Energy-efficient End-to-End Communication System with Spiking Neural Networks

Energy-efficient End-to-End Communication System with Spiking Neural Networks Pooja Plavilayil Anil∗ , Te-Chuan Chiu† , and Nguyen Van Huynh∗ ∗ School of Computer Science and Informatics, University of Liverpool, UK

I. I NTRODUCTION The evolution towards 6G is expected to enable several emerging data-intensive applications, thus imposing stringent requirements for latency and data rates [1]. 6G aims to employ higher-dimensional multiple-input multiple-output (MIMO) systems to meet these performance requirements [2]. A conventional MIMO system consists of several signal processing blocks, as illustrated in Fig. 1. However, optimising individual blocks separately may limit overall system performance. To address this, end-to-end (E2E) learning [3] uses learned transmitter and receiver, as illustrated in Fig. 1, enabling joint optimisation under a common communication objective [4]. For example, [5] demonstrates joint training of neural transmitters and receivers using reward feedback without prior channel knowledge, achieving better performance than the evaluated alternatives. The feasibility of practical implementation of real-time artificial neural network (ANN) based E2E receiver processing is also demonstrated in [6], where a standard-compliant 5G New Radio (NR) neural receiver achieves inference latency below 1 ms.

Transmitter

Receiver H

s

Modulation

Precoding

𝑁

…

Abstract—2030 is expected to witness the first commercial 6G systems. However, traditional modular communication architectures cannot meet the latency, optimisation, and integration requirements demanded by various sub-millisecond, data-intensive emerging 6G applications. End-to-end (E2E) communication addresses these limitations by replacing traditional processing blocks with neural networks. Nevertheless, conventional artificial neural networks (ANNs) in E2E systems use dense computation. This results in substantial energy consumption and computational resource requirements, which may not be feasible in resource constrained devices. This paper addresses the aforementioned challenge by developing a spiking neural network (SNN) encoder that targets lower encoder inference energy while maintaining communication reliability. In particular, the SNN encoder combines sparse spike activity, sinusoidal temporal modulation, and weighted temporal aggregation to map one-hot encoded messages to distinguishable transmit signals. The model is evaluated across antenna configurations and SNN timesteps to investigate the bit error rate (BER)-energy trade-off. The simulation results show that the SNN encoder achieves comparable BER under suitable timestep selections, while reducing the average estimated encoder energy by 68.93%, 52.20%, and 35.69% for SNN timesteps 2, 3, and 4, respectively, across five antenna configurations. These findings highlight the potential of the proposed SNN encoder for energy-efficient E2E communication systems. Index Terms—End-to-end communication, AI-native networks, spiking neural networks, neuromorphic communication, and sustainable 6G.

…

arXiv:2611.05550v1 [cs.NI] 3 Nov 2026

† Department of Computer Science, National Tsing Hua University, Taiwan

𝑁

Decoding Channel Estimation

Demodulation

MIMO Channel Layer

s

Transmitter

End-to-End MIMO

𝑠̂

𝑠̂

Receiver

System

Fig. 1. End-to-end MIMO communication. Individual blocks in the traditional communication system are replaced by neural networks at the transmitter and receiver, which are jointly trained.

Along with latency and detection performance, the energy per inference is also an important consideration in E2E communication, as larger MIMO configurations can increase neural computation and memory access costs. Specifically, conventional dense ANNs perform multiply-and-accumulate (MAC) operations across their connections, thus increasing energy consumption. This motivates the investigation of an energy-efficient alternative neural network for the E2E communication system. In this context, spiking neural networks (SNNs) represent and process information using discrete events called spikes, where the information is encoded through spike timing and firing rates. As spike activity is typically sparse and spike triggered synaptic computations use accumulate (AC) operations rather than MAC, SNNs can offer potential energy-efficiency advantages [7]. Several studies have investigated SNNs for communication systems, especially at the receiver, demonstrating promising error rate performance and energy savings. The hybrid SNN transformer receiver in [8] achieves performance close to that of a receiver with perfect channel state information (CSI). The hybrid ANN–SNN receiver in [9] jointly performs channel estimation, equalisation, and demapping, achieving performance comparable to ANN-based receivers while consuming less energy. Beyond simulation, [10] demonstrates the detection of MIMO-OFDM symbols using a model implemented on Loihi. The results show lower energy per sample while maintaining an accuracy comparable to the evaluated deep neural network

