integrated gradients

**Integrated Gradients** is an **attribution method that assigns importance scores to input features by accumulating gradients along a straight-line path from a baseline to the actual input** — satisfying key axioms (completeness, sensitivity) that vanilla gradients violate. **How Integrated Gradients Works** - **Baseline**: A reference input $x'$ (typically all zeros, black image, or PAD tokens). - **Path**: Interpolate linearly from $x'$ to $x$: $x(alpha) = x' + alpha(x - x')$ for $alpha in [0,1]$. - **Integration**: $IG_i = (x_i - x_i') int_0^1 frac{partial F(x(alpha))}{partial x_i} dalpha$ — accumulated gradient × input difference. - **Approximation**: Approximate the integral with a Riemann sum using 20-300 interpolation steps. **Why It Matters** - **Completeness Axiom**: Attributions sum exactly to the difference $F(x) - F(x')$ — every bit of the prediction is accounted for. - **Sensitivity**: If a feature matters (changing it changes the prediction), it gets non-zero attribution. - **Implementation**: Simple to implement — just requires gradient computation at interpolated inputs. **Integrated Gradients** is **following the gradient along the path** — accumulating feature importance from a baseline to the input for principled, complete attribution.