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Knapsack and Top-k operators are useful for selecting discrete subsets of variables. However, their integration into neural networks is challenging as they are piecewise constant, yielding gradients that are zero almost everywhere. This codebase casts these operators as dynamic programs, and provides differentiable relaxations by regularizing the underlying recursions. It includes efficient parallel algorithms via Numba, supporting both deterministic and stochastic forward passes, as well as vector-Jacobian products for the backward pass. Supported regularization types: - Shannon entropy (dense and equivariant operators) - Gini entropy (sparse operators) - 1.5-Tsallis entropy (sparse and smooth operators) Installation Simply copy relevant functions to your project. 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