II. E ND - TO -E ND MIMO C OMMUNICATION M ODEL Let M = {m1 , m2 , . . . , mM } denote the set of M possible messages, and S = s1 , s2 , . . . , sM denote the corresponding set of one-hot encoded vectors. In an E2E MIMO system, the transmitter DNN maps a message to a complex transmit signal matrix according to the mapping, fθt : S → CNt ×T , where θt represents the encoder parameters, Nt is the number of transmitter antennas and T denotes the number of channel uses. The encoded transmitter signal, Xk ∈ CNt ×T , can then be expressed as: Xk = fθt (sk ). (1) At the receiver, the DNN decoder produces message logits as: zk = fθr (Yk , Ĥk ), (2) where zk ∈ RM contains the logits corresponding to M possible messages, Yk ∈ CNr ×T is the received signal matrix corresponding to the transmitted message mk , and Ĥk ∈ CNr ×Nt is the estimated channel matrix available at the receiver. The detected message, m̂k , is then obtained as: m̂k = mîk ,

îk = arg max zk,i .

(3)

i∈{1,...,M }

III. P ROPOSED F RAMEWORK The framework of the proposed model is illustrated in Fig. 2. The channel is modelled as an independent and identically distributed (i.i.d.) Rayleigh fading channel with

Transmitter

Receiver Pilot transmission and channel estimation

LS Estimator

Channel + AWGN

Message

One-hot encoding NN Encoder Power normalization

Received signal

Orthogonal Pilot Symbols

Transmitted signal

(DNN) models. In addition to receiver processing, jointly trained SNN encoders and decoders are developed for remote classification of sensor information and remote inference using semantic communications in [11] and [12], respectively. While the neuromorphic receiver investigates detection and receiver processing, the cited E2E neuromorphic models study task-oriented inference. Their objectives hence differ from transmitter side encoding for reliable message recovery. This motivates investigating whether an SNN encoder can maintain BER comparable to an ANN encoder, while reducing the encoder energy. However, this requires introducing temporal structure into non-temporal one-hot encoded messages. In addition, spike outputs need to be converted into continuous valued transmit signals, while reducing spike activity and retaining distinguishable message representations. To address these critical challenges, the proposed SNN encoder uses sinusoidal temporal modulation, weighted temporal aggregation, and spike penalty. Temporal modulation introduces timedependent currents, weighted temporal aggregation combines outputs across timesteps to form continuous-valued transmit signals, and the spike penalty encourages sparse spike activity. Experiments across different SNN timesteps and antenna configurations demonstrate the trade-off between BER and the estimated encoder inference energy. The results show that, with appropriate timestep selection for each antenna configuration, the proposed encoder achieves BER comparable to or lower than the conventional ANN encoder while consuming less estimated encoder inference energy.

Estimated Channel

NN Decoder

Decoded Message

Fig. 2. Proposed system model. Orthogonal pilots enable LS channel estimation. The encoder maps one-hot messages to power-normalised transmit signals, and the decoder recovers the messages using the received signals and estimated channel.

additive white Gaussian noise (AWGN). As the channel is not known in advance, it is estimated at the receiver using orthogonal pilot signals. If H is the channel matrix, Xp is the transmitted pilot signal, and N is the AWGN, then the received pilot signal is Yp = HXp +N. The channel is estimated using the least squares (LS) method [13] and the estimated channel Ĥ is given by: H −1 . Ĥ = Yp XH p (Xp Xp )

(4)

As shown in Fig. 2, the encoder output is normalised to satisfy the transmitter energy constraint as follows: x̄k xk = q , (5) 2 1 ∥ x̄ ∥ + ϵ k 2 Nt D where x̄k denotes the unnormalised encoder output, D is the dimension of the encoder output, and ϵ = 10−8 is a small constant introduced for numerical stability. For the study, ANN-based and SNN-based encoders are developed. In both cases, decoding is performed using the same ANN decoder architecture. The ANN encoder contains two fully connected layers with 256 and 64 nodes, respectively, each followed by a normalisation layer and ReLU activation function. The output layer has 2Nt T nodes and produces the transmit signal. The input of the shared ANN decoder consists of flattened received signal y ∈ R2Nr T concatenated with the estimated CSI, Ĥ ∈ R2Nr Nt . The decoder contains three fully connected hidden layers with 128, 64, and 32 nodes, followed by layer normalisation and GeLU activation function. The output layer has M nodes, which produce logits, z ∈ RB×M , where B is the batch size. A. Proposed SNN Transmitter For a fair comparison, the SNN and ANN encoders share the same input and network depth. Spiking neurons integrate input currents through membrane potential dynamics [14], and emit

