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Herein, a novel on\u2010chip training method called direct gradient calculation (DGC) is proposed to substitute conventional backpropagation (BP). In this method, the gradients of a cost function with respect to the weights are calculated directly by sequentially applying a small temporal change to each weight and then measuring the change in cost value. DGC achieves a similar accuracy to that of BP while performing a handwritten digit classification task, validating its training feasibility. In particular, DGC can be applied to analog hardware\u2010based convolutional NNs (CNNs), which is considered to be a challenging task, enabling appropriate on\u2010chip training. A hybrid method is also proposed that efficiently combines DGC and BP for training CNNs, and the method achieves a similar accuracy to that of BP and DGC while enhancing the training speed. Furthermore, networks utilizing DGC maintain a higher level of accuracy than those using BP in the presence of variations in hardware (such as synaptic device conductance and neuron circuit component variations) while requiring fewer circuit components.<\/jats:p><\/jats:sec>","DOI":"10.1002\/aisy.202100064","type":"journal-article","created":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T03:21:31Z","timestamp":1625455291000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Direct Gradient Calculation: Simple and Variation\u2010Tolerant On\u2010Chip Training Method for Neural Networks"],"prefix":"10.1002","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1157-0127","authenticated-orcid":false,"given":"Hyungyo","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering and Inter-University Semiconductor Research Center Seoul National University  1 Gwanak-ro, Gwanak-gu Seoul 08826 South Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2998-8174","authenticated-orcid":false,"given":"Joon","family":"Hwang","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering and Inter-University Semiconductor Research Center Seoul National University  1 Gwanak-ro, Gwanak-gu Seoul 08826 South Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7676-8938","authenticated-orcid":false,"given":"Dongseok","family":"Kwon","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering and Inter-University Semiconductor Research Center Seoul National University  1 Gwanak-ro, Gwanak-gu Seoul 08826 South Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4519-135X","authenticated-orcid":false,"given":"Jangsaeng","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering and Inter-University Semiconductor Research Center Seoul National University  1 Gwanak-ro, Gwanak-gu Seoul 08826 South Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1426-1944","authenticated-orcid":false,"given":"Min-Kyu","family":"Park","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering and Inter-University Semiconductor Research Center Seoul National University  1 Gwanak-ro, Gwanak-gu Seoul 08826 South Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7260-9224","authenticated-orcid":false,"given":"Jiseong","family":"Im","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering and Inter-University Semiconductor Research Center Seoul National University  1 Gwanak-ro, Gwanak-gu Seoul 08826 South Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2962-2458","authenticated-orcid":false,"given":"Byung-Gook","family":"Park","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering and Inter-University Semiconductor Research Center Seoul National University  1 Gwanak-ro, Gwanak-gu Seoul 08826 South Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3559-9802","authenticated-orcid":false,"given":"Jong-Ho","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering and Inter-University Semiconductor Research Center Seoul National University  1 Gwanak-ro, Gwanak-gu Seoul 08826 South Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,7,5]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"crossref","unstructured":"A.Krizhevsky I.Sutskever G. 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