论文标题
从无限宽的神经网络散装稀疏的插值：一种原子规范方法
Convexifying Sparse Interpolation with Infinitely Wide Neural Networks: An Atomic Norm Approach
论文作者
论文摘要
这项工作通过稀疏（神经元计数），无限宽，单个隐藏的层神经网络，研究了具有泄漏的整流线性单位激活的问题。使用[Chandrasekaran等，2012]的原子规范框架，我们得出了对该问题的几个不同约束的网络的重量和偏见的相应原子集的凸壳的简单特征，从而获得了这些问题的等效凸构。还提出了将我们提议的框架扩展到二进制分类问题的适度扩展。我们通过实验探索所得制剂的功效，并与通过梯度下降训练的网络进行比较。
This work examines the problem of exact data interpolation via sparse (neuron count), infinitely wide, single hidden layer neural networks with leaky rectified linear unit activations. Using the atomic norm framework of [Chandrasekaran et al., 2012], we derive simple characterizations of the convex hulls of the corresponding atomic sets for this problem under several different constraints on the weights and biases of the network, thus obtaining equivalent convex formulations for these problems. A modest extension of our proposed framework to a binary classification problem is also presented. We explore the efficacy of the resulting formulations experimentally, and compare with networks trained via gradient descent.
