8 problems

Let $\mathscr{L}$ be a rich loss space, for example the space of all continuous losses satisfying mild growth conditions, and let optimality be defined by a natural optimality noti…

Let $p,q>0$ be distinct exponents, and for each $r>0$ let $\mathcal{L}_r$ be the class of losses whose local behavior near $a=\theta$ is $c(\theta)|\theta-a|^r+o(|\theta-a|^r)$ wit…

Loss decomposition conjecture. The loss may also be decomposed into two parts: one controlling the error from invariance, and the other controlling the error from the target.

Rotational-invariance conjecture. If the activation function $csigma$ is a smooth function that is not linear and the data set contains $cgeq 2$ data points, then

L2–Morse conjecture. For neural networks with nonlinear activation functions and enough data points, the L2-regularized loss function becomes Morse.

Two-scale loss conjecture. The two-scale loss network performs much better on misclassified objects by decreasing the difference between the probability of the correct class and th…

Consider a classification network trained with the traditional single-scale loss and compare it with the two-scale loss. For a misclassified object, its assigned maximal class prob…

Mass comparison conjecture. The total mass of poorly classified objects for the two-scale minimizant cannot exceed a constant multiple of the mass of marginally classified objects: