ZIQISHINIANDAIYILAI，RENLIANSHIBIEYIJINGCHENGWEILEJISUANJISHIJUEHESHENGWUSHIBIELINGYUBEIYANJIUZUIDUODEZHUTIZHIYI。JIYURENGONGSHEJIDETEZHENGHECHUANTONGJIQIXUEXIJISHUDECHUANTONGFANGFAJINLAIYIBEISHIYONGFEICHANGDAXINGDESHUJUJIXUNLIANDESHENDUSHENJINGWANGLUOQUDAI。ZAIZHEIPIANLUNWENZHONG，WOMENDUILIUXINGDERENLIANSHIBIEFANGFAJINXINGLEQUANMIANQIEZUIXINDEWENXIANZONGJIE，QIZHONGJIBAOKUOCHUANTONGFANGFA(JIYUJIHEDEFANGFA、ZHENGTIFANGFA、JIYUTEZHENGDEFANGFAHEHUNHEFANGFA)，YEYOUSHENDUXUEXIFANGFA。

引言

RENLIANSHIBIESHIZHINENGGOUSHIBIEHUOYANZHENGTUXIANGHUOSHIPINZHONGDEZHUTIDESHENFENDEJISHU。SHOUGERENLIANSHIBIESUANFADANSHENGYUQISHINIANDAICHU [1,2]。ZINEIYIHOU，TAMENDEZHUNQUEDUYIJINGDAFUTISHENG，XIANZAIXIANGBIYUZHIWENHUOHONGMOSHIBIE [3] DENGCHUANTONGSHANGBEIRENWEIGENGJIAWENJIANDESHENGWUSHIBIEFANGFA，RENMENWANGWANGGENGPIANAIRENLIANSHIBIE。RANGRENLIANSHIBIEBIQITASHENGWUSHIBIEFANGFAGENGSHOUXINJIANG11XUAN5DEYIDABUTONGZHICHUSHIRENLIANSHIBIEBENZHISHANGSHIFEIQINRUXINGDE。BIRU，ZHIWENSHIBIEXUYAOYONGHUJIANGSHOUZHIANZAICHUANGANQISHANG，HONGMOSHIBIEXUYAOYONGHUYUXIANGJIKAODEHENJIN，YUYINSHIBIEZEXUYAOYONGHUDASHENGSHUOHUA。XIANGDUIERYAN，XIANDAIRENLIANSHIBIEXITONGJINXUYAOYONGHUCHUYUXIANGJIDESHIYENEI(JIASHETAMENYUXIANGJIDEJULIYEHELI)。ZHEISHIDERENLIANSHIBIECHENGWEILEDUIYONGHUZUIYOUHAODESHENGWUSHIBIEFANGFA。ZHEIYEYIWEIZHERENLIANSHIBIEDEQIANZAIYINGYONGFANWEIGENGGUANG，YINWEITAYEKEBEIBUSHUZAIYONGHUBUQIWANGYUXITONGHEZUODEHUANJINGZHONG，BIRUJIANKONGXITONGZHONG。RENLIANSHIBIEDEQITACHANGJIANYINGYONGHAIBAOKUOFANGWENKONGZHI、QIZHAJIANCE、SHENFENRENZHENGHESHEJIAOMEITI。

DANGBEIBUSHUZAIWUYUESHUTIAOJIANDEHUANJINGZHONGSHI，YOUYURENLIANTUXIANGZAIXIANSHISHIJIEZHONGDECHENGXIANJUYOUGAODUDEKEBIANXING(ZHEILEIRENLIANTUXIANGTONGCHANGBEICHENGWEIZIRANRENLIAN(faces in-the-wild))，SUOYIRENLIANSHIBIEYESHIZUIYOUTIAOZHANXINGDESHENGWUSHIBIEFANGFAZHIYI。RENLIANTUXIANGKEBIANDEDIFANGBAOKUOTOUBUZISHI、NIANLING、ZHEDANG、GUANGZHAOTIAOJIANHERENLIANBIAOQING。TU 1 JICHULEZHEIXIEQINGKUANGDESHILI。