Encoded output

Layer Norm 3

Weighted Temporal Aggregation

LIF 3

Output FC 3

LIF 2

Layer Norm 2

FC 2

LIF 1

Layer Norm 1

Sinusoidal temporal modulation

Input FC 1

One-hot encoded message

Processed over 𝑇 time steps

Fig. 3. SNN encoder architecture. A dense input projection and sinusoidal temporal modulation precede fully connected and LIF layers processed over Ts timesteps, followed by weighted temporal aggregation.

spikes upon reaching a threshold [15]. As shown in Fig. 3, the one-hot encoded message is passed through the input layer and 𝑆 [𝑡] then through the first hidden layer, which is a fully connected layer (FC1) with 256 neurons. This maps the one-hot input to a static 256 dimensional representation. As this representation is time-invariant, a sinusoidal temporal modulation is applied to introduce temporal variability as in (6).    2πt c[t] = 1 + µ sin Ts − 1 (6) × (W1 sk + b1 ) , t = 0, . . . , Ts − 1, where c[t] is the input current at time step t, Ts is the number of SNN time steps, and µ, empirically chosen as 0.8, controls the modulation amplitude. W1 sk +b1 is the static FC1 output. The resulting time-varying representation passes through normalisation and leaky integrate-and-fire (LIF) neurons [16]. This is followed by fully connected layers of 64 and 2Nt T neurons, with normalisation and LIF processing. All these layers are processed over Ts timesteps. The output layer membrane potentials, v[t], are aggregated over Ts so that the later timesteps receive larger weights than the earlier ones, as below: x=

Ts X

t

wt v[t],

where wt = PTs −1 . τ =0 τ

t=1

(7)

The aggregated output is then passed through the final normalisation layer. During backpropagation, the SuperSpike surrogate gradient [17] approximates the derivative of the spike generation function, with α = 100 controlling its sharpness around the firing threshold. B. Problem Formulation The transmitter and receiver are jointly trained with the objective of minimising the expected cross-entropy loss, expressed as: "Z   LCE (θt , θr ) = Emk ,Hk ℓ fθr (Yk , Ĥk ), mk 



#

× p Yk | fθt (sk ), Hk dYk ,

(8)

Layer Normalization

𝑆 [𝑡]

Input layer

where ℓ(·) denotes the cross-entropy loss for an individual dimension: M prediction, Hk is the actual MIMO channel matrix, and p(Yk | fθt (sk ), Hk ) is the conditional received signal distribution. The integral averages over received signal randomness, while the outer expectation averages over messages and channel realisations. The training objective is then to find the transmitter and receiver parameters that minimise this expected loss. For the ANN-based encoder, the total loss is given by LANN = LCE . For the SNN-based encoder, two additional regularisation terms are introduced to encourage sparse spikes and discourage a non-zero mean in the power normalised transmitter output. The total SNN objective becomes: LSNN = LCE + λsp Lsp + λmean Lmean ,

(9)

where λsp is the spike penalty coefficient and λmean is the mean output penalty coefficient. Through trial and error, λsp is empirically chosen as 10−4 and λmean as 5 × 10−4 . Lsp is the spike penalty, calculated as the mean spike activity over the SNN timesteps and LIF layers, given as: Lsp =

Ts −1 X 3 1 X āℓ [t], Ts t=0

(10)

ℓ=1

where āℓ [t] denotes the mean spike activity of the LIF layer ℓ at the SNN timestep t. Lmean penalises the batch averaged squared mean of each sample’s transmitter output, encouraging zero-mean transmit signals. !2 B D 1 X 1 X Lmean = xb,d , (11) B D b=1

d=1

where B is the batch size, xb,d is the power normalised transmitter output and D = 2Nt T . IV. E NCODER E NERGY C ONSUMPTION M ODEL For the study, energy per inference is calculated, which is the estimated energy needed to encode one message into a transmit signal. It consists of the computational energy (Ecomp ) and the energy for memory access (Ememory ) [18]. The energy model uses the estimates reported in [19], derived from post layout analysis for SpiNNaker2 development in 22FDX technology. The paper reports the energy for one

