@inproceedings{gilmer2019adversarial,
	title={Adversarial examples are a natural consequence of test error in noise},
	author={Gilmer, Justin and Ford, Nicolas and Carlini, Nicholas and Cubuk, Ekin},
	booktitle={International Conference on Machine Learning},
	pages={2280--2289},
	year={2019},
	organization={PMLR}
}
@inproceedings{cohen2019certified,
	title={Certified adversarial robustness via randomized smoothing},
	author={Cohen, Jeremy and Rosenfeld, Elan and Kolter, Zico},
	booktitle={International Conference on Machine Learning},
	pages={1310--1320},
	year={2019},
	organization={PMLR}
}

@article{yang2020closer,
	title={A closer look at accuracy vs. robustness},
	author={Yang, Yao-Yuan and Rashtchian, Cyrus and Zhang, Hongyang and Salakhutdinov, Russ R and Chaudhuri, Kamalika},
	journal={Advances in neural information processing systems},
	volume={33},
	pages={8588--8601},
	year={2020}
}
@article{bartlett2017spectrally,
  title={Spectrally-normalized margin bounds for neural networks},
  author={Bartlett, Peter L and Foster, Dylan J and Telgarsky, Matus J},
  journal={Advances in neural information processing systems},
  volume={30},
  year={2017}
}
@article{gouk2021regularisation,
  title={Regularisation of neural networks by enforcing lipschitz continuity},
  author={Gouk, Henry and Frank, Eibe and Pfahringer, Bernhard and Cree, Michael J},
  journal={Machine Learning},
  volume={110},
  number={2},
  pages={393--416},
  year={2021},
  publisher={Springer}
}
@article{keskar2016large,
  title={On large-batch training for deep learning: Generalization gap and sharp minima},
  author={Keskar, Nitish Shirish and Mudigere, Dheevatsa and Nocedal, Jorge and Smelyanskiy, Mikhail and Tang, Ping Tak Peter},
  journal={arXiv preprint arXiv:1609.04836},
  year={2016}
}

@inproceedings{nieves2021sparse,
 author = {Perez-Nieves, Nicolas and Goodman, Dan},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan},
 pages = {11795--11808},
 publisher = {Curran Associates, Inc.},
 title = {Sparse Spiking Gradient Descent},
 url = {https://proceedings.neurips.cc/paper/2021/file/61f2585b0ebcf1f532c4d1ec9a7d51aa-Paper.pdf},
 volume = {34},
 year = {2021}
}
@article{neftci2019surrogate,
  title={Surrogate gradient learning in spiking neural networks: Bringing the power of gradient-based optimization to spiking neural networks},
  author={Neftci, Emre O and Mostafa, Hesham and Zenke, Friedemann},
  journal={IEEE Signal Processing Magazine},
  volume={36},
  number={6},
  pages={51--63},
  year={2019},
  publisher={IEEE}
}
@article{orchard2015converting,
  title={Converting static image datasets to spiking neuromorphic datasets using saccades},
  author={Orchard, Garrick and Jayawant, Ajinkya and Cohen, Gregory K and Thakor, Nitish},
  journal={Frontiers in neuroscience},
  volume={9},
  pages={437},
  year={2015},
  publisher={Frontiers Media SA}
}
@article{xiao2017fashion,
  title={Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms},
  author={Xiao, Han and Rasul, Kashif and Vollgraf, Roland},
  journal={arXiv preprint arXiv:1708.07747},
  year={2017}
}
@article{cramer2020heidelberg,
  title={The heidelberg spiking data sets for the systematic evaluation of spiking neural networks},
  author={Cramer, Benjamin and Stradmann, Yannik and Schemmel, Johannes and Zenke, Friedemann},
  journal={IEEE Transactions on Neural Networks and Learning Systems},
  year={2020},
  publisher={IEEE}
}
@article{zenke2018superspike,
  title={Superspike: Supervised learning in multilayer spiking neural networks},
  author={Zenke, Friedemann and Ganguli, Surya},
  journal={Neural computation},
  volume={30},
  number={6},
  pages={1514--1541},
  year={2018},
  publisher={MIT Press One Rogers Street, Cambridge, MA 02142-1209, USA journals-info~…}
}
@article{cramer2022surrogate,
  title={Surrogate gradients for analog neuromorphic computing},
  author={Cramer, Benjamin and Billaudelle, Sebastian and Kanya, Simeon and Leibfried, Aron and Gr{\"u}bl, Andreas and Karasenko, Vitali and Pehle, Christian and Schreiber, Korbinian and Stradmann, Yannik and Weis, Johannes and others},
  journal={Proceedings of the National Academy of Sciences},
  volume={119},
  number={4},
  pages={e2109194119},
  year={2022},
  publisher={National Acad Sciences}
}
@article{eshraghian2021training,
  title={Training spiking neural networks using lessons from deep learning},
  author={Eshraghian, Jason K and Ward, Max and Neftci, Emre and Wang, Xinxin and Lenz, Gregor and Dwivedi, Girish and Bennamoun, Mohammed and Jeong, Doo Seok and Lu, Wei D},
  journal={arXiv preprint arXiv:2109.12894},
  year={2021}
}
@article{davies2018loihi,
  title={Loihi: A neuromorphic manycore processor with on-chip learning},
  author={Davies, Mike and Srinivasa, Narayan and Lin, Tsung-Han and Chinya, Gautham and Cao, Yongqiang and Choday, Sri Harsha and Dimou, Georgios and Joshi, Prasad and Imam, Nabil and Jain, Shweta and others},
  journal={Ieee Micro},
  volume={38},
  number={1},
  pages={82--99},
  year={2018},
  publisher={IEEE}
}
@inproceedings{bu2021optimal,
  title={Optimal ANN-SNN Conversion for High-accuracy and Ultra-low-latency Spiking Neural Networks},
  author={Bu, Tong and Fang, Wei and Ding, Jianhao and Dai, PengLin and Yu, Zhaofei and Huang, Tiejun},
  booktitle={International Conference on Learning Representations},
  year={2021}
}

