两篇新的arXiv论文探讨了在神经网络中实现ReLU（Rectified Linear Unit）函数的先进数学技术。第一篇论文《张量积精炼迭代的精确ReLU实现》将现有理论扩展到二维，证明了标量二进精炼算子迭代可以通过固定宽度和与迭代次数成比例的深度来实现精确的ReLU。第二篇论文《齐次曲线精炼的ReLU实现的精确环路控制器》引入了一个“精确环路控制器”，以实现分段线性曲线的类似精确ReLU实现，为该问题提供了一种更几何的方法。 AI
影响 这些论文引入了理解和实现ReLU激活函数的新颖数学框架，可能影响未来的神经网络架构和优化技术。
排序理由 两篇在arXiv上发表的学术论文，详细介绍了神经网络中ReLU实现的新数学方法。
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arXiv:2605.03917v1 Announce Type: cross Abstract: We study scalar dyadic refinement operators on R^2 of the form (Vf)(x,y) = sum_{(j,k) in Z^2} c_{j,k} f(2x-j, 2y-k), where only finitely many mask coefficients c_{j,k} are nonzero. Under a fixed support-window hypothesis, we prove…
We study scalar dyadic refinement operators on R^2 of the form (Vf)(x,y) = sum_{(j,k) in Z^2} c_{j,k} f(2x-j, 2y-k), where only finitely many mask coefficients c_{j,k} are nonzero. Under a fixed support-window hypothesis, we prove that for every compactly supported continuous pie…
arXiv:2605.01655v1 Announce Type: cross Abstract: We study homogeneous refinement operators \((V\gamma)(t)=\sum_{j\in\mathbb Z}A_j\gamma(Mt-j)\), acting on compactly supported continuous piecewise linear curves \(\gamma:\mathbb R\to\mathbb R^p\), where \(M\ge2\) and only finitely…