Adversarial Training and Provable Defenses: Bridging the Gap S 0 - - PowerPoint PPT Presentation

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Adversarial Training and Provable Defenses: Bridging the Gap S 0 - - PowerPoint PPT Presentation

Nov 11, 2022 274 likes β€’459 views

Adversarial Training and Provable Defenses: Bridging the Gap S 0 1 1 = 1 2 3 Conv + ReLU Conv + ReLU Linear =

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SLIDE 1

Adversarial Training and Provable Defenses: Bridging the Gap

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SLIDE 2

π‘€βˆž

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SLIDE 3

𝑦 S0 𝑦 β„Žπœ„ = β„Žπœ„

𝑙 ∘ β„Žπœ„ π‘™βˆ’1 ∘ β‹― ∘ β„Žπœ„ 1

β„Žπœ„

1

β„Žπœ„

2

β„Žπœ„

3

Conv + ReLU Conv + ReLU Linear

𝑦′ ∈ 𝑇0(𝑦) 𝑦1

β€²

𝑦2

β€²

𝑦3

β€² = β„Žπœ„(𝑦′)

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SLIDE 4

π‘‘π‘ˆβ„Žπœ„ 𝑦′ + 𝑒 < 0, βˆ€π‘¦β€² ∈ 𝑇0(𝑦) β„Žπœ„

1

β„Žπœ„

2

β„Žπœ„

3

Conv + ReLU Conv + ReLU Linear

𝑦′ ∈ 𝑇0(𝑦) 𝑦1

β€²

𝑦2

β€²

𝑦3

β€² = β„Žπœ„(𝑦′)

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SLIDE 5

𝐷0 𝑦 = 𝑇0(𝑦) 𝐷1 𝑦 𝐷2 𝑦 𝐷3 𝑦 β„Žπœ„

1

β„Žπœ„

2

β„Žπœ„

3

Conv + ReLU Conv + ReLU

Guarantees: π‘‘π‘ˆβ„Žπœ„ 𝑦′ + 𝑒 < 0, βˆ€π‘¦β€² ∈ 𝑇0(𝑦)

Check output condition: π‘‘π‘ˆπ‘¦3

β€² + 𝑒 < 0, βˆ€π‘¦3 β€² ∈ 𝐷3 𝑦

Linear

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SLIDE 6

β„’ min

πœ„ 𝐹 𝑦,𝑧 ~𝐸

max

π‘¦β€²βˆˆπ‘‡0(𝑦) β„’(β„Žπœ„ 𝑦′ , 𝑧)

lower upper

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SLIDE 7
  • lower
  • upper
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SLIDE 8

𝐷0 𝑦 = 𝑇0(𝑦) 𝐷1 𝑦 𝐷2 𝑦 𝐷3 𝑦 β„Žπœ„

1

β„Žπœ„

2

β„Žπœ„

3

π‘‘π‘ˆπ‘¦3

β€² + 𝑒 < 0 β†’ certification fails

𝑦1

β€²

𝑦2

β€²

𝑦1

β€²

𝑦3

β€²

𝑦2

β€²

𝑦3

β€²

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SLIDE 9

𝑇0(𝑦) 𝐷1 𝑦 , 𝐷2 𝑦 , 𝐷3(𝑦)

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SLIDE 10

𝐷0 𝑦 = 𝑇0(𝑦) 𝐷1 𝑦 𝐷2 𝑦 𝐷3 𝑦 β„Žπœ„

1

β„Žπœ„

2

β„Žπœ„

3

Conv + ReLU Conv + ReLU Linear

𝑦1

β€²

𝑦2

β€²

𝑦1

β€²

β„’(𝑦3

β€², 𝑧)

𝑦2

β€²

𝑦3

β€²

π›Όπœ„β„’(𝑦3

β€², 𝑧)

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SLIDE 11
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SLIDE 12

projection

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π·π‘š 𝑦 = π‘π‘š + π΅π‘šπ‘“ 𝑓 ∈ βˆ’1, 1 π‘›π‘š π‘π‘š π΅π‘š π‘€βˆž πœ— 𝑏0 = 𝑦 𝐡0 = πœ—π½

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SLIDE 14

𝑦1

β€² ≔ 2𝑓1 βˆ’ 𝑓2

𝑦2

β€² ≔ 𝑓1 + 𝑓2

𝑓2 𝑓1 𝑦2

β€²

𝑦1

β€²

Key idea

𝑦′ = π‘π‘š + π΅π‘šπ‘“

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SLIDE 15

Method Accuracy (%) Certified Robustness (%)

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SLIDE 16

Method Accuracy (%) Certified Robustness (%)

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SLIDE 17