@article{bengio2013estimating,
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  year={2013}
}

@article{cao2015spiking,
  title={Spiking deep convolutional neural networks for energy-efficient object recognition},
  author={Cao, Yongqiang and Chen, Yang and Khosla, Deepak},
  journal={International Journal of Computer Vision},
  volume={113},
  number={1},
  pages={54--66},
  year={2015},
  publisher={Springer}
}

@inproceedings{diehl2015fast,
  title={Fast-classifying, high-accuracy spiking deep networks through weight and threshold balancing},
  author={Diehl, Peter U and Neil, Daniel and Binas, Jonathan and Cook, Matthew and Liu, Shih-Chii and Pfeiffer, Michael},
  booktitle={2015 International Joint Conference on Neural Networks (IJCNN)},
  pages={1--8},
  year={2015},
  organization={ieee}
}

@INPROCEEDINGS{alawad2017stochastic,
  author={Alawad, Mohammed and Yoon, Hong-Jun and Tourassi, Georgia},
  booktitle={2017 IEEE International Conference on Big Data (Big Data)}, 
  title={Energy efficient stochastic-based deep spiking neural networks for sparse datasets}, 
  year={2017},
  volume={},
  number={},
  pages={311-318},
  doi={10.1109/BigData.2017.8257939}}



@ARTICLE{davidson2021comparison,
AUTHOR={Davidson, Simon and Furber, Steve B.},  	 
TITLE={Comparison of Artificial and Spiking Neural Networks on Digital Hardware},      	
JOURNAL={Frontiers in Neuroscience},      	
VOLUME={15},           	
YEAR={2021},      	  
URL={https://www.frontiersin.org/articles/10.3389/fnins.2021.651141},      	
DOI={10.3389/fnins.2021.651141},     	
ISSN={1662-453X},     
ABSTRACT={Despite the success of Deep Neural Networks—a type of Artificial Neural Network (ANN)—in problem domains such as image recognition and speech processing, the energy and processing demands during both training and deployment are growing at an unsustainable rate in the push for greater accuracy. There is a temptation to look for radical new approaches to these applications, and one such approach is the notion that replacing the abstract neuron used in most deep networks with a more biologically-plausible spiking neuron might lead to savings in both energy and resource cost. The most common spiking networks use rate-coded neurons for which a simple translation from a pre-trained ANN to an equivalent spike-based network (SNN) is readily achievable. But does the spike-based network offer an improvement of energy efficiency over the original deep network? In this work, we consider the digital implementations of the core steps in an ANN and the equivalent steps in a rate-coded spiking neural network. We establish a simple method of assessing the relative advantages of rate-based spike encoding over a conventional ANN model. Assuming identical underlying silicon technology we show that most rate-coded spiking network implementations will not be more energy or resource efficient than the original ANN, concluding that more imaginative uses of spikes are required to displace conventional ANNs as the dominant computing framework for neural computation.}
}

