nsl.lib.random_in_norm_ball

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Generates a random sample in a norm ball, conforming the given structure.

This function expects tensor_structure to represent a batch of examples, where the tensors in the structure are features. The norms are calculated in the whole feature space (including all tensors).

For L-inf norm, each feature dimension can be sampled independently from a uniform distribution. For L2 and L1 norms, we use the result (Corollary 4 in Barthe et al., 2005) that the first n coordinates of a uniformly random point on the p-norm unit sphere in R^(n+p) are uniformly distributed in the p-norm unit ball in R^n. For L2 norm, we draw random points on the unit sphere from the standard normal distribution which density is proportional to exp(-x^2)(Corollary 1 in Harman and Lacko, 2010). For L1 norm, we draw random points on the 1-norm unit sphere from the standard Laplace distribution which density is proportional to exp(-|x|). More details on the papers: https://arxiv.org/abs/math/0503650 and https://doi.org/10.1016/j.jmva.2010.06.002

tensor_structure A (nested) collection of batched, floating-point tensors. Only the structure (number of tensors, shape, and dtype) is used, not the values. The first dimension of each tensor is the batch size and must all be equal.
radius The radius of the norm ball to sample from.
norm_type One of nsl.configs.NormType which specifies the norm of the norm ball.

A (nested) collection of tensors in the same structure as tensor_structure but has its values drawn randomly. The norm of each example in the batch is less than or equal to the given radius.