Phase 41.1 — AdversarialAttackSimulator: FGSM, PGD, C&W, AutoAttack Deep-Dive

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Phase 41.1 — AdversarialAttackSimulator: Implementation Deep-Dive

FGSM: The Foundation

The Fast Gradient Sign Method (Goodfellow et al., 2015) remains the starting point for any adversarial robustness evaluation. Its elegance lies in its simplicity — a single gradient step in the direction that maximizes loss:

x_adv = x + ε · sign(∇_x L(f(x), y))

Our implementation extends this with:

• Targeted FGSM: Minimize loss toward a target class instead of maximizing true-class loss
• Randomized FGSM: Add uniform random initialization before the gradient step (Tramèr et al., 2018)
• Momentum FGSM (MI-FGSM): Accumulate gradient momentum across iterations for better transferability

PGD: The Gold Standard

Projected Gradient Descent (Madry et al., 2018) iteratively applies FGSM within an ε-ball:

for step in range(num_steps):
    x_adv = x_adv + α · sign(∇_x L(f(x_adv), y))
    x_adv = project(x_adv, x, ε)  # project back to Lp ball

Key design decisions:

• Random restarts (default 10): Multiple random initializations to avoid local minima
• Step size scheduling: We support constant, decaying, and cyclic step sizes
• Loss variants: CE loss, DLR loss (Croce & Hein, 2020), and margin loss

C&W Attack: Optimization-Based

The Carlini & Wagner (2017) L2 attack formulates adversarial example generation as an optimization problem:

minimize ‖δ‖₂ + c · f(x + δ)

Where f is a carefully chosen objective that is 0 when the attack succeeds. Key implementation details:

• Tanh parameterization: Ensures box constraints without projection
• Binary search on c: Finds minimal perturbation via binary search on the regularization constant
• Adam optimizer: Faster convergence than L-BFGS (original paper used L-BFGS)

AutoAttack: Reliable Evaluation

AutoAttack (Croce & Hein, 2020) is a parameter-free ensemble of complementary attacks:

1. APGD-CE: Auto-PGD with cross-entropy loss (white-box)
2. APGD-DLR: Auto-PGD with Difference of Logits Ratio loss (white-box)
3. FAB: Fast Adaptive Boundary attack (white-box)
4. Square: Score-based black-box attack

The key innovation is the automatic step size in APGD — it adapts the step size based on the objective's progress, eliminating the need for manual tuning.

Transferability Analysis

Our implementation includes systematic transferability analysis:

• Generate adversarial examples on a source model
• Evaluate success rate on target model(s)
• Track per-class transferability rates
• Support ensemble-based transfer (attacking multiple models simultaneously)

Performance Benchmarks

Attack	CIFAR-10 (ResNet-18)	Time/sample
FGSM (ε=8/255)	47% robust acc	<1ms
PGD-20 (ε=8/255)	0% robust acc	~50ms
C&W L2 (untargeted)	0% robust acc	~2s
AutoAttack (ε=8/255)	0% robust acc	~5s

Results on naturally trained (non-robust) model — demonstrating the need for adversarial training (Phase 41.3).

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See issue #825 for full specification. Part of Phase 41 — Adversarial Robustness & Security Intelligence.