TABLE I S IMULATION AND M ODEL PARAMETERS Parameter Message classes, M Antenna configurations, Nt × Nr Channel uses, T Channel model Channel estimation Training SNR Evaluation SNR Training epochs Batch size Training samples Validation samples Test samples/SNR ANN encoder SNN encoder SNN Timesteps −1 −1 , τsyn SNN τmem SNN threshold, Vth Decoder Encoder learning rate Decoder learning rate

Value 16 1 × 1, 2 × 2, 4 × 4, 8 × 8, 16 × 16 2 i.i.d. Rayleigh fading + AWGN LS 6 + ∆ dB, ∆ ∼ U (−1, 1) 0–12 dB 4000 512 2.048 × 106 1.024 × 106 1.024 × 108 256–64 256–64 Ts = 2, 3, 4 100, 200 0.3 128–64–32 5 × 10−4 7 × 10−4

MAC operation (EMAC ) as 293 fJ and the energy per read access from a 2K-word static random-access memory (SRAM) (ESRAM,read ) as 296 fJ. The authors assume that the SRAM write back energy (ESRAM,write ) is approximately the same as the read cost and the energy per accumulation operation (EAC ) is one-fifth of the MAC energy cost. The ANN encoder energy is estimated from its MAC operations and associated memory accesses. Let the number of MAC operations be denoted by NMAC , input dimension be M , hidden-layer sizes be N1 , N2 , and output dimension be Nout , then the NMAC is calculated as: (12)

where Nout = 2Nt T . Based on [19], each dense connection update energy is modelled as EANN,op = Eread + Eread + EMAC + Ewrite . Hence the ANN energy per inference EANN becomes: EANN = NMAC × EANN,op . (13) B. SNN Encoder Energy The SNN encoder contains a dense input projection layer followed by spike driven synaptic computation and timedependent LIF neuron updates. The estimated energy comprises of these three energy contributions. The first SNN layer has a fully connected dense layer before temporal modulation, giving the number of MAC operations in the layer as NMAC,in = M N1 . The energy for the layer is: Ein = NMAC,in EANN,op .

Esyn = Nsyn Esyn,event .

(15)

The author derives the LIF update energy in [18] as Elif,upd = 2EAC + 2EMAC . Let NLIF be the total number of LIF neurons in all layers of the SNN encoder, then NLIF = N1 + N2 + Nout . Hence, the energy used for LIF update ELIF is: ELIF = NLIF Ts Elif,upd .

(16)

Therefore, the total SNN encoder energy per inference ESNN is: ESNN = Ein + Esyn + ELIF . (17) The energy evaluation therefore represents analytical energy estimates under adopted hardware assumptions rather than direct measurements on neuromorphic hardware. For the estimate, additional SRAM accesses for LIF time-step state updates, bias additions, normalisation, temporal modulation and aggregation, and spike generation costs are omitted. These exclusions motivate hardware measurements to assess actual energy consumption. V. S IMULATION R ESULTS

A. ANN Encoder Energy

NMAC = M N1 + N1 N2 + N2 Nout ,

the average number of synaptic events per inference, S1 and S2 be the mean spike counts per inference in LIF layer 1 and LIF layer 2, respectively, across all Ts time steps. Then, Nsyn = S1 N2 + S2 Nout . Hence, the total synaptic energy per inference, (Esyn ) is:

(14)

In the subsequent layers, the sparse spikes generated by the LIF neurons drive the synaptic operations and associated memory accesses, enabling AC operations. The energy needed for each synaptic event (Esyn,event ) can be written as Esyn,event = 2Eread + EAC + Ewrite [19]. Let Nsyn be

In this section, we compare the BER and the estimated encoder energy per inference of the proposed SNN-based model against an ANN reference baseline proposed in [3]. Both systems have the same depth and employ the same decoder and are evaluated under the same channel conditions. The simulations use Rayleigh fading with AWGN, LS channel estimation and no CSI available at the transmitter. The simulation and training settings are summarised in Table I. The experiments are conducted across 1×1, 2×2, 4×4, 8×8, and 16 × 16 antenna configurations and Ts = 2, 3, 4 to examine the BER-energy trade-off in different antenna regimes. A. BER Performance The BER performance of the proposed SNN model and its ANN counterpart across MIMO configurations and timesteps is shown in Fig. 4. Across all evaluated configurations, the BER decreases consistently with increasing SNR. In 1 × 1, the SNN achieves a BER close to that of the ANN in all evaluated timesteps. The nearly overlapping curves for Ts = 2, 3, 4 suggest that the limited improvement in BER with additional timesteps may be attributed to the lower dimensionality of the transmitted signal. In 2 × 2 and 4 × 4, the ANN has a slightly lower BER than the SNN, across all evaluated SNR range, with only minor improvements with increase in timesteps. Spike activity regularisation in the SNN may constrain the transmit signal representation, whereas the ANN is not subject to this constraint. For 8 × 8, Ts = 3, 4 achieve similar BER while outperforming the ANN, whereas Ts = 2 causes considerable

