标题： 几何与过度参数化下两层神经网络全局最小值的局部恢复 显示英文标题

标题： Geometry and Local Recovery of Global Minima of Two-layer Neural Networks at Overparameterization

摘要： 在适度的假设下，我们研究了两层神经网络在全局最小值附近的损失景观的几何结构。 利用新的技术，我们证明了：(i) 随着样本量的增长，具有零泛化误差的全局最小值如何在几何上与其他全局最小值分离；以及 (ii) 梯度流动力学的局部收敛特性和速率。 我们的结果表明，两层神经网络可以在过度参数化的区域内被局部恢复。 显示英文摘要

摘要： Under mild assumptions, we investigate the geometry of the loss landscape for two-layer neural networks in the vicinity of global minima. Utilizing novel techniques, we demonstrate: (i) how global minima with zero generalization error become geometrically separated from other global minima as the sample size grows; and (ii) the local convergence properties and rate of gradient flow dynamics. Our results indicate that two-layer neural networks can be locally recovered in the regime of overparameterization.