Full-Grad (Full-Gradient Representation) is an attribution method that combines input gradients with bias gradients across all layers — providing a complete, full-gradient saliency map that accounts for both the sensitivity and the bias terms throughout the entire network.

How Full-Grad Works

• Input Gradient: Standard gradient $partial f / partial x$ captures input sensitivity.
• Bias Gradients: For each layer $l$, compute $partial f / partial b_l$ — the sensitivity to each layer's bias.
• Aggregation: Full saliency = input gradient × input + sum of bias gradients mapped to input space.
• Completeness: The full-gradient satisfies $f(x) = sum ( ext{input contributions}) + sum ( ext{bias contributions})$.

Why It Matters

• Complete Attribution: Unlike vanilla gradients or Grad-CAM, Full-Grad accounts for ALL sources of the prediction.
• Bias Terms: Standard gradient methods ignore bias terms — Full-Grad includes their contribution.
• High Quality: Produces cleaner, more faithful saliency maps that better highlight relevant input regions.

Full-Grad is the complete gradient picture — combining input and bias gradients for fully faithful attribution across the entire network.