无限宽有界范数网络在函数空间中看起来如何？
How do infinite width bounded norm networks look in function space?
摘要：
我们考虑的问题是，具有无限数量单元（无限宽度）的ReLU网络可以捕获哪些函数，但是整个网络的欧几里得范数（系统中所有权重的平方和，除了每个单元的非正则化偏置项）是有界的;或者等价地，近似给定函数所需的最小范数是什么。对于函数$f : \mathbb R \rightarrow \mathbb R$和一个单一的隐藏层，我们表明，表示$f$的最小网络范数是$\max(\int |f''(x)| dx, |f'(-\infty) + f'(+\infty)|)$，因此，最小范数适合一个样本是由线性样条插值。
英文摘要：
We consider the question of what functions can be captured by ReLU networks with an unbounded number of units (infinite width), but where the overall network Euclidean norm (sum of squares of all weights in the system, except for an unregularized bias term for each unit) is bounded; or equivalently what is the minimal norm required to approximate a given function. For functions $f : \mathbb R \rightarrow \mathbb R$ and a single hidden layer, we show that the minimal network norm for representing $f$ is $\max(\int |f''(x)| dx, |f'(-\infty) + f'(+\infty)|)$, and hence the minimal norm fit for a sample is given by a linear spline interpolation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