@ARTICLE{yan2022sparsereg,
AUTHOR={Yan, Yulong and Chu, Haoming and Jin, Yi and Huan, Yuxiang and Zou, Zhuo and Zheng, Lirong}, 
TITLE={Backpropagation With Sparsity Regularization for Spiking Neural Network Learning},      
JOURNAL={Frontiers in Neuroscience},      
VOLUME={16},           
YEAR={2022},      
URL={https://www.frontiersin.org/articles/10.3389/fnins.2022.760298},       
DOI={10.3389/fnins.2022.760298},      
ISSN={1662-453X},   
ABSTRACT={The spiking neural network (SNN) is a possible pathway for low-power and energy-efficient processing and computing exploiting spiking-driven and sparsity features of biological systems. This article proposes a sparsity-driven SNN learning algorithm, namely backpropagation with sparsity regularization (BPSR), aiming to achieve improved spiking and synaptic sparsity. Backpropagation incorporating spiking regularization is utilized to minimize the spiking firing rate with guaranteed accuracy. Backpropagation realizes the temporal information capture and extends to the spiking recurrent layer to support brain-like structure learning. The rewiring mechanism with synaptic regularization is suggested to further mitigate the redundancy of the network structure. Rewiring based on weight and gradient regulates the pruning and growth of synapses. Experimental results demonstrate that the network learned by BPSR has synaptic sparsity and is highly similar to the biological system. It not only balances the accuracy and firing rate, but also facilitates SNN learning by suppressing the information redundancy. We evaluate the proposed BPSR on the visual dataset MNIST, N-MNIST, and CIFAR10, and further test it on the sensor dataset MIT-BIH and gas sensor. Results bespeak that our algorithm achieves comparable or superior accuracy compared to related works, with sparse spikes and synapses.}}

@inproceedings{ba2013adaptivedrop,
 author = {Ba, Jimmy and Frey, Brendan},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {C.J. Burges and L. Bottou and M. Welling and Z. Ghahramani and K.Q. Weinberger},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Adaptive dropout for training deep neural networks},
 url = {https://proceedings.neurips.cc/paper/2013/file/7b5b23f4aadf9513306bcd59afb6e4c9-Paper.pdf},
 volume = {26},
 year = {2013}
}

@inproceedings{blanc2018adaptivesoftmax,
  author    = {Guy Blanc and
               Steffen Rendle},
  editor    = {Jennifer G. Dy and
               Andreas Krause},
  title     = {Adaptive Sampled Softmax with Kernel Based Sampling},
  booktitle = {Proceedings of the 35th International Conference on Machine Learning,
               {ICML} 2018, Stockholmsm{\"{a}}ssan, Stockholm, Sweden, July
               10-15, 2018},
  series    = {Proceedings of Machine Learning Research},
  volume    = {80},
  pages     = {589--598},
  publisher = {{PMLR}},
  year      = {2018},
  url       = {http://proceedings.mlr.press/v80/blanc18a.html},
  timestamp = {Wed, 03 Apr 2019 18:17:30 +0200},
  biburl    = {https://dblp.org/rec/conf/icml/BlancR18.bib},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}

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  title={Unsupervised learning of digit recognition using spike-timing-dependent plasticity},
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  journal={Frontiers in computational neuroscience},
  volume={9},
  pages={99},
  year={2015},
  publisher={Frontiers Media SA}
}
@inproceedings{kim2020spiking,
  title={Spiking-yolo: spiking neural network for energy-efficient object detection},
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  booktitle={Proceedings of the AAAI conference on artificial intelligence},
  volume={34},
  pages={11270--11277},
  year={2020}
}
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  title={Deep learning with spiking neurons: opportunities and challenges},
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  journal={Frontiers in neuroscience},
  pages={774},
  year={2018},
  publisher={Frontiers}
}
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  journal={Advances in neural information processing systems},
  volume={31},
  year={2018}
}
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  title={A theoretical and empirical comparison of gradient approximations in derivative-free optimization},
  author={Berahas, Albert S and Cao, Liyuan and Choromanski, Krzysztof and Scheinberg, Katya},
  journal={Foundations of Computational Mathematics},
  volume={22},
  number={2},
  pages={507--560},
  year={2022},
  publisher={Springer}
}
@inproceedings{li2021rethinking,
 author = {Li, Yuhang and Guo, Yufei and Zhang, Shanghang and Deng, Shikuang and Hai, Yongqing and Gu, Shi},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {M. Ranzato and A. Beygelzimer and Y. Dauphin and P.S. Liang and J. Wortman Vaughan},
 pages = {23426--23439},
 publisher = {Curran Associates, Inc.},
 title = {Differentiable Spike: Rethinking Gradient-Descent for Training Spiking Neural Networks},
 url = {https://proceedings.neurips.cc/paper_files/paper/2021/file/c4ca4238a0b923820dcc509a6f75849b-Paper.pdf},
 volume = {34},
 year = {2021}
}

