论文标题
单调微分排序网络
Monotonic Differentiable Sorting Networks
论文作者
论文摘要
可区分的排序算法允许对排序和排名监督进行培训，其中仅知道样品的排序或排名。已经提出了各种方法来应对这一挑战，从基于最佳的基于运输的sindhorn分类算法到使经典排序网络可区分。当前可区分排序方法的一个问题是它们是非单调的。为了解决这个问题，我们提出了一种新颖的有条件互换操作的放松，该操作可以保证在可区分的分类网络中单调性。我们介绍了一个Sigmoid功能系列，并证明它们产生了单调的可区分分类网络。单调性确保梯度始终具有正确的符号，这在基于梯度的优化中是一个优势。我们证明，单调可区分的排序网络对以前的可区分排序方法有所改善。
Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal transport-based differentiable Sinkhorn sorting algorithms to making classic sorting networks differentiable. One problem of current differentiable sorting methods is that they are non-monotonic. To address this issue, we propose a novel relaxation of conditional swap operations that guarantees monotonicity in differentiable sorting networks. We introduce a family of sigmoid functions and prove that they produce differentiable sorting networks that are monotonic. Monotonicity ensures that the gradients always have the correct sign, which is an advantage in gradient-based optimization. We demonstrate that monotonic differentiable sorting networks improve upon previous differentiable sorting methods.
