Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
機械学習とセキュリティ
Search
setten-QB
July 07, 2020
Science
8
1.9k
機械学習とセキュリティ
機械学習モデルへの攻撃とその対策についての概要
setten-QB
July 07, 2020
Tweet
Share
More Decks by setten-QB
See All by setten-QB
第4回 確率・統計の基礎勉強会
settenqb
0
160
確率・統計の基礎勉強会3
settenqb
0
240
確率・統計勉強会2
settenqb
0
150
確率・統計の基礎勉強会1
settenqb
1
250
Other Decks in Science
See All in Science
Machine Learning for Materials (Lecture 8)
aronwalsh
0
410
ultraArmをモニター提供してもらった話
miura55
0
190
Machine Learning for Materials (Lecture 6)
aronwalsh
0
510
いまAI組織が求める企画開発エンジニアとは?
roadroller
2
1.3k
Transformers are Universal in Context Learners
gpeyre
0
550
(論文読み)贈り物の交換による地位の競争と社会構造の変化 - 文化人類学への統計物理学的アプローチ -
__ymgc__
1
100
WeMeet Group - 採用資料
wemeet
0
3.2k
『データ可視化学入門』を PythonからRに翻訳した話
bob3bob3
1
500
LIMEを用いた判断根拠の可視化
kentaitakura
0
340
Celebrate UTIG: Staff and Student Awards 2024
utig
0
460
(2024) Livres, Femmes et Math
mansuy
0
110
山形とさくらんぼに関するレクチャー(YG-900)
07jp27
1
220
Featured
See All Featured
How To Stay Up To Date on Web Technology
chriscoyier
788
250k
Unsuck your backbone
ammeep
668
57k
Build your cross-platform service in a week with App Engine
jlugia
229
18k
The Straight Up "How To Draw Better" Workshop
denniskardys
232
140k
A better future with KSS
kneath
238
17k
[RailsConf 2023 Opening Keynote] The Magic of Rails
eileencodes
28
9.1k
Optimizing for Happiness
mojombo
376
70k
Building Better People: How to give real-time feedback that sticks.
wjessup
364
19k
For a Future-Friendly Web
brad_frost
175
9.4k
Bootstrapping a Software Product
garrettdimon
PRO
305
110k
Performance Is Good for Brains [We Love Speed 2024]
tammyeverts
6
410
Building Applications with DynamoDB
mza
90
6.1k
Transcript
ػցֶशͱηΩϡϦςΟ ௨৴ࣄۀձࣾ ΄͛΄͛։ൃ෦ 2# !TFUUFO@2# %BUB4DJFODF$BGÉ!৽॓
ػցֶशºηΩϡϦςΟ Ø %PT߈ܸΛػցֶशͰݕ Ø ϚϧΣΞΛػցֶशͰݕ ػցֶशΛηΩϡϦςΟʹԠ༻ ػցֶशϞσϧࣗମͷηΩϡϦςΟ ػցֶशͰߏஙͨ͠ϞσϧʢػցֶशϞσϧʣΛΈࠐΜͩγεςϜͰ ैདྷͷγεςϜͱҟͳͬͨݻ༗ͷ߈ܸ͕ͳ͞ΕΔϦεΫ͕༗Δ ͦͷͨΊɼػցֶशϞσϧಛ༗ͷηΩϡϦςΟରࡦ͕ඞཁ
2
"EWFSTBSJBM"UUBDL ϞσϧΛὃ͢߈ܸ .PEFM&YUSBDUJPO ϞσϧΛ౪Ή߈ܸ .PEFM*OWFSTJPO ֶशσʔλʹؔ͢ΔใΛ෮ݩ͢Δ߈ܸ
None
"EWFSTBSJBM"UUBDL ܇࿅͞ΕͨػցֶशϞσϧΛὃ͢߈ܸ ݩͷը૾ ఢରతઁಈ "EWFSTBSJBM&YBNQMF ʢςφΨβϧʣ (PPEGFMMPX FUBM ΑΓҾ༻
5
ఢରతઁಈΛݟ͚ͭΔͨΊʹ argmin " , s.t. + ≠ argmin " ,
s.t. + = # ಛఆͷΫϥεʹޡྨͤ͞Δ͜ͱΛతͱͨ͠ "EWFSTBSJBM"UUBDL ޡྨͤ͞ΔΫϥεࢦఆͤͣ ͱʹ͔͘Ͳ͔͜ͷΫϥεʹޡྨͤ͞Δ͜ͱΛ తͱͨ͠"EWFSTBSJBM"UUBDL 6
දతͳ"EWFSTBSJBM"UUBDL (PPEGFMMPX FUBM !"# = + sign ∇ ℓ
, /PUBUJPO ɿઁಈڧʢͲΕ͙Β͍ઁಈΛڧ͘༩͑Δ͔Λද͢ʣ ℓɿଛࣦؔ 3FNBSL '(4.Ұͷޯ্ঢͰ࠷దԽΛऴྃ͢Δ͕ɼ͜ΕΛෳճʹ֦ுͨ͠ͷ͕#*.Ͱɼ CBMMʹऩ·ΔΑ͏ͳ੍ͷͱͰޯ্ঢΛ܁Γฦ͢ɽ '(4.#*.! ϊϧϜͰͷઁಈΛੜ͓ͯ͠Γɼ%FFQGPPM͜ͷϊϧϜΛ" ʹɼ $8# ʹͨ͠ͷͱݟΔ͜ͱ͕Ͱ͖Δɽ 7
8IJUF#PY4FUUJOHʹ͓͚Δఢରతઁಈͷݟ͚ͭํ '(4.BUUBDL (PPEGFMMPX FUBM #*. ,VSBLJO FUBM BUUBDL.*'(4.