图 1：在自然人脸图像中找到的典型变化。(a)头部姿势，(b)年龄，(c)光照，(d)面部表情，(e)遮挡。

RENLIANSHIBIEJISHUZHEIXIENIANYIJINGFASHENGLEZHONGDADEBIANHUA。CHUANTONGFANGFAYILAIYURENGONGSHEJIDETEZHENG(BIRUBIANHEWENLIMIAOSHULIANG)YUJIQIXUEXIJISHU(BIRUZHUCHENGFENFENXI、XIANXINGPANBIEFENXIHUOZHICHIXIANGLIANGJI)DEZUHE。RENGONGSHEJIZAIWUYUESHUHUANJINGZHONGDUIBUTONGBIANHUAQINGKUANGWENJIANDETEZHENGSHIHENKUNNANDE，ZHEISHIDEGUOQUDEYANJIUZHECEZHONGYANJIUZHENDUIMEIZHONGBIANHUALEIXINGDEZHUANYONGFANGFA，BIRUNENGYINGDUIBUTONGNIANLINGDEFANGFA [4,5]、NENGYINGDUIBUTONGZISHIDEFANGFA [6]、NENGYINGDUIBUTONGGUANGZHAOTIAOJIANDEFANGFA [7,8] DENG。JINDUANSHIJIAN，CHUANTONGDERENLIANSHIBIEFANGFAYIJINGBEIJIYUJUANJISHENJINGWANGLUO(CNN)DESHENDUXUEXIFANGFAJIETI。SHENDUXUEXIFANGFADEZHUYAOYOUSHISHITAMENKEYONGFEICHANGDAXINGDESHUJUJIJINXINGXUNLIAN，CONGERXUEXIDAOBIAOZHENGZHEIXIESHUJUDEZUIJIATEZHENG。WANGLUOSHANGKEYONGDEDALIANGZIRANRENLIANTUXIANGYIRANGYANJIUZHEKESHOUJIDAODAGUIMODERENLIANSHUJUJI [9-15]，ZHEIXIETUXIANGBAOHANLEZHENSHISHIJIEZHONGDEGEZHONGBIANHUAQINGKUANG。SHIYONGZHEIXIESHUJUJIXUNLIANDEJIYU CNN DERENLIANSHIBIEFANGFAYIJINGSHIXIANLEFEICHANGGAODEZHUNQUEDU，YINWEITAMENNENGGOUXUEDAORENLIANTUXIANGZHONGWENJIANDETEZHENG，CONGERNENGGOUYINGDUIZAIXUNLIANGUOCHENGZHONGSHIYONGDERENLIANTUXIANGSUOCHENGXIANCHUDEZHENSHISHIJIEBIANHUAQINGKUANG。CIWAI，SHENDUXUEXIFANGFAZAIJISUANJISHIJUEFANGMIANDEBUDUANPUJIYEZAIJIASURENLIANSHIBIEYANJIUDEFAZHAN，YINWEI CNN YEZHENGBEIYONGYUJIEJUEXUDUOQITAJISUANJISHIJUERENWU，BIRUMUBIAOJIANCEHESHIBIE、FENGE、GUANGXUEZIFUSHIBIE、MIANBUBIAOQINGFENXI、NIANLINGGUJIDENG。

RENLIANSHIBIEXITONGTONGCHANGYOUYIXIAGOUJIANMOKUAIZUCHENG：

人脸检测 。人脸检测器用于寻找图像中人脸的位置，如果有人脸，就返回包含每张人脸的边界框的坐标。如图 3a 所示。

人脸对齐 。人脸对齐的目标是使用一组位于图像中固定位置的参考点来缩放和裁剪人脸图像。这个过程通常需要使用一个特征点检测器来寻找一组人脸特征点，在简单的 2D 对齐情况中，即为寻找最适合参考点的最佳仿射变换。图 3b 和 3c 展示了两张使用了同一组参考点对齐后的人脸图像。更复杂的 3D 对齐算法(如 [16])还能实现人脸正面化，即将人脸的姿势调整到正面向前。

人脸表征 。在人脸表征阶段，人脸图像的像素值会被转换成紧凑且可判别的特征向量，这也被称为模板(template)。理想情况下，同一个主体的所有人脸都应该映射到相似的特征向量。

人脸匹配 。在人脸匹配构建模块中，两个模板会进行比较，从而得到一个相似度分数，该分数给出了两者属于同一个主体的可能性。

图 2：人脸识别的构建模块。

HENDUORENRENWEIRENLIANBIAOZHENGSHIRENLIANSHIBIEXITONGZHONGZUIZHONGYAODEZUJIAN，ZHEIYESHIBENLUNWENDIERJIESUOGUANZHUDEZHONGDIAN。

