This lecture: Deep-enough linear ResNet has a global minimum in 1-vicinity of zero and does not have any other critical points there (following https://arxiv.org/abs/1611.04231). Some known results about shallow non-linear networks. All minima of wide-enough shallow sigmoid network are global (following https://ieeexplore.ieee.org/document/410380).
Next lecture announcement: RECAP: All minima of wide-enough shallow sigmoid network are global (https://ieeexplore.ieee.org/document/410380). Generalization to deep sigmoid networks (https://arxiv.org/abs/1704.08045).