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Hitting Sets and Reconstruction for Dense Orbits in $\text{VP}_e$ and $ΣΠΣ$ Circuits
In this paper we study polynomials in $\text{VP}_e$ (polynomial-sized formulas) and in $\Sigma\Pi\Sigma$ (polynomial-size depth-$3$ circuits) whose orbits, under the action of the affine group $\text{GL}_n^{\text{aff}}(\mathbb{F})$, are $\mathit{dense}$ in their ambient class.
Computational Complexity
Learnability can be undecidable
We show that, in some cases, a solution to the ‘estimating the maximum’ problem is equivalent to the continuum hypothesis.
A learning problem that is independent of the set theory ZFC axioms
We consider the following statistical estimation problem: given a family F of real valued functions over some domain X and an i. i. d.
Teaching and compressing for low VC-dimension
We further construct sample compression schemes of size $k$ for $C$, with additional information of $k \log(k)$ bits.
