Slide 1

Slide 1 text

YOPO You Only Propagate Once: Accelerating Adversarial Training via Maximal Principle #Dinghuai_Zhang #Tianyuan_Zhang #Yiping_Lu #Zhanxing_Zhu #Bin_Dong Keio JNLab B4 Tomoki Tanimura

Slide 2

Slide 2 text

#JCMJPHSBQIZ "DDFQUFECZ*$$7 "VUIPST %JOHIVBJ@;IBOH5JBOZVBO@;IBOH:JQJOH@-V;IBOYJOH@;IV #JO@%POH "⒏MJBUJPO 1FLJOH6OJWFSTJUZ

Slide 3

Slide 3 text

0WFSWJFX 3FEVDFUIFDPNQVUBUJPOBMDPTUPGUIF"EWFSTBSJBM5SBJOJOH 3FEVDFUIFOVNCFSPGGPSXBSEBOECBDLQSPQPGBEWFSTBSJBMJOOFS NBYJNJ[BUJPO

Slide 4

Slide 4 text

Preliminaries

Slide 5

Slide 5 text

8IBUJT"EWFSTBSJBM&YBNQMFT "EWFSTBSJBM&YBNQMFTJTUIFJOQVUUPGPPMUIFNBDIJOFMFBSOJOH NPEFMXJUITNBMMQFSUVSCBUJPO "&T /BUVSBM*OQVU 1FSUVSCBUJPO

Slide 6

Slide 6 text

5IJTJTQBOEB 5IJTJTHJCCPO 5IJTJTQBOEB 5IJTJTQBOEB .PEFM )VNBO "&T /BUVSBM*OQVU 1FSUVSCBUJPO

Slide 7

Slide 7 text

"DDVSBDZGPS"EWFSTBSJBM&YBNQMFT 4UBOEBSEUSBJOFENPEFMDBO`UDMBTTJGZBOZ"&TDPSSFDUMZFWFOJGDMBTTJGZ NPTUPGDMFBOEBUBDPSSFDUMZ )PXXFDMBTTJGZ"&TDPSSFDUMZ "EWFSTBSJBM5SBJOJOH

Slide 8

Slide 8 text

3FTFBSDIBCPVU"EWFSTBSJBM&YBNQMFT "UUBDL .FUIPETUPDSFBUF"&TGPSUIFNPEFM &H1(% '(4. ʜ %FGFOTFT .FUIPETGPSDPOTUSVDUJOHBSPCVTUDMBTTJpFSGPSBEWFSTBSJBMFYBNQMFT &H"EWFSTBSJBM5SBJOJOH 53"%&4 ʜ 4FUUJOHT 8IJUFCPYXFLOPXFWFSZUIJOHBCPVUEFGFOTFT FHNPEFM IQBSBNT EBUB FUD #MBDLCPYXFLOPXPOMZJOQVUBOEPVUQVUQBJSBCPVUUIFEFGFOTFT

Slide 9

Slide 9 text

"UUBDL '(4. 1(% '(4. 'BTU(SBEJFOU4JHO.FUIPE 6QEBUFUIFJOQVUUPNBYJNJ[FUIFMPTTGVODUJPOVTJOHHSBETJHOPODF XIFSF YJTUIFJOQVU DMFBO JNBHF Y?BEWJTUIFQFSUVSCFEBEWFSTBSJBMJNBHF + JTUIFDMBTTJpDBUJPOMPTTGVODUJPO Z@USVJTUSVFMBCFMGPSUIFJOQVUY 1(% 1SPKFDU(SBEJFOU%FTDFOU 6QEBUFUIFJOQVUCZBQQMZJOH'(4.JUFSBUJWFMZ .PTUQPXFSGVM

Slide 10

Slide 10 text

%FGFOTF "EWFSTBSJBM5SBJOJOH "5 5SBJOUIFNPEFMXJUIUIFEBUBTFUJODMVEJOH"&T XIFSF YJTUIFDMFBOJOQVU MJTUIFMPTTGVODUJPO FUBJTUIFBEWFSTBSJBM QFSUVCBUJPO ZJTUIFUSVFMBCFM *OPOFJUFSBUJPO $SFBUF"&TGPSUIFJOQVUXJUI1(%PSTPNFBUUBDLNFUIPE 5SBJOUIFNPEFMXJUIUIFDSFBUFE"&T