%POHFUBM %FFQGPPM .PPTBWJ%F[GPPMJ FUBM /FXUPO'PPM +BOHFUBM +4." 1BQFSOPU FUBM (SBEJFOU #BTFE 0CKFDUJWF 'VODUJPO #BTFE $8 $BSMJOJ FUBM &"% $IFOFUBM 0QU.BSHJO 8BSSFOFUBM ˞8IJUF#PY4FUUJOHɿଛࣦؔͷޯ͕ܭࢉͰ͖ͨΓɼϞσϧͷDPOGJEFODFTDPSFΛΔ͜ͱ͕Ͱ͖Δઃఆ 8
"EWFSTBSJBM"UUBDLͷରࡦɿ"EWFSTBSJBM5SBJOJOH Ϟσϧͷֶश࣌ʹBEWFSTBSJBMFYBNQMFTͰl༧छz͓͚ͯ͠ BEWFSTBSJBMFYBNQMFTʹର͢Δϩόετੑ্͕ΔΜ͡Όͳ͍͔ʁ 9 ℓ!"# , () ≔ ℓ !"#,
!"# + 1 − ℓ , *EFB 3FTVMU n ࣮ࡍʹBEWFSTBSJBMFYBNQMFTʹର͢Δϩόετੑ্͢Δ ҰํͰʜ n ֶशʹཁ͢Δ͕࣌ؒ૿͑Δ n "EWFSTBSJBMFYBNQMFTͷϩόετੑBEWFSTBSJBMFYBNQMFTͷ࡞Γํʹґଘ͢Δ n ѱҙͷͳ͍ϊΠζ͕ͬͨը૾Λ͏·͘ྨͰ͖ͳ͘ͳΔ ͱ͍ͬͨൃੜ͢Δ
"EWFSTBSJBM"UUBDL ϞσϧΛὃ͢߈ܸ .PEFM&YUSBDUJPO ϞσϧΛ౪Ή߈ܸ .PEFM*OWFSTJPO ֶशσʔλʹؔ͢ΔใΛ෮ݩ͢Δ߈ܸ
.PEFM&YUSBDUJPOɿϞσϧΛ౪Ή & "SDIJUFDUVSF %FDJTJPO#PVOEBSZ 'VODUJPOBMJUZ ϨΠϠʔͷχϡʔϩϯͷ ͞Βʹ׆ੑԽؔͳͲͷ ϞσϧͷߏΛ౪ΉλΠϓ ϞσϧͷܾఆڥքΛ ౪ΉλΠϓ
ϞσϧʹΑΔ ೖྗͱग़ྗͷରԠؔΛ ౪ΉλΠϓ 11
.PEFM&YUSBDUJPOͷओཁͳΞϓϩʔν $ , $ $%& ' : ℝ( → ֶश
), ) )%& * +: ℝ( → ֶश 0SJHJOBM.PEFM 4VCTUJUVUF.PEFM "1*ʹΑͬͯฦ͞ΕΔ Λతมͱͯ͠ར༻͢Δ͜ͱͰཧϞσϧΛߏங͢Δɽ දతͳݚڀͱͯ͠$PSSFJB4JMWBFUBM 0SFLPOEZ FUBM ͕ڍ͛ΒΕΔɽ 12
4VCTUJUVUF.PEFMʹؔ͢Δ߈ %FGFODF 0GGFODF "1*ୟ͚ΔճΛ੍ݶ গͳ͍ԠճͰ 4VCTUJUVUF.PEFMΛߏங͢Δํ๏͕ఏҊ͞ΕΔ 0SFLPOEZ FUBM 3PTFOCFSHFUBM
13
"EWFSTBSJBM"UUBDL ϞσϧΛὃ͢߈ܸ .PEFM&YUSBDUJPO ϞσϧΛ౪Ή߈ܸ .PEFM*OWFSTJPO ֶशσʔλʹؔ͢ΔใΛ෮ݩ͢Δ߈ܸ