SNN Ts=2

ANN 0.4

SNN Ts=3

SNN Ts=4

SNN Ts=4

0.1

0.02

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0.1

0.01 0.005 0.002

0.05 0

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6 SNR(dB)

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SNN Ts=3

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0.0002 0.0001 0.00005 0.00002 10-5 0

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(e) 16 × 16 Fig. 4. BER comparison of ANN and SNN encoders across SNN timesteps and MIMO antenna configurations.

degradation. The increased spatial dimensionality in the larger antenna configuration and additional temporal integration in higher timesteps may enable the SNN to construct a more favourable arrangement of message representations. In 16×16, although Ts = 2, 3 increases the BER considerably, the SNN achieves lower BER for Ts = 4. This suggests that the additional temporal processing may help the SNN to exploit larger transmit signal dimensions effectively. Overall, these results strongly indicate that the timesteps required to maintain comparable BER depends on the antenna configuration. B. Encoder Energy Comparison The estimated encoder energy per inference of the ANN and SNN transmitters across antenna dimensions and timesteps is compared in Fig. 5. Across all five antenna configurations, the

SNN encoder consumes less energy than its ANN counterpart, with average reductions of 68.93%, 52.20%, and 35.69% for Ts = 2, 3, 4, respectively. Also, the SNN energy increases with Ts , as additional timesteps involve further synaptic and LIF operations. In 1 × 1, Ts = 2 provides the lowest energy with minor BER difference compared to the higher timesteps. In 8 × 8, Ts = 3 provides a favourable trade-off between energy and BER, as it achieves BER comparable to Ts = 4 with lower estimated energy. For 16 × 16, reducing Ts saves energy but considerably worsens BER, with Ts = 4 retaining both lower BER and lower estimated encoder energy than the ANN. Consequently, the timestep must be selected according to the antenna configuration to preserve BER performance while reducing energy consumption. It is worth noting that energy accounting only covers encoder inference, excluding training,

Estimated encoder energy per inference (nJ)

ANN total

SNN input projection

SNN synaptic

SNN LIF updates

30 25 20 15 10

Ts =2

Ts =3

Ts =4

Ts =4 Ts =2

Ts =3

Ts =3

Ts =4

Ts =2

Ts =3 Ts =2

Ts =4

Ts =4

Ts =3 Ts =2

5 0

1#1

2#2

4#4

8#8

16#16

MIMO antenna configuration

Fig. 5. Analytical encoder energy per inference for ANN and SNN across five MIMO antenna configurations, with SNN energy decomposed into dense input projection (FC1), spike-driven synaptic operations, and LIF neuron updates.

decoder processing, and channel estimation. The findings are limited to the evaluated SNR range, CSI assumptions, antenna configurations, and training methods. C ONCLUSION The study investigated the ability of SNN encoders to reduce encoder processing energy while maintaining reliable message recovery. The model uses sinusoidal temporal modulation to represent static messages through time-dependent currents, as well as weighted temporal aggregation to produce continuous valued transmit signals. Across the evaluated antenna configurations, the SNN achieves BER comparable to or lower than its ANN counterpart, while consuming less estimated encoder inference energy. Fewer timesteps lead to greater energy savings, however, the results point to timestep selection as a significant model choice for balancing communication reliability and encoder energy consumption in SNN-based transmitters. Future work will investigate receiver loss feedback for nondifferentiable channels, learned pilots, CSI compression and its availability at the transmitter. Further directions include developing spiking decoders and CSI compressors, investigating realistic channel models, neuromorphic hardware energy validation, and extending energy accounting to the decoder, CSI compressor, and channel estimator. R EFERENCES [1] M. Z. Chowdhury, M. Shahjalal, S. Ahmed, and Y. Jang, “6g wireless communication systems: Applications, requirements, technologies, challenges, and research directions,” IEEE Open Journal of the Communications Society, vol. 1, pp. 957–975, 2019. [2] Y. Huo et al., “Technology trends for massive mimo towards 6g,” Sensors, vol. 23, no. 13, p. 6062, 2023. [3] T. O’Shea and J. Hoydis, “An introduction to deep learning for the physical layer,” IEEE Transactions on Cognitive Communications and Networking, vol. 3, pp. 563–575, 2017. [4] M. Chafii, L. Bariah, S. Muhaidat, and M. Debbah, “Twelve scientific challenges for 6g: Rethinking the foundations of communications theory,” IEEE Communications Surveys & Tutorials, vol. 25, no. 2, pp. 868–904, 2023. [5] B. Zhang, N. Van Huynh, D. Thai Hoang, D. N. Nguyen, and Q.-V. Pham, “Ddpg-e2e: A novel policy gradient approach for end-to-end communication systems,” IEEE Transactions on Cognitive Communications and Networking, vol. 11, no. 3, pp. 1738–1751, 2025.

