Fast Gradient Sign Method

The Fast Gradient Sign Method (FGSM) is the foundational adversarial attack introduced by Goodfellow et al. in 2014, demonstrating that neural networks can be fooled by perturbations so small they are invisible to humans. The method exploits the local linearity of high-dimensional classifiers: it takes a single step in the direction of the input's loss gradient, scaled by a tiny epsilon, to produce a misclassified input. FGSM is not merely a trick but a diagnostic: it reveals that what networks learn is not human-like conceptual structure but fragile statistical correlations in input space. The method generalizes naturally to iterative variants like the Basic Iterative Method and projected-gradient attacks, but its real contribution is conceptual — it proved that adversarial examples are not rare pathological cases but structural features of the geometry of neural network decision boundaries.