 256 during
the 310 training epochs with a cosine-decay learning rate whose initial value
is 0.0005. The optimizer used is Lamb. The SPS module divides the image into N
= 196 patches. Standard data augmentation techniques, such as random
augmentation and mixup, are also employed during training. We compare our
method with other SNN methods of similar size trained on ImageNet-1K, as shown
in Tab. 6.

Table 6: Performance on ImageNet-1K [70]. Note, “Spike", “Para", and “Step" in all Table headers of this paper denote “Spike-driven", “Parameters", and “Timestep".  Methods | Architecture |  Spike |  Param (M) |  Step | Acc.(%)
---|---|---|---|---|---
ANN2SNN | ResNet-34 [84] | ✓ | 21.8 | 250 | 61.5
VGG-16 [85] | ✓ | - | 16 | 65.1
SCNN | SEW-Res-SNN [83] | ✗ | 25.6 | 4 | 67.8
MS-Res-SNN [71] | ✓ | 21.8 | 4 | 69.4
Att-MS-Res-SNN [86] | ✗ | 22.1 | 1 | 69.2
Spiking- | Spikformer [14] | ✗ | 16.8 | 4 | 70.2
Transformer | Spike-driven Transformer [13] | ✓ | 16.8 | 4 | 72.3
SMLP | STM(Ours) | ✓ | 12.2 | 4 | 72.1

###  B.2 Stage-wise Training of the End-to-end Model

Although our model is end-to-end differentiable, directly implementing end-to-
end training can lead to unstable loss convergence. To mitigate this issue, we
divide our training process into three stages:

##### Stage 1: Perception Module Training

In the first stage, we focus on training the perception module while disabling
the prediction and planning modules. This means that the prediction module
within the network remains inactive, and the decoder does not output instance
flow information related to prediction. During this stage, we use a learning
rate of $1e-3$ and train the model for 20 epochs.

Figure 6: MS-ResNet and SEW-ResNet.

##### Stage 2: Prediction Module Training

In the second stage, we enable the prediction module, which predicts the
movement of instances on the BEV for the next three steps. We train the model
for an additional 10 epochs during this stage.

##### Stage 3: Planning Module Training

Finally, we start training the planning module, using real trajectories to
supervise the model’s planning results. In both the prediction and planning
stages, we set the learning rate to $2e-4$ to fine-tune the model from the
perception stage. Throughout all stages, we employ the Adam optimizer to
update the model parameters. By incrementally introducing the prediction and
planning modules, we ensure that each component is well-trained before
integrating them into the end-to-end framework.

##  Appendix C Experiments

###  C.1 Datasets

The nuScenes dataset [81] is a comprehensive, publicly available dataset
tailored for autonomous driving research. It encompasses 1,000 manually
selected driving scenes from Boston and Singapore—cities renowned for their
dense traffic and complex driving environments. Each scene, lasting 20
seconds, showcases a variety of driving maneuvers, traffic conditions, and
unforeseen events, reflecting the intricate dynamics of urban driving. The
dataset aims to foster the development of advanced methods that ensure safety
in densely populated urban settings, featuring dozens of objects per scene. It
includes around 1.4 million camera images, 390,000 LIDAR sweeps, 1.4 million
RADAR sweeps, and 1.4 million object-bounding boxes across 40,000 keyframes.

Data Preprocessing. In preparation for modeling, we preprocess the images by
cropping and resizing the original dimensions from $\mathbb{R}^{3\times
900\times 1600}$ to $\mathbb{R}^{3\times 224\times 480}$. Additionally, we
incorporate temporal data by including the past three frames for each
sequence, denoted as $I_{t}^{n}\in\mathbb{R}^{3\times 224\times 480}$, where
$t\in\\{1,2,3\\}$ represents the frame indices, and $n\in\\{1,\ldots,6\\}$
indexes the cameras.

###  C.2 Evaluation Metrics

In this section, we introduce the metrics used to assess the predictive
capabilities of our model for video prediction. Specifically, we utilize
Intersection over Union (IoU), Panoptic Quality (PQ), Recognition Quality
(RQ), and Segmentation Quality (SQ) as defined by Kim et al. [87].

##### Intersection over Union (IoU)

The IoU metric evaluates the overlap between the predicted and ground truth
segmentation masks. It is calculated as:

$IoU=\frac{|\text{Prediction}\cap\text{Ground
Truth}|}{|\text{Prediction}\cup\text{Ground Truth}|}$ (14)

where $|\cdot|$ denotes the number of pixels in the respective set.

##### Panoptic Quality (PQ)

Panoptic Quality (PQ) is a comprehensive metric that combines both
segmentation and recognition quality. It accounts for both true positive
matches and penalizes false positives and false negatives. PQ is defined as:

$PQ=\frac{\sum_{(p,g)\in TP}IoU(p,g)}{|TP|+\frac{1}{2}|FP|+\frac{1}{2}|FN|}$

where $TP$ represents the set of true positive matches between predicted
segments $p$ and ground truth segments $g$, $FP$ denotes false positives, and
$FN$ denotes false negatives.