[6] R. Wiesmayr, S. Cammerer, F. A. Aoudia, J. Hoydis, J. Zakrzewski, and A. Keller, “Design of a standard-compliant real-time neural receiver for 5g nr,” in 2025 IEEE International Conference on Machine Learning for Communication and Networking (ICMLCN), 2025, pp. 1–6. [7] M. Davies, A. Wild, G. Orchard, Y. Sandamirskaya, G. A. F. Guerra, P. Joshi, P. Plank, and S. R. Risbud, “Advancing neuromorphic computing with loihi: A survey of results and outlook,” Proceedings of the IEEE, vol. 109, no. 5, pp. 911–934, 2021. [8] R. M A N S, V. S. T, T. Hegde, and H. P. S V, “Spiketimerx - a divide-attention based snn-transformer neural receiver for multi-carrier communication,” in 2025 IEEE Future Networks World Forum (FNWF), 2025, pp. 1–6. [9] A. Gupta, O. Dizdar, Y. Chen, F. Emre Kadan, A. Sattarzadeh, and S. Wang, “Neuromorphicrx: From neural to spiking receiver,” IEEE Transactions on Wireless Communications, vol. 25, pp. 10 161–10 174, 2026. [10] S. Liu, Y. Liang, and Y. Yi, “Dnn-snn co-learning for sustainable symbol detection in 5g systems on loihi chip,” IEEE Transactions on Sustainable Computing, vol. 9, no. 2, pp. 170–181, 2024. [11] N. Skatchkovsky, H. Jang, and O. Simeone, “End-to-end learning of neuromorphic wireless systems for low-power edge artificial intelligence,” in 2020 54th Asilomar Conference on Signals, Systems, and Computers, 2020, pp. 166–173. [12] J. Chen, N. Skatchkovsky, and O. Simeone, “Neuromorphic wireless cognition: Event-driven semantic communications for remote inference,” IEEE Transactions on Cognitive Communications and Networking, vol. 9, no. 2, pp. 252–265, 2023. [13] S. M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory. Prentice Hall, 1993. [14] W. Gerstner, W. M. Kistler, R. Naud, and L. Paninski, Neuronal Dynamics: From Single Neurons to Networks and Models of Cognition. Cambridge University Press, 2014. [15] K. Yamazaki, V.-K. Vo-Ho, D. Bulsara, and N. T. H. Le, “Spiking neural networks and their applications: A review,” Brain Sciences, vol. 12, 2022. [16] J.-Q. Yang, R. Wang, Z.-P. Wang, Q.-Y. Ma, J.-Y. Mao, Y. Ren, X. Yang, Y. Zhou, and S. Han, “Leaky integrate-and-fire neurons based on perovskite memristor for spiking neural networks,” Nano Energy, vol. 74, p. 104828, 2020. [17] F. Zenke and S. Ganguli, “Superspike: Supervised learning in multilayer spiking neural networks,” Neural Computation, vol. 30, pp. 1514 – 1541, 2017. [18] P. Lunghi, S. Silvestrini, D. Dold, G. Meoni, A. Hadjiivanov, and D. Izzo, “Energy efficiency analysis of spiking neural networks for space applications,” Astrodynamics, vol. 9, no. 6, p. 909–932, Oct. 2025. [19] S. Davidson and S. B. Furber, “Comparison of artificial and spiking neural networks on digital hardware,” Frontiers in Neuroscience, vol. 15, 2021.

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