MLmagnituudi

MLmagnituudi is a metric used in machine learning to quantify the magnitude of a model’s response to changes in its input. It serves as a measure of how sensitive a model’s predictions are to perturbations in the input space, focusing on the scale of the local gradient or Jacobian.

Definition and variants: For a differentiable model f: R^n -> R, the local MLmagnituudi at input x can be defined as M(x) = ||∇f(x)||2, the Euclidean norm of the input gradient. For models with vector outputs, a common variant is M(x) = ||Jf(x)||F, the Frobenius norm of the Jacobian. A global measure across an input distribution p(x) is M = E_{x~p}[M(x)]. Depending on the application, one may use L1, L2, or spectral norms, or focus on a per-layer Jacobian as a hierarchical version.

Computation: If the model is differentiable, gradients are obtained via automatic differentiation. For non-differentiable models or black-box settings, finite-difference approximations or surrogate models may be employed to estimate the local magnitude.

Applications: MLmagnituudi is used to audit robustness to input perturbations, compare sensitivity across architectures or training procedures, and monitor stability during deployment. It can complement saliency maps and feature-attribution methods by providing a scalar sense of overall sensitivity.

Limitations: The value depends on the chosen input distribution and output scale, so cross-task comparisons require normalization. It does not capture all aspects of robustness, such as vulnerability to high-leverage, low-gradient perturbations, and can be computationally intensive for high-dimensional inputs.

Origin and status: The term has appeared in some experimental, non-standard discussions within the ML community and is not universally standardized.