{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T22:34:50Z","timestamp":1769639690022,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,16]],"date-time":"2022-09-16T00:00:00Z","timestamp":1663286400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China Youth Fund","award":["62004146"],"award-info":[{"award-number":["62004146"]}]},{"name":"National Natural Science Foundation of China Youth Fund","award":["2021M692498"],"award-info":[{"award-number":["2021M692498"]}]},{"name":"National Natural Science Foundation of China Youth Fund","award":["2021A1515012293"],"award-info":[{"award-number":["2021A1515012293"]}]},{"name":"China Postdoctoral Science Foundation funded project","award":["62004146"],"award-info":[{"award-number":["62004146"]}]},{"name":"China Postdoctoral Science Foundation funded project","award":["2021M692498"],"award-info":[{"award-number":["2021M692498"]}]},{"name":"China Postdoctoral Science Foundation funded project","award":["2021A1515012293"],"award-info":[{"award-number":["2021A1515012293"]}]},{"name":"Natural Science Foundation of Guangdong, China","award":["62004146"],"award-info":[{"award-number":["62004146"]}]},{"name":"Natural Science Foundation of Guangdong, China","award":["2021M692498"],"award-info":[{"award-number":["2021M692498"]}]},{"name":"Natural Science Foundation of Guangdong, China","award":["2021A1515012293"],"award-info":[{"award-number":["2021A1515012293"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Spiking neural networks (SNNs) can utilize spatio-temporal information and have the characteristic of energy efficiency, being a good alternative to deep neural networks (DNNs). The event-driven information processing means that SNNs can reduce the expensive computation of DNNs and save a great deal of energy consumption. However, high training and inference latency is a limitation of the development of deeper SNNs. SNNs usually need tens or even hundreds of time steps during the training and inference process, which causes not only an increase in latency but also excessive energy consumption. To overcome this problem, we propose a novel training method based on backpropagation (BP) for ultra-low-latency (1\u20132 time steps) SNNs with multi-threshold. In order to increase the information capacity of each spike, we introduce the multi-threshold Leaky Integrate and Fired (LIF) model. The experimental results show that our proposed method achieves average accuracy of 99.56%, 93.08%, and 87.90% on MNIST, FashionMNIST, and CIFAR10, respectively, with only two time steps. For the CIFAR10 dataset, our proposed method achieves 1.12% accuracy improvement over the previously reported directly trained SNNs with fewer time steps.<\/jats:p>","DOI":"10.3390\/sym14091933","type":"journal-article","created":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T04:28:55Z","timestamp":1663648135000},"page":"1933","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Direct Training via Backpropagation for Ultra-Low-Latency Spiking Neural Networks with Multi-Threshold"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3827-8820","authenticated-orcid":false,"given":"Changqing","family":"Xu","sequence":"first","affiliation":[{"name":"Guangzhou Institute of Technology, Xidian University, Xi\u2019an 710071, China"},{"name":"School of Microelectronics, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Yi","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Microelectronics, Xidian University, Xi\u2019an 710071, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5065-4374","authenticated-orcid":false,"given":"Dongdong","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Microelectronics, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Yintang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Microelectronics, Xidian University, Xi\u2019an 710071, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gerstner, W., and Kistler, W.M. 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