LaPrune: Controllable Differentiable Sparsity at Million Scale

Abstract:Top-$k$ selection determines which components of a sparse model remain active. Hard selection blocks gradients, while continuous relaxations often couple mask hardness to the selected mass. We introduce LaPrune, a mathematically exact-budget differentiable layer that controls the normalized second moment while preserving the selected mass. A LapSum barrier preserves the selection mass, and a normalized second-moment constraint moves the mask from a dense equal-mass allocation toward hard top-$k$ at each budget. We derive a population prediction of the saturated fraction, a near-binary limiting law, and a tight worst-case guarantee on the near-zero fraction. The normalized hardness parameter is invariant to score scale, while a fixed LapSum temperature is not.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2608.04057 [cs.LG]

(or arXiv:2608.04057v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.04057 Focus to learn more arXiv-issued DOI via DataCite

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