##### Recognition Quality (RQ)

Recognition Quality (RQ) measures the accuracy of object recognition and
classification. It is given by:

$RQ=\frac{|TP|}{|TP|+\frac{1}{2}|FP|+\frac{1}{2}|FN|}$

##### Segmentation Quality (SQ)

Segmentation Quality (SQ) evaluates the quality of the predicted segments’
spatial accuracy. It is defined as:

$SQ=\frac{\sum_{(p,g)\in TP}IoU(p,g)}{|TP|}$

###  C.3 More Visualizations

We present three additional visual examples in Fig 7 to further showcase the
performance of our SAD model on the nuScenes dataset. These examples
demonstrate the model’s ability to generate safe and collision-free
trajectories in various driving scenarios, highlighting its effectiveness in
autonomous driving applications.

Figure 7: More Qualitative Results of the SAD Model on the nuScenes Dataset.
(a) displays six camera view inputs utilized by the model. (b) illustrates the
planning result of the ANN model, and (c) presents the planning results of our
SAD model. The comparison shows that our SAD model can achieve performance
comparable to that of the ANN model and successfully generate a safe
trajectory.

##  Appendix D Detail of Cost Function

In the method section, we briefly introduced the Cost Function $f$, a multi-
component function designed to evaluate the suitability of planned
trajectories for self-driving vehicles. We follow the cost function in ST-P3
[73], each component of the cost function addresses a specific aspect of the
trajectory planning, as detailed below:

Safety Cost. This component ensures that the planned trajectories do not
result in collisions. The model must account for the dynamic positioning of
other vehicles and road elements, avoiding overlap with the grids they occupy.
Furthermore, a safe distance must be maintained, especially at high
velocities, to prevent any potential accidents.

Cost Volume. Road environments are complex, with numerous unpredictable
elements affecting trajectory planning. It is impractical to manually
enumerate all possible scenarios and associated costs. To address this, we
utilize a learned cost volume produced by the prediction module head mentioned
earlier. To prevent the cost volume from disproportionately influencing the
trajectory evaluation, we clip its values to maintain balanced decision-
making.

Comfort and Progress. To ensure that the trajectories are not only safe but
also comfortable for passengers, this component penalizes excessive lateral
acceleration, jerk, and high curvature. Additionally, the efficiency of the
trajectory is critical; thus, paths that effectively progress towards the
target destination receive positive reinforcement.

These components collectively ensure that the cost function comprehensively
assesses both the safety and quality of the trajectories planned by the self-
driving vehicle.

##  Appendix E Theoretical Energy Consumption Calculation

In the experimental section of our paper, we utilize energy consumption as a
metric to evaluate the efficiency of various models. This appendix outlines
the methodology employed to compute the theoretical energy consumption of our
SNN architecture. The calculation process involves two main steps: first,
determining the synaptic operations (SOPs) for each architectural component,
and second, estimating the cumulative energy consumption based on these
operations.

The synaptic operations within each block of the SNN are calculated using the
following equation:

$\operatorname{SOPs}(l)=fr\times T\times\operatorname{FLOPs}(l)$ (15)

where $l$ denotes the ordinal number of the block within the SNN, $fr$
represents the firing rate of the input spike train to the block, $T$
indicates the time step of the neuron, and $\operatorname{FLOPs}(l)$ refers to
the floating-point operations within the block, primarily consisting of
multiply-and-accumulate (MAC) operations.

To compute the SNN’s theoretical energy consumption, we consider both MAC and
spike-based accumulation (AC) operations, utilizing 45 nm technology. The
energy costs are $E_{MAC}=4.6\,\text{pJ}$ for MAC operations and
$E_{AC}=0.9\,\text{pJ}$ for AC operations. Based on the methodologies outlined
in [86], we calculate the energy consumption of the SNN as follows:

$\displaystyle E_{SNN}$
$\displaystyle=E_{MAC}\times\mathrm{FLOP}_{\mathrm{SNN}_{\mathrm{Conv}}}^{1}$
(16)
$\displaystyle+E_{AC}\times\left(\sum_{n=2}^{N}\mathrm{SOP}_{\mathrm{SNN}_{\mathrm{Conv}}}^{n}+\sum_{m=1}^{M}\mathrm{SOP}_{\mathrm{SNN}_{\mathrm{FC}}}^{m}\right)$

Here, $N$ and $M$ denote the number of convolutional (Conv) and fully
connected (FC) layers, respectively. The terms
$\mathrm{FLOP}_{\mathrm{SNN}_{\mathrm{Conv}}}$ and
$\mathrm{SOP}_{\mathrm{SNN}_{\mathrm{Conv}}}$,
$\mathrm{SOP}_{\mathrm{SNN}_{\mathrm{FC}}}$ represent the FLOPs for the first
Conv layer and SOPs for the subsequent $n^{th}$ Conv and $m^{th}$ FC layers.

For the ANN model, the formula for computing the theoretical energy
consumption is more straightforward, as all neurons operate in floating point:

$E_{ANN}=E_{MAC}\times\mathrm{FLOP}_{\mathrm{ANN}}$ (17)

Here, $\mathrm{FLOP}_{\mathrm{ANN}}$ represents the FLOPs of the ANN model.