图 3：(a)人脸检测器找到的边界框。(b)和(c)：对齐后的人脸和参考点。

深度学习方法

JUANJISHENJINGWANGLUO(CNN)SHIRENLIANSHIBIEFANGMIANZUICHANGYONGDEYILEISHENDUXUEXIFANGFA。SHENDUXUEXIFANGFADEZHUYAOYOUSHISHIKEYONGDALIANGSHUJULAIXUNLIAN，CONGERXUEDAODUIXUNLIANSHUJUZHONGCHUXIANDEBIANHUAQINGKUANGWENJIANDERENLIANBIAOZHENG。ZHEIZHONGFANGFABUXUYAOSHEJIDUIBUTONGLEIXINGDELEINEICHAYI(BIRUGUANGZHAO、ZISHI、MIANBUBIAOQING、NIANLINGDENG)WENJIANDETEDINGTEZHENG，ERSHIKEYICONGXUNLIANSHUJUZHONGXUEDAOTAMEN。SHENDUXUEXIFANGFADEZHUYAODUANBANSHITAMENXUYAOSHIYONGFEICHANGDADESHUJUJILAIXUNLIAN，ERQIEZHEIXIESHUJUJIZHONGXUYAOBAOHANZUGOUDEBIANHUA，CONGERKEYIFANHUADAOWEICENGJIANGUODEYANGBENSHANG。XINGYUNDESHI，YIXIEBAOHANZIRANRENLIANTUXIANGDEDAGUIMORENLIANSHUJUJIYIBEIGONGKAI [9-15]，KEBEIYONGLAIXUNLIAN CNN MOXING。CHULEXUEXIPANBIETEZHENG，SHENJINGWANGLUOHAIKEYIJIANGWEI，BINGKEBEIXUNLIANCHENGFENLEIQIHUOSHIYONGDULIANGXUEXIFANGFA。CNN BEIRENWEISHIDUANDAODUANKEXUNLIANDEXITONG，WUXUYURENHEQITATEDINGFANGFAJIEHE。

YONGYURENLIANSHIBIEDE CNN MOXINGKEYISHIYONGBUTONGDEFANGFALAIXUNLIAN。QIZHONGZHIYISHIJIANGGAIWENTIDANGZUOSHIYIGEFENLEIWENTI，XUNLIANJIZHONGDEMEIGEZHUTIDOUDUIYINGYIGELEIBIE。XUNLIANWANZHIHOU，KEYITONGGUOQUCHUFENLEICENGBINGJIANGZHIQIANCENGDETEZHENGYONGZUORENLIANBIAOZHENGERJIANGGAIMOXINGYONGYUSHIBIEBUCUNZAIYUXUNLIANJIZHONGDEZHUTI [99]。ZAISHENDUXUEXIWENXIANZHONG，ZHEIXIETEZHENGTONGCHANGBEICHENGWEIPINGJINGTEZHENG(bottleneck features)。ZAIZHEIDIYIGEXUNLIANJIEDUANZHIHOU，GAIMOXINGKEYISHIYONGQITAJISHULAIJINYIBUXUNLIAN，YIWEIMUBIAOYINGYONGYOUHUAPINGJINGTEZHENG(BIRUSHIYONGLIANHEBEIYESI [9] HUOSHIYONGYIGEBUTONGDESUNSHIHANSHULAIWEIDIAOGAI CNN MOXING [10])。LINGYIZHONGXUEXIRENLIANBIAOZHENGDECHANGYONGFANGFASHITONGGUOYOUHUAPEIDUIDERENLIAN [100,101] HUORENLIANSANYUANZU [102] ZHIJIANDEJULIDULIANGLAIZHIJIEXUEXIPINGJINGTEZHENG。

