nsl.lib.maximize_within_unit_norm

Solves the maximization problem weights^T*x with the constraint norm(x)=1.

nsl.lib.maximize_within_unit_norm(
    weights, norm_type, epsilon=1e-06
)

This op solves a batch of maximization problems at one time. The first axis of weights is assumed to be the batch dimension, and each "row" is treated as an independent maximization problem.

This op is mainly used to generate adversarial examples (e.g., FGSM proposed by Goodfellow et al.). Specifically, the weights are gradients, and x is the adversarial perturbation. The desired perturbation is the one causing the largest loss increase. In this op, the loss increase is approximated by the dot product between the gradient and the perturbation, as in the first-order Taylor approximation of the loss function.

weights A Tensor or a collection of Tensor objects representing a batch of weights to define the maximization objective. If this is a collection, the first dimension of all Tensor objects should be the same (i.e. batch size).
norm_type One of nsl.configs.NormType, the type of the norm in the constraint.
epsilon A lower bound value for the norm to avoid division by 0.

A Tensor or a collection of Tensor objects (with the same structure and shape as weights) representing a batch of adversarial perturbations as the solution to the maximization problems.