提出线性时间可微顶K选择方法，提升推荐系统训练效率与性能。

Cascade ranking is a widely adopted paradigm in large-scale information retrieval systems for Top-K item selection. However, the Top-K operator is non-differentiable, hindering end-to-end training. Existing methods include Learning-to-Rank approaches (e.g., LambdaLoss), which optimize ranking metrics like NDCG and suffer from objective misalignment, and differentiable sorting-based methods (e.g., ARF, LCRON), which relax permutation matrices for direct Top-K optimization but introduce gradient conflicts through matrix aggregation. A promising alternative is to directly construct a differentiable approximation of the Top-K selection operator, bypassing the use of soft permutation matrices. However, even state-of-the-art differentiable Top-K operator (e.g., LapSum) require $O(n \log n)$ complexity due to their dependence on sorting for solving the threshold. Thus, we propose DFTopK, a novel differentiable Top-K operator achieving optimal $O(n)$ time complexity. By relaxing normalization constraints, DFTopK admits a closed-form solution and avoids sorting. DFTopK also avoids the gradient conflicts inherent in differentiable sorting-based methods. We evaluate DFTopK on both the public benchmark RecFLow and an industrial system. Experimental results show that DFTopK significantly improves training efficiency while achieving superior performance, which enables us to scale up training samples more efficiently. In the online A/B test, DFTopK yielded a +1.77% revenue lift with the same computational budget compared to the baseline. To the best of our knowledge, this work is the first to introduce differentiable Top-K operators into recommendation systems and the first to achieve theoretically optimal linear-time complexity for Top-K selection. We have open-sourced our implementation to facilitate future research in both academia and industry.