SHIYONGSHENJINGWANGLUOLAIZUORENLIANSHIBIEBINGBUSHISHENMEXINSIXIANG。1997 NIANJIUYOUYANJIUZHEWEIRENLIANJIANCE、YANBUDINGWEIHERENLIANSHIBIETICHULEYIZHONGMINGWEI「JIYUGAILVJUECEDESHENJINGWANGLUO(PBDNN)」[103] DEZAOQIFANGFA。ZHEIZHONGRENLIANSHIBIE PDBNN BEIFENCHENGLEMEIYIGEXUNLIANZHUTIYIGEQUANLIANJIEZIWANGLUO，YIJIANGDIYINZANGDANYUANDESHULIANGHEBIMIANGUONIHE。YANJIUZHESHIYONGMIDUHEBIANTEZHENGFENBIEXUNLIANLELIANGGE PBDNN，RANHOUJIANGTAMENDESHUCHUZUHEQILAIDEDAOZUIZHONGFENLEIJUEDING。LINGYIZHONGZAOQIFANGFA [104] ZEZUHESHIYONGLEZIZUZHIYINGSHE(SOM)HEJUANJISHENJINGWANGLUO。ZIZUZHIYINGSHE [105] SHIYILEIYIWUJIANDUFANGSHIXUNLIANDESHENJINGWANGLUO，KEJIANGSHURUSHUJUYINGSHEDAOGENGDIWEIDEKONGJIAN，TONGSHIYENENGBAOLIUSHURUKONGJIANDETUOPUXINGZHI(JIZAIYUANSHIKONGJIANZHONGXIANGJINDESHURUZAISHUCHUKONGJIANZHONGYEXIANGJIN)。ZHUYI，ZHEILIANGZHONGZAOQIFANGFADOUBUSHIYIDUANDAODUANDEFANGSHIXUNLIANDE([103] ZHONGSHIYONGLEBIANTEZHENG，[104] ZHONGSHIYONGLE SOM)，ERQIETICHUDESHENJINGWANGLUOJIAGOUYEDOUHENQIAN。[100] ZHONGTICHULEYIZHONGDUANDAODUANDERENLIANSHIBIE CNN。ZHEIZHONGFANGFASHIYONGLEYIZHONGLUANSHENGSHIJIAGOU，BINGSHIYONGLEYIGEDUIBISUNSHIHANSHU [106] LAIJINXINGXUNLIAN。ZHEIGEDUIBISUNSHISHIYONGLEYIZHONGDULIANGXUEXILIUCHENG，QIMUBIAOSHIZUIXIAOHUADUIYINGTONGYIZHUTIDETEZHENGXIANGLIANGDUIZHIJIANDEJULI，TONGSHIZUIDAHUADUIYINGBUTONGZHUTIDETEZHENGXIANGLIANGDUIZHIJIANDEJULI。GAIFANGFAZHONGSHIYONGDE CNN JIAGOUYEHENQIAN，QIEXUNLIANSHUJUJIYEJIAOXIAO。

SHANGMIANTIDAODEFANGFADOUWEINENGQUDETUPOXINGDECHENGGUO，ZHUYAOYUANYINSHISHIYONGLENENGLIBUZUDEWANGLUO，QIEXUNLIANSHINENGYONGDESHUJUJIYEXIANGDUIJIAOXIAO。ZHIDAOZHEIXIEMOXINGDEDAOKUOZHANBINGSHIYONGDALIANGSHUJU [107] XUNLIANHOU，YONGYURENLIANSHIBIEDESHOUGESHENDUXUEXIFANGFA [99,9] CAIDADAOLEDANGQIANZUIJIASHUIPING。YOUQIZHIDEYITIDESHI Facebook DE DeepFace [99]，ZHEISHIZUIZAODEYONGYURENLIANSHIBIEDE CNN FANGFAZHIYI，QISHIYONGLEYIGENENGLIHENQIANGDEMOXING，ZAI LFW JIZHUNSHANGSHIXIANLE 97.35% DEZHUNQUEDU，JIANGZHIQIANZUIJIABIAOXIANDECUOWULVJIANGDILE 27%。YANJIUZHESHIYONG softmax SUNSHIHEYIGEBAOHAN 440 WANZHANGRENLIAN(LAIZI 4030 GEZHUTI)DESHUJUJIXUNLIANLEYIGE CNN。BENLUNWENYOULIANGGEQUANXINDEGONGXIAN：(1)YIGEJIYUMINGQUEDE 3D RENLIANJIANMODEGAOXIAODERENLIANDUIQIXITONG;(2)YIGEBAOHANJUBULIANJIEDECENGDE CNN JIAGOU [108,109]，ZHEIXIECENGBUTONGYUCHANGGUIDEJUANJICENG，KEYICONGTUXIANGZHONGDEMEIGEQUYUXUEDAOBUTONGDETEZHENG。ZAINEITONGSHI，DeepID XITONG [9] TONGGUOZAITUKUAI(patch)SHANGXUNLIAN 60 GEBUTONGDE CNN ERDEDAOLEXIANGJINDEJIEGUO，ZHEIXIETUKUAIBAOHANSHIGEQUYU、SANZHONGBILIYIJI RGB HUOHUIDUTONGDAO。ZAICESHIJIEDUAN，HUICONGMEIGETUKUAITIQUCHU 160 GEPINGJINGTEZHENG，JIASHANGQISHUIPINGFANZHUANHOUDEQINGKUANG，KEXINGCHENGYIGE 19200 WEIDETEZHENGXIANGLIANG(160×2×60)。LEISIYU [99]，XINTICHUDE CNN JIAGOUYESHIYONGLEJUBULIANJIEDECENG。QIYANZHENGJIEGUOSHITONGGUOZAIZHEIZHONGYOU CNN TIQUCHUDE 19200 WEITEZHENGXIANGLIANGSHANGXUNLIANYIGELIANHEBEIYESIFENLEIQI [48] DEDAODE。XUNLIANGAIXITONGSUOSHIYONGDESHUJUJIBAOHAN 202599 ZHANGRENLIANTUXIANG，LAIZI 10177 WEIMINGREN [9]。

