The problem of computing minimally sparse solutions of under-determined linear systems is $NP$ hard in general. Subsets with extra properties, may allow efficient algorithms, most notably problems with the restricted isometry property (RIP) can be solved by convex $\ell_1$-minimization. While these classes have been very successful, they leave out many practical applications. In this paper, we consider adaptable classes that are tractable after training on a curriculum of increasingly difficult samples. The setup is intended as a candidate model for a human mathematician, who may not be able to tackle an arbitrary proof right away, but may be successful in relatively flexible subclasses, or areas of expertise, after training on a suitable curriculum.

翻译：求解欠定线性系统的最小稀疏解问题通常是 $NP$ 难的。具有额外性质的子集可能允许高效算法，最值得注意的是具有限制等距性质（RIP）的问题可通过凸 $\ell_1$-最小化求解。尽管这些类别非常成功，但它们排除了许多实际应用。在本文中，我们考虑在逐步增加难度的样本课程训练后可处理的自适应类别。该设置旨在作为人类数学家的候选模型，其可能无法立即解决任意证明，但在经过适当课程训练后，可能在相对灵活的子类或专业领域中获得成功。