5 problems

Invariance conjecture. The output of Algorithm is independent of how the set of constituents is split by Algorithm.

Let $F$ be a generic smooth function constructed as a composition according to a feedforward neural-network architecture, with constituent functions either of lower arity or of the…

Let $\mathcal{N}$ be a feedforward neural network with inputs labeled by the coordinate functions $x_1,\dots,x_n$, and let $F=F(x_1,\dots,x_n)$ be smooth near a point…

Fix a feedforward neural network hierarchy in which constituent functions have fewer inputs than the resulting superposition, and let $F$ be a smooth function of the network inputs…

Let $F=F(x_1,\dots,x_n)$ be a smooth function represented by a feedforward neural network whose constituent functions have lower arity, or whose neurons apply a smooth univariate a…