DUIYUJIYU CNN DERENLIANSHIBIEFANGFA，YINGXIANGZHUNQUEDUDEYINSUZHUYAOYOUSANGE：XUNLIANSHUJU、CNN JIAGOUHESUNSHIHANSHU。YINWEIZAIDADUOSHUSHENDUXUEXIYINGYONGZHONG，DOUXUYAODAXUNLIANJILAIFANGZHIGUONIHE。YIBANERYAN，WEIFENLEIRENWUXUNLIANDE CNN DEZHUNQUEDUHUISUIMEILEIDEYANGBENSHULIANGDEZENGZHANGERTISHENG。ZHEISHIYINWEIDANGLEINEICHAYIXINJIANG11XUAN5SHI，CNN MOXINGNENGGOUXUEXIDAOGENGWENJIANDETEZHENG。DANSHI，DUIYURENLIANSHIBIE，WOMENGANXINGQUDESHITIQUCHUNENGGOUFANHUADAOXUNLIANJIZHONGWEICENGCHUXIANGUODEZHUTISHANGDETEZHENG。YINCI，YONGYURENLIANSHIBIEDESHUJUJIHAIXUYAOBAOHANDALIANGZHUTI，ZHEIYANGMOXINGYENENGXUEXIDAOXINJIANG11XUAN5LEIJIANCHAYI。[110] YANJIULESHUJUJIZHONGZHUTIDESHULIANGDUIRENLIANSHIBIEZHUNQUEDUDEYINGXIANG。ZAIZHEIXIANGYANJIUZHONG，SHOUXIANYIJIANGXUXINGSHIANZHAOMEIGEZHUTIDETUXIANGSHULIANGDUIYIGEDASHUJUJIJINXINGLEPAIXU。RANHOU，YANJIUZHETONGGUOZHUJIANZENGDAZHUTISHULIANGERSHIYONGXUNLIANSHUJUDEBUTONGZIJIXUNLIANLEYIGE CNN。DANGSHIYONGLETUXIANGSHULIANGZUIDUODE 10000 GEZHUTIJINXINGXUNLIANSHI，DEDAODEZHUNQUEDUSHIZUIGAODE。ZENGJIAXINJIANG11XUAN5ZHUTIHUIJIANGDIZHUNQUEDU，YINWEIMEIGEEWAIZHUTIKEYONGDETUXIANGFEICHANGSHAO。LINGYIXIANGYANJIU [111] YANJIULEGENGKUANDUDESHUJUJIGENGHAO，HAISHIGENGSHENDUDESHUJUJIGENGHAO(RUGUOYIGESHUJUJIBAOHANXINJIANG11XUAN5ZHUTI，ZERENWEITAGENGKUAN;LEISIDI，RUGUOMEIGEZHUTIBAOHANDETUXIANGXINJIANG11XUAN5，ZERENWEITAGENGSHEN)。ZHEIXIANGYANJIUZONGJIEDAO：RUGUOTUXIANGSHULIANGXIANGDENG，ZEGENGKUANDESHUJUJINENGDEDAOGENGHAODEZHUNQUEDU。YANJIUZHERENWEIZHEISHIYINWEIGENGKUANDUDESHUJUJIBAOHANXINJIANG11XUAN5LEIJIANCHAYI，YINERNENGGENGHAODIFANHUADAOWEICENGJIANGUODEZHUTISHANG。BIAO 1 ZHANSHILEMOUXIEZUICHANGYONGYUXUNLIANRENLIANSHIBIE CNN DEGONGKAISHUJUJI。