Slide 11

Slide 11 text

*GZPVVTF1(% JUFSBUJPO'(4. GPS"5 "5JTUIFUJNFT DPNQVUBUJPODPTUGPSUIFTUBOEBSEUSBJOJOH 4UBOEBSE5SBJOJOH GPXBSEBOECBDLQSPQ "EWFSTBSJBM5SBJOJOH GPSXBSEBOECBDLQSPQ GPSXBSEBOECBDLQSPQ GPS1(% 7FSZIJHIDPNQVUBUJPOBMDPTU /PUFUIBU*`N/05("/ (FOFSBUJWF"EWFSTBSJBM/FUXPSL

Slide 12

Slide 12 text

Approach

Slide 13

Slide 13 text

:010 /FXQPXFSGVMBOEF⒎FDUJWFEFGFOTFNFUIPE 5IJTDPNQVUBUJPOBMDPTUJTUJNFTMPXFSUIBO"5 3FEVDFUIFOVNCFSPGGPSXBSEBOECBDLQSPQ

Slide 14

Slide 14 text

0QUJNJ[BUJPO1SPCMFNBT%J⒎FSFOUJBM(BNF 5IFSPCVTUPQUJNJ[BUJPOQSPCMFNDBOCFXSJUUFOBTBEJ⒎FSFOUJBM HBNF 6TFUIFNPEFM`TMBZFSBTBUJNF

Slide 15

Slide 15 text

.PEFMQBSBNFUFS NBYJNJ[FUIFMPTTGVODUJPO 1FSUVSCBUJPO NBYJNJ[FUIFMPTTGVODUJPO θ J(θ, η) η

Slide 16

Slide 16 text

/PUBUJPO "EWFSTBSJBM5SBJOJOH JTUIFMBZFSTGSPN JTUIFpSTUMBZFS gθ f0

Slide 17

Slide 17 text

1(%"MHPSJUIN *OFWFSZJUFSBUJPO UIFQFSUVSCBUJPO JTVQEBUFECZPOFGVMM GPSXBSEBOECBDLXBSE η

Slide 18

Slide 18 text

:010NOBMHPSJUIN :010IBTUIFBOPVUFSJUFSBUJPOBOEBOJOOFSJUFSBUJPO 0VUFSJUFSBUJPO N JTUIFTBNFBT1(% 'VMMGPSXBSEBOECBDLQSPQ *OUIFJOOFSJUFSBUJPO O UIFQFSUVSCBUJPO JTVQEBUFEVTJOHPOMZ pSTUMBZFSGPSXBSEBOECBDLQSPQ #ZpYJOHUIFpSTUMBZFS`TPVUQVUHSBEJFOUBTBpYFEWBMVF η p

Slide 19

Slide 19 text

%J⒎FSFODFCFUXFFO1(%BOE:010 :010NO 1(%

Slide 20

Slide 20 text

1(% :010

Slide 21

Slide 21 text

.FSJUTPG:010 $PNQVUBUJPOBM$PTU 1(% GVMMGPSXBSEBOECBDLXBSE :010 GVMMGPSXBSEBOECBDLXBSE pSTUMBZFSGPSXBSEBOECBDLXBSE OFHMJHJCMFBHBJOTUGVMMPOF .BYJNJ[FUIFF⒎FDUPGGVMMGPSXBSEBOECBDLXBSE #FDBVTF:010DBOXFMMEFTJHOUIFQFSUVSCBUJPOXJUIUIFJOOFSJUFSBUJPO

Slide 22

Slide 22 text

The Pontryagin's Maximum Principle for Adversarial Training

Slide 23

Slide 23 text

5IJTDIBQUFSJTBXPOEFSGVMNBHJDUIFPSFNBOEQSPPG 5IJTDIBQUFSJTMFGUUPUIFSFBEFS

Slide 24

Slide 24 text

Experiment

Slide 25

Slide 25 text

5JNFF⒏DJFODZ :010`TUSBJOJOHJTGBTUFSUIBO"5

Slide 26

Slide 26 text

3FTVMUTPO./*45 :010JTDPNQBSBCMFUP1(% NPTUQPXFSGVM"5

Slide 27

Slide 27 text

3FTVMUTPO$*'"3 :010BDIJFWFTIJHIFSBDDVSBDZUIBO1(%

Slide 28

Slide 28 text

5SBJOJOHUJNFBOE"DDVSBDZ :010BDIJFWFTUIFIJHIFTUBEWBDDXJUIMPXUSBJOJOHUJNF

Slide 29

Slide 29 text

Conclusion

Slide 30

Slide 30 text

$PODMVTJPO 1SPQPTF:010 :PV0OMZ1SPQBHBUF0ODF OPUPOMZPODF /FXEFGFOTFNFUIPEXIJDIBDIJFWFTCPUIPGUIFIJHIBEWFSTBSJBM BDDVSBDZBOEMPXDPNQVUBUJPOBMDPTU GBTUFSUIBO"5