7 papers
A polylogarithmic bound for list replicability
Ari Blondal, Hamed Hatami, Pooya Hatami +2
Zhang [Zha26] recently posted a manuscript announcing that the list-replicability number of every class of binary concepts on domain points is …
Sign-Rank, Index, and List Replicability: Connections and Separations
Ari Blondal, Hamed Hatami, Pooya Hatami +2
In learning theory, the sign-rank of a binary concept class captures the smallest dimension in which it can be represented by points and halfspaces. Despite tremendous interest, lo…
Tight list replicability bounds via a novel sphere covering theorem
Ari Blondal, Hamed Hatami, Pooya Hatami +2
In recent years, list replicability has emerged as a framework for formalizing reproducibility in learning theory. A central question is how the required list size relates to the a…
Simplicial covering dimension of extremal concept classes
Ari Blondal, Hamed Hatami, Pooya Hatami +2
Dimension theory is a branch of topology concerned with defining and analyzing dimensions of geometric and topological spaces in purely topological terms. In this work, we adapt th…
Borsuk-Ulam and Replicable Learning of Large-Margin Halfspaces
Ari Blondal, Hamed Hatami, Pooya Hatami +2
We prove that the list replicability number of -dimensional -margin half-spaces satisfies \[ \frac{d}{2}+1 \le \mathrm{LR}(H^d_γ) \le d, \] which grows with dimension. This r…
Free-fermionic ice, the Yang-Baxter equation and skein relations
Chavdar Lalov
In his famous ASM paper, Kuperberg uses a skein relation to give an algebraic proof of a Yang-Baxter equation where the Boltzmann weights satisfy the field-free condition. In this…
Self-avoiding Walks of Lattice Strips
Rumen Dangovski, Chavdar Lalov
We study self-avoiding walks on restricted square lattices, more precisely on the lattice strips and . We obtain the v…