表 1：公开的大规模人脸数据集。

YONGYURENLIANSHIBIEDE CNN JIAGOUCONGNEIXIEZAI ImageNet DAGUIMOSHIJUESHIBIETIAOZHANSAI(ILSVRC)SHANGBIAOXIANYOUYIDEJIAGOUSHANGQUDELEHENDUOLINGGAN。JUGELIZI，[11] ZHONGSHIYONGLEYIGEDAIYOU 16 CENGDE VGG WANGLUO [112] BANBEN，[10] ZHONGZESHIYONGLEYIGEXIANGSIDANGENGXIAODEWANGLUO。[102] ZHONGTANSUOLELIANGZHONGBUTONGLEIXINGDE CNN JIAGOU：VGG FENGGEDEWANGLUO [112] HE GoogleNet FENGGEDEWANGLUO [113]。JISHIZHEILIANGZHONGWANGLUOSHIXIANLEXIANGDANGDEZHUNQUEDU，DAN GoogleNet FENGGEDEWANGLUODECANSHUSHULIANGSHAO 20 BEI。GENGJINDUANSHIJIAN，CANCHAWANGLUO(ResNet)[114] YIJINGCHENGWEILEHENDUOMUBIAOSHIBIERENWUDEZUISHOUPIANAIDEXUANZE，QIZHONGBAOKUORENLIANSHIBIE [115-121]。ResNet DEZHUYAOCHUANGXINDIANSHIYINRULEYIZHONGSHIYONGJIEJINGLIANJIEDEGOUJIANMOKUAILAIXUEXICANCHAYINGSHE，RUTU 7 SUOSHI。JIEJINGLIANJIEDESHIYONGNENGRANGYANJIUZHEXUNLIANGENGSHENDUDEJIAGOU，YINWEITAMENYOUZHUYUKUACENGDEXINXILIUDONG。[121] DUIBUTONGDE CNN JIAGOUJINXINGLEQUANMIANDEYANJIU。ZAIZHUNQUEDU、SUDUHEMOXINGDAXIAOZHIJIANDEZUIJIAQUANHENGSHISHIYONGDAIYOUYIGECANCHAMOKUAI(LEISIYU [122] ZHONGTICHUDENEIZHONG)DE 100 CENG ResNet DEDAODE。

图 7：[114] 中提出的原始的残差模块。

XUANZEYONGYUXUNLIAN CNN FANGFADESUNSHIHANSHUYIJINGCHENGWEIJINLAIRENLIANSHIBIEZUIHUOYUEDEYANJIULINGYU。JISHISHIYONG softmax SUNSHIXUNLIANDE CNN YIJINGFEICHANGCHENGGONG [99,9,10,123]，DANYEYOUYANJIUZHERENWEISHIYONGZHEIZHONGSUNSHIHANSHUWUFAHENHAODIFANHUADAOXUNLIANJIZHONGWEICHUXIANGUODEZHUTISHANG。ZHEISHIYINWEI softmax SUNSHIYOUZHUYUXUEXINENGZENGDALEIJIANCHAYIDETEZHENG(YIBIANZAIXUNLIANJIZHONGQUBIEBUTONGDELEI)，DANBUYIDINGHUIJIANGDILEINEICHAYI。YANJIUZHEYIJINGTICHULEYIXIENENGHUANJIEZHEIYIWENTIDEFANGFA。YOUHUAPINGJINGTEZHENGDEYIZHONGJIANDANFANGFASHISHIYONGPANBIESHIZIKONGJIANFANGFA，BIRULIANHEBEIYESI [48]，JIUXIANG [9,124,125,126,10,127] ZHONGSUOZUODENEIYANG。LINGYIZHONGFANGFASHISHIYONGDULIANGXUEXI。BIRU，[100,101] ZHONGSHIYONGLEPEIDUIDEDUIBISUNSHILAIZUOWEIWEIYIDEJIANDUXINHAO，[124-126] ZHONGHAIJIEHESHIYONGLEFENLEISUNSHI。RENLIANSHIBIEFANGMIANZUICHANGYONGDEDULIANGXUEXIFANGFASHISANYUANZUSUNSHIHANSHU [128]，ZUIZAOZAI [102] ZHONGBEIYONGYURENLIANSHIBIERENWU。SANYUANZUSUNSHIDEMUBIAOSHIYIYIDINGYULIANGFENKAIZHENGLIDUIZHIJIANDEJULIHEFULIDUIZHIJIANDEJULI。CONGSHUXUEXINGSHISHANGJIANG，DUIYUMEIGESANYUANZU i，XUYAOMANZUYIXIATIAOJIAN [102]：

