Jacobian Matrix
In AI explainability, the matrix of all first-order partial derivatives of a model’s outputs w.r.t. its inputs, used to assess sensitivity and feature importance.
A mathematical tool that quantifies how slight changes in each input dimension affect each output dimension - in neural networks, it can be used to compute saliency maps or measure local sensitivity. Governance uses Jacobian-based metrics to identify vulnerabilities (e.g., adversarial sensitivity) and to generate explanations highlighting which input features most influence a given decision.
In a medical-imaging AI, engineers compute the Jacobian for each pixel with respect to the “tumor” probability. High-magnitude regions on the saliency map reveal which image areas drive the diagnosis, helping radiologists verify that the model focuses on plausible anatomical features rather than artifacts.
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