trades

**TRADES** (TRadeoff-inspired Adversarial DEfense via Surrogate-loss minimization) is a **robust training method that explicitly balances clean accuracy and adversarial robustness** — decomposing the robust risk into natural error plus a boundary error regularization term. **TRADES Formulation** - **Objective**: $min_ heta mathbb{E}[underbrace{L(f(x), y)}_{ ext{natural loss}} + eta underbrace{max_{|delta|leqepsilon} KL(f(x) | f(x+delta))}_{ ext{robustness regularizer}}]$. - **Natural Loss**: Standard cross-entropy on clean inputs (maintains clean accuracy). - **Robustness Term**: KL divergence between clean and adversarial predictions (encourages consistent predictions). - **Trade-Off ($eta$)**: Higher $eta$ = more robust but lower clean accuracy. Lower $eta$ = higher clean accuracy but less robust. **Why It Matters** - **Better Trade-Off**: TRADES achieves better accuracy-robustness trade-offs than standard adversarial training. - **Theoretical Foundation**: Grounded in the decomposition of robust risk (Zhang et al., 2019). - **Tunable**: The $eta$ parameter gives explicit control over the accuracy-robustness trade-off. **TRADES** is **the balanced defense** — explicitly optimizing both clean accuracy and adversarial robustness with a tunable trade-off parameter.