QIZHONG x_a SHIMAOTUXIANG，x_p SHITONGYIZHUTIDETUXIANG，x_n SHILINGYIGEBUTONGZHUTIDETUXIANG，f SHIMOXINGXUEXIDAODEYINGSHEGUANXI，α SHIJIAZAIZHENGLIDUIHEFULIDUIJULIZHIJIANDEYULIANG。ZAISHIJIANZHONG，SHIYONGSANYUANZUSUNSHIXUNLIANDE CNN DESHOULIANSUDUBISHIYONG softmax DEMAN，ZHEISHIYINWEIXUYAODALIANGSANYUANZU(HUODUIBISUNSHIZHONGDEPEIDUI)CAINENGFUGAIZHENGGEXUNLIANJI。JINGUANZHEIGEWENTIKEYITONGGUOZAIXUNLIANJIEDUANXUANZEKUNNANDESANYUANZU(JIWEIFANYULIANGTIAOJIANDESANYUANZU)LAIHUANJIE [102]，DANCHANGJIANDEZUOFASHIZAIDIYIGEXUNLIANJIEDUANSHIYONG softmax SUNSHIXUNLIAN，ZAIDIERGEXUNLIANJIEDUANSHIYONGSANYUANZUSUNSHILAIDUIPINGJINGTEZHENGJINXINGDIAOZHENG [11,129,130]。YANJIUZHEMENYIJINGTICHULESANYUANZUSUNSHIDEYIXIEBIANTI。BIRU [129] ZHONGSHIYONGLEDIANJIZUOWEIXIANGSIDUDULIANG，ERBUSHIOUJILIDEJULI;[130] ZHONGTICHULEYIZHONGGAILVSHISANYUANZUSUNSHI;[131,132] ZHONGTICHULEYIZHONGXIUGAIBANDESANYUANZUSUNSHI，TAYENENGZUIXIAOHUAZHENGLIHEFULIFENSHUFENBUDEBIAOZHUNCHA。YONGYUXUEXIPANBIETEZHENGDELINGYIZHONGSUNSHIHANSHUSHI [133] ZHONGTICHUDEZHONGXINSUNSHI(centre loss)。ZHONGXINSUNSHIDEMUBIAOSHIZUIXIAOHUAPINGJINGTEZHENGYUTAMENDUIYINGLEIBIEDEZHONGXINZHIJIANDEJULI。TONGGUOSHIYONG softmax SUNSHIHEZHONGXINSUNSHIJINXINGLIANHEXUNLIAN，JIEGUOBIAOMING CNN XUEXIDAODETEZHENGNENGGOUYOUXIAOZENGDALEIJIANCHAYI(softmax SUNSHI)HEJIANGDILEINEIGETICHAYI(ZHONGXINSUNSHI)。XIANGBIYUDUIBISUNSHIHESANYUANZUSUNSHI，ZHONGXINSUNSHIDEYOUDIANSHIGENGGAOXIAOHEGENGRONGYISHIXIAN，YINWEITABUXUYAOZAIXUNLIANGUOCHENGZHONGGOUJIANPEIDUIHUOSANYUANZU。LINGYIZHONGXIANGGUANDEDULIANGXUEXIFANGFASHI [134] ZHONGTICHUDEFANWEISUNSHI(range loss)，ZHEISHIWEIGAISHANSHIYONGBUPINGHENGSHUJUJIDEXUNLIANERTICHUDE。FANWEISUNSHIYOULIANGGEZUJIAN。LEINEIDESUNSHIZUJIANSHIZUIXIAOHUATONGYILEIYANGBENZHIJIANDE k-ZUIDAJULI，ERLEIJIANDESUNSHIZUJIANSHIZUIDAHUAMEIGEXUNLIANPIZHONGZUIJINDELIANGGELEIZHONGXINZHIJIANDEJULI。TONGGUOSHIYONGZHEIXIEJIDUANANLI，FANWEISUNSHIWEIMEIGELEIDOUSHIYONGTONGYANGDEXINXI，ERBUGUANMEIGELEIBIEZHONGYOUDUOSHAOYANGBENKEYONG。LEISIYUZHONGXINSUNSHI，FANWEISUNSHIXUYAOYU softmax SUNSHIJIEHEQILAIYIBIMIANSUNSHIJIANGZHILING [133]。