ʢٛͷʣ.PEFM*OWFSTJPO"UUBDL ֶशσʔλʹؔ͢ΔใΛ෮ݩ͢Δ߈ܸ 1SPQFSUZ*OGFSFODF"UUBDL .PEFM*OWFSTJPO"UUBDL దͳ ͕Ϟσϧͷֶशσʔληοτʹؚ·Ε͍ͯΔ͔ʁ Λ໌Β͔ʹ͢Δ߈ܸ ֶशσʔληοτʹؔ͢Δੑ࣭Λਪଌ͢Δ߈ܸ FH͕͍ਓυϨεΛண͍ͯΔਓ͕ ੑผྨͷϞσϧͷֶशσʔλʹؚ·Ε͍ͯΔ͔ʁ
ֶशσʔλΛ෮ݩ͢Δ߈ܸ ˞.PEFM*OWFSTJPO"UUBDLʹ.FNCFSTIJQ*OGFSFODF1SPQFSUZ*OGFSFODFΛؚΊΔ͔ʹॾઆ͋Γ 15
("/Λ༻͍ͨ.PEFM*OWFSTJPO ,VTBOP FUBM ิॿσʔληοτ ) , )%& * ,
, ∼$$( ℱ′ ֶशσʔληοτ $ , $ $%& ' , ∼$$( ℱ ΫΤϦ & ,, … * , Ԡ (& ,), … * , (FOFSBUPS Ͱ ℱ ʢͬΆ͍ͷʣΛۙࣅ αϯϓϦϯά (FOFSBUPS͔Β ֶशσʔλͬΆ͍ͷΛੜ 16
σʔλͷҰ෦͔ΒΓͷ෦Λ෮ݩ ֶशσʔλ ∈ ℝ( ͔ΒҰ෦ͷಛྔ͚ͩΛൈ͖ग़ͯ͠ ࡞ͨ͠ϕΫτϧ " ∈ ℝ-, <
͔Β ΓͷಛྔΛ෮ݩ͢Δ จͰ " ࿙Ӯͯ͠ͳ͍ηϯγςΟϒͰͳ͍ಛྔͰ ΓͷಛྔηϯγςΟϒͳಛྔͩͱఆ͍ͯ͠Δ ("/Λ༻͍ͨ.PEFM*OWFSTJPO ;IBOFUBM 17
͍ɼϜζ͘Ͷʜʁ ./*45Λֶशσʔλͱͨ͠ྨϞσϧʹରͯ͠.PEFM *OWFSTJPO"UUBDLΛߦͬͨ݁Ռ ิॿσʔλखॻ͖จࣈͷࣈͱΞϧϑΝϕοτ ࣮ࡍʹ෮ݩͯ͠Έͨ݁Ռ 18
None
ػցֶशϞσϧͷ߈ܸʹؔ͢Δݚڀ ͬͺΓ"EWFSTBSJBM"UUBDL͕μϯτπͳײ͡ ݚڀ͞ΕͯΔײ ֶशσʔλΛͯ͢෮ݩ͢ΔλΠϓͷ.PEFM*OWFSTJPO"UUBDL͕Ұ൪ͦ͠͏ ʢ࣮ࡍʹ͔ͬͨ͠ʣ ߈ܸͷ͠͞ n "EWFSTBSJBM"UUBDLσʔλ͕ߴ࣍ݩʹͳΔͱෆՄආతʹੜ͡ΔͨΊ ຊ࣭తʹରࡦ͕ࠔʁ n
.PEFM&YUSBDUJPO"UUBDLΫΤϦ੍ݶ͕༗ޮʹࢥ͑Δ͕ ΫΤϦ੍ݶͷͱͰ͋ΔఔͷϞσϧෳ͕ग़དྷ͓ͯΓ ࠓޙͷಈʹ ରࡦͷ͠͞ 20
3FGFSFODF (PPEGFMMPX *+ 4IMFOT + 4[FHFEZ $ &YQMBJOJOHBOEIBSOFTTJOHBEWFSTBSJBMFYBNQMFT BS9JW
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
3FGFSFODF 8BSSFO ) #P - %BXO 4 %FDJTJPO#PVOEBSZ"OBMZTJTPG"EWFSTBSJBM&YBNQMFT*OUFSOBUJPOBM $POGFSFODFPG-FBSOJOH3FQSFTFOUBUJPOT
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