It　is　well-known　that　second-order　optimizer　can　accelerate　the　training　of　deep　neural　networks,　however,　the　huge　computation　cost　of　second-order　optimization　makes　it　impractical　to　apply　in　real　practice.　In　order　to　reduce　the　cost,　many　methods　have　been　proposed　to　approximate　a　second-order　matrix.　Inspired　by　KFAC,　we　propose　a　novel　Trace-based　Hardware-driven　layer-ORiented　Natural　Gradient　Descent　Computation　method,　called　THOR,　to　make　the　second-order　optimization　applicable　in　the　real　application　models.　Specifically,　we　gradually　increase　the　update　interval　and　use　the　matrix　trace　to　determine　which　blocks　of　Fisher　Information　Matrix　(FIM)　need　to　be　updated.　Moreover,　by　resorting　the　power　of　hardware,　we　have　designed　a　hardware-driven　approximation　method　for　computing　FIM　to　achieve　better　performance.　To　demonstrate　the　effectiveness　of　THOR,　we　have　conducted　extensive　experiments.　The　results　show　that　training　ResNet-50　on　ImageNet　with　THOR　only　takes　66.7　minutes　to　achieve　a　top-1　accuracy　of　75.9　%　under　an　8　Ascend　910　environment　with　MindSpore,　a　new　deep　learning　computing　framework.　Moreover,　with　more　computational　resources,　THOR　can　only　takes　2.7　minutes　to　75.9　%　with　256　Ascend　910.　Copyright　©　2021,　Association　for　the　Advancement　of　Artificial　Intelligence　(www.aaai.org).　All　rights　reserved