integrated hessians

**Integrated Hessians** is an **attribution method that captures feature interactions by integrating second-order derivatives (the Hessian) along a path from a baseline to the input** — extending Integrated Gradients to detect pairwise feature interactions that first-order methods miss. **How Integrated Hessians Works** - **Interaction Attribution**: $IH_{ij} = (x_i - x_i')(x_j - x_j') int_0^1 frac{partial^2 F}{partial x_i partial x_j} dalpha$ along the interpolation path. - **Pairwise**: Captures how pairs of features jointly influence the prediction (cross-terms). - **Completeness**: Integrated Hessians + Integrated Gradients together fully decompose the prediction. - **Approximation**: Computed using finite differences or automatic differentiation of the Hessian. **Why It Matters** - **Interaction Detection**: Reveals which feature pairs interact — critical for semiconductor processes where variables interact strongly. - **Beyond Additivity**: First-order methods (IG, SHAP) assume additive contributions — Integrated Hessians captures non-additive effects. - **Process Insight**: In pharmaceutical/semiconductor processes, interaction effects often dominate main effects. **Integrated Hessians** is **the second-order attribution** — capturing how pairs of features jointly influence predictions beyond their individual contributions.