Fast LapSum: Exact Differentiable Top-$k$ at Million Scale

arXiv:2608.06912v3 Announce Type: replace Abstract: 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

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