Fast LapSum: Exact Differentiable Top-$k$ at Million Scale
Selecting the top-$k$ elements is a fundamental operation for inducing sparsity in large-scale models and optimization problems, enabling robust expert activation, token routing or attention pruning. However, hard top-$k$ is non-differentiable, while existing differentiable alternatives become increasingly expensive as the number of coordinates grows. We introduce Fast LapSum, a scalable solver for the LapSum soft top-$k$ formulation that preserves an exact selection mass of $k$, while supporting end-to-end differentiation. In Fast LapSum, we reduce sorting cost using probabilistic bracketing, which restricts sorting to a narrow band of scores around the threshold using a binomial order-s...
| Authors | Jakub Antczak, Joanna Wojciechowicz, Kamil Książek et al. |
|---|---|
| Primary category | cs.AI |
| Published | 7 August 2026 |
| Last updated at source | 8 October 2026 |
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