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Towards formal verification of neural networks

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  • 21. • 2 8 C K 3 M K K K ? / / K T IP K?L O K A M I IA KM A K MPIK L 1 +MC IK LCI I MCI? ? / L CK BLL K C S K I? K B ? : K A M I OI 8 C M B ? 8RLM / : ( CMM , PPP O L IKB A ? M I 5 L C K O( ?A • , 0 KM I I MKI K • , --- IM PK MM M R MC K • , /I ? ? I? 0C B 8 LI O K 8. ) L ? • .?? B M A M I L MI L ? I LMK M KI B M I
  • 22.
  • 23. • 4R LF" 6TH IMT I " LF" LC R" D V SD H HB HML M CDDN LDR LD TM I "X 0. ( HLSH DC I" G N- HS M F A ,) G N - FH GRA BMK SD HCDDN C S • - K FD 0 H HB HML 0 2.: " K FD9D " 9 " :/ • - MB CSD H MAR LD • - 1H B D HW HML" 7 VD AV 7 VD
  • 24.
  • 25. • 2 = T 0 /=LLA 1 1 GG 3 G = = J DA ALBAL 7AG KGAR, . ABB A MJG AL BJL AL BS C AAK A L=G A JL M 0. ( + D K, =LR JLC = M + ( ) D KM, C D J C S = TT 7AG KGAR0= ( + • , = L JL A JGG M J = J = A MSM A BJL = A = L L=B .0. • , GJ =G CGJ =G = ALM=L =G LJ M AMM • , " 57. MJG AL AR A A J D= GA 7A5: • 57. 5 A=L 7A=G .L D A • 57. MJG AL M M =GGS =MA J =G M KGAR A DJ
  • 26. • , = (-- 2 = = =A A A = = 2 2 =A = 2 =2 = =D = 2= . • . 2 2= AA 2A 2 . 2 2A H I H • ) D A A = 2 = 2 A A ,0 A D 2 A 2A A = • 2 = . = ,0 A D = =A = 2A A • 0 A 2 2= = 2 2 A A D
  • 27. • : FC 6 B F B 6 -/) B A C : 6 / - 6 A C 0 F / - / F • 6 0 F B 6 -/) B A • , A 6 C B :CC ( B B BA AB 6 • + BCA CB A A A B C 6 B C 6 A 6B • !" = ∑%& ∈( )",+!+ A !+ ∈ , • ( B A B . ( B A B • -" ≤ !" ≤ /" A !" ∈ , ∪ 1 • : B A C B A BB C α ∶ , ∪ 1 → ℝ B : C: C ∀!+ ∈ 1. -+≤ α(!+) ≤ /+ 6 CA C B C B C: A 6B C A C B
  • 28. • , . 0 0 !", !$ ∈ & : 0 !$ = ReLU(!") • 0 : 0 0 0 1 0 0 0 A • ) 0 0 , A- 1A 0 :0 , . 0 A 0 % 0 0 A ( A
  • 29. • B? C? A C? . B? , • K ?G I B A B?? BA B A K B GA AA ) G • + BG C B A B? • (G A IB L BB ?? M 0 3 AB B?G BA
  • 30. - - - - - • - I .F D L FE F 3 " I E . " .F M E E MF I + N L F :I • I+ : FD F E • + , F I FE LF E 12/5 • + F F: L I F: I E II • + 51 0 E N FE F 07 1 N3FF //5 E E FEI E F FE
  • 31. - - - - - I L B E E F F E I E= 4 B N B E + B E ( I 5, IEBL E F BB = N F I I ) 5EBL 13 N B E I I =E = N I • I E A L = E E P I E= EL = N 4 1 E F = 4 1 = I B IEB E 0= I B I 02 .,50-1. • I B I = B E E F 005 0 B 0 = I B 5 I E = F I = N I 5, IEBL B I 5E I =E E I F EF E 3 I 3 I
  • 32. - - - - - • • ure 3: Two pairs of vehicle trajectories, where the first one is non-colliding, and the second one