9 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…
Communication complexity of point-line incidences over the reals
Marcel K. Goh, Hamed Hatami
We construct a point-line incidence problem over the reals whose randomized communication complexity is constant, but whose deterministic communication complexity is linear even wh…
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…
Lower Bounds for Approximate Sign Rank
Riju Bindua, Hamed Hatami, Hasti Karimi +1
We prove new upper and lower bounds on -approximate sign-rank, a relaxation of sign-rank introduced by Chornomaz, Moran, and Waknine (STOC 2025). We show that every …
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…
Stability and List-Replicability for Agnostic Learners
Ari Blondal, Shan Gao, Hamed Hatami +1
Two seminal papers--Alon, Livni, Malliaris, Moran (STOC 2019) and Bun, Livni, and Moran