hopskipjump

**HopSkipJump** is a **query-efficient decision-based adversarial attack that uses gradient estimation at the decision boundary** — improving upon the Boundary Attack with smarter step sizes and boundary-aware gradient estimation for faster convergence. **How HopSkipJump Works** - **Binary Search**: Find the exact decision boundary between the clean and adversarial points. - **Gradient Estimation**: Estimate the boundary gradient using Monte Carlo sampling (random projections). - **Step**: Move along the estimated gradient direction while staying near the boundary. - **Iterate**: Repeat binary search → gradient estimation → step with decreasing step sizes. **Why It Matters** - **Query Efficient**: Converges to strong adversarial examples with far fewer model queries than Boundary Attack. - **$L_2$ and $L_infty$**: Works for both distance metrics — flexible threat model. - **Practical**: Effective against real-world deployed models with limited API access. **HopSkipJump** is **smart boundary navigation** — combining binary search, gradient estimation, and careful stepping for efficient decision-based adversarial attacks.