DANGJIEHEBUTONGDESUNSHIHANSHUSHI，HUICHUXIANYIGEKUNNAN，JIXUNZHAOMEIYIXIANGZHIJIANDEZHENGQUEPINGHENG。ZUIJINYIDUANSHIJIAN，YIYOUYANJIUZHETICHULEJIZHONGXIUGAI softmax SUNSHIDEFANGFA，ZHEIYANGTAWUXUYUQITASUNSHIJIEHEYENENGXUEXIPANBIETEZHENG。YIZHONGYIBEIZHENGMINGKEYIZENGJIAPINGJINGTEZHENGDEPANBIENENGLIDEFANGFASHITEZHENGGUIYIHUA [115,118]。BIRU，[115] TICHUGUIYIHUATEZHENGYIJUYOUDANWEI L2 FANSHU，[118] TICHUGUIYIHUATEZHENGYIJUYOULINGJUNZHIHEDANWEIFANGCHA。YIGECHENGGONGDEFANGFAYIJINGZAI softmax SUNSHIZHONGMEILEIZHIJIANDEJUECEBIANJIEZHONGYINRULEYIGEYULIANG [135]。WEILEJIANDAN，WOMENJIESHAOYIXIASHIYONG softmax SUNSHIJINXINGERYUANFENLEIDEQINGKUANG。ZAIZHEIZHONGQINGKUANGXIA，MEILEIZHIJIANDEJUECEBIANJIE(RUGUOPIANZHIWEILING)KEYOUXIASHIJIDING：

QIZHONG x SHITEZHENGXIANGLIANG，W_1 HE W_2 SHIDUIYINGMEILEIDEQUANZHONG，θ_1 HE θ_2 SHI x FENBIEYU W_1 HE W_2 ZHIJIANDEJIAODU。TONGGUOZAISHANGSHIZHONGYINRUYIGECHENGFAYULIANG，ZHEILIANGGEJUECEBIANJIEKEYIBIANDEGENGJIAYANGE：

RUTU 8 SUOSHI，ZHEIGEYULIANGKEYIYOUXIAODIZENGDALEIBIEZHIJIANDEQUFENCHENGDUYIJIGEZILEIBIEZHINEIDEJINCOUXING。GENJUJIANGGAIYULIANGZHENGHEJINSUNSHIDEFANGSHI，YANJIUZHEMENYIJINGTICHULEDUOZHONGKEYONGFANGFA [116,119-121]。BIRU [116] ZHONGDUIQUANZHONGXIANGLIANGJINXINGLEGUIYIHUAYIJUYOUDANWEIFANSHU，ZHEIYANGSHIDEJUECEBIANJIEJINQUJUEYUJIAODU θ_1 HE θ_2。[119,120] ZHONGZETICHULEYIZHONGJIAXINGYUXIANYULIANG。XIANGBIYUCHENGFAYULIANG [135,116]，JIAXINGYULIANGGENGRONGYISHIXIANHEYOUHUA。ZAIZHEIXIANGGONGZUOZHONG，CHULEGUIYIHUAQUANZHONGXIANGLIANG，TEZHENGXIANGLIANGYERU [115] ZHONGYIYANGJINXINGLEGUIYIHUAHEBILIDIAOZHENG。[121] ZHONGTICHULELINGYIZHONGJIAXINGYULIANG，TAJIYOU [119,120] NEIYANGDEYOUDIAN，HAIYOUGENGHAODEJIHEJIESHIFANGSHI，YINWEIZHEIGEYULIANGSHIJIAZAIJIAODUSHANGDE，ERBUSHIYUXIANSHANG。BIAO 2 ZONGJIELEYOUYULIANGDE softmax SUNSHIDEBUTONGBIANTIDEJUECEBIANJIE。ZHEIXIEFANGFASHIRENLIANSHIBIELINGYUDEDANGQIANZUIJIA。

图 8：在两个类别之间的决策边界中引入一个余量 m 的效果。(a)softmax 损失，(b)有余量的 softmax 损失。

表 2：有余量的 softmax 损失的不同变体的决策边界。注意这些决策边界针对的是二元分类案例中的类别 1。