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}
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  title={A primer on zeroth-order optimization in signal processing and machine learning: Principals, recent advances, and applications},
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  year={2020},
  publisher={IEEE}
}
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@article{zhang2020temporal,
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  volume={33},
  pages={12022--12033},
  year={2020}
}
@article{rathi2020enabling,
  title={Enabling deep spiking neural networks with hybrid conversion and spike timing dependent backpropagation},
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  year={2020}
}
@article{rathi2020diet,
  title={Diet-snn: Direct input encoding with leakage and threshold optimization in deep spiking neural networks},
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  year={2020}
}
@article{deng2022temporal,
  title={Temporal efficient training of spiking neural network via gradient re-weighting},
  author={Deng, Shikuang and Li, Yuhang and Zhang, Shanghang and Gu, Shi},
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  year={2022}
}
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  title={Liaf-net: Leaky integrate and analog fire network for lightweight and efficient spatiotemporal information processing},
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  journal={IEEE Transactions on Neural Networks and Learning Systems},
  volume={33},
  number={11},
  pages={6249--6262},
  year={2021},
  publisher={IEEE}
}
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  title={Efficient processing of spatio-temporal data streams with spiking neural networks},
  author={Kugele, Alexander and Pfeil, Thomas and Pfeiffer, Michael and Chicca, Elisabetta},
  journal={Frontiers in Neuroscience},
  volume={14},
  pages={439},
  year={2020},
  publisher={Frontiers Media SA}
}
@article{fang2021deep,
  title={Deep residual learning in spiking neural networks},
  author={Fang, Wei and Yu, Zhaofei and Chen, Yanqi and Huang, Tiejun and Masquelier, Timoth{\'e}e and Tian, Yonghong},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={21056--21069},
  year={2021}
}
@article{sengupta2019going,
  title={Going deeper in spiking neural networks: VGG and residual architectures},
  author={Sengupta, Abhronil and Ye, Yuting and Wang, Robert and Liu, Chiao and Roy, Kaushik},
  journal={Frontiers in neuroscience},
  volume={13},
  pages={95},
  year={2019},
  publisher={Frontiers Media SA}
}
@article{wu2018spatio,
  title={Spatio-temporal backpropagation for training high-performance spiking neural networks},
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  journal={Frontiers in neuroscience},
  volume={12},
  pages={331},
  year={2018},
  publisher={Frontiers Media SA}
}
@inproceedings{zheng2021going,
  title={Going deeper with directly-trained larger spiking neural networks},
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  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={35},
  pages={11062--11070},
  year={2021}
}
@inproceedings{wu2019direct,
  title={Direct training for spiking neural networks: Faster, larger, better},
  author={Wu, Yujie and Deng, Lei and Li, Guoqi and Zhu, Jun and Xie, Yuan and Shi, Luping},
  booktitle={Proceedings of the AAAI conference on artificial intelligence},
  volume={33},
  pages={1311--1318},
  year={2019}
}
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  publisher={Frontiers Media SA}
}
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  year={2022}
}
@misc{spconv2022,
    title={Spconv: Spatially Sparse Convolution Library},
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    howpublished = {\url{https://github.com/traveller59/spconv}},
    year={2022}
}
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@inproceedings{gehrig2019end,
  title={End-to-end learning of representations for asynchronous event-based data},
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  year={2019}
}
@inproceedings{schaefer2022aegnn,
  title={Aegnn: Asynchronous event-based graph neural networks},
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  pages={12371--12381},
  year={2022}
}
@inproceedings{zhou2022spikformer,
  title={Spikformer: When Spiking Neural Network Meets Transformer},
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  booktitle={The Eleventh International Conference on Learning Representations},
  year={2022}
}
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  year={2018}
}
@article{kim2023sharing,
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}
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}