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A general approximation lower bound in $L^p$ norm, with applications to feed-forward neural networks
Given two sets $F$, $G$ of real-valued functions, we first prove a general lower bound on how well functions in $F$ can be approximated in $L^p(\mu)$ norm by functions in $G$, for any $p \geq 1$ and any probability measure $\mu$.
Existence, Stability and Scalability of Orthogonal Convolutional Neural Networks
Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness.
The loss landscape of deep linear neural networks: a second-order analysis
We characterize, among all critical points, which are global minimizers, strict saddle points, and non-strict saddle points.
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