In this paper, we present an approach to automated solving of triangle
ruler-and-compass construction problems using finite-domain constraint solvers.
The constraint model is described in the MiniZinc modeling language, and is
based on the automated planning. The main benefit of using general constraint
solvers for such purpose, instead of developing dedicated tools, is that we can
rely on the efficient search that is already implemented within the solver,
enabling us to focus on geometric aspects of the problem. We may also use the
solver's built-in optimization capabilities to search for the shortest possible
constructions. We evaluate our approach on 74 solvable problems from the
Wernick's list, and compare it to the dedicated triangle construction solver
ArgoTriCS. The results show that our approach is comparable to dedicated tools,
while it requires much less effort to implement. Also, our model often finds
shorter constructions, thanks to the optimization capabilities offered by the
constraint solvers.

这篇论文介绍了一种使用有限域约束求解器自动解决三角形尺规作图问题的方法，并通过与专用工具进行比较，证明了该方法不仅具有相当的性能，而且实现起来需要更少的工作量。

使用约束求解器自动化三角尺和指南针构造

Automation of Triangle Ruler-and-Compass Constructions Using Constraint  Solvers

We analyze geometric aspects of the gradient descent algorithm in Deep
Learning (DL) networks. In particular, we prove that the globally minimizing
weights and biases for the $\mathcal{L}^2$ cost obtained constructively in
[Chen-Munoz Ewald 2023] for underparametrized ReLU DL networks can generically
not be approximated via the gradient descent flow. We therefore conclude that
the method introduced in [Chen-Munoz Ewald 2023] is disjoint from the gradient
descent method.

我们分析了深度学习网络中梯度下降算法的几何方面。具体而言，我们证明了对于欠参数的 ReLU 深度学习网络，Chen-Munoz Ewald 2023 论文中构建性地获得的全局最小成本所对应的权重和偏差通常无法通过梯度下降流逼近。因此，我们得出结论，Chen-Munoz Ewald 2023 论文中介绍的方法与梯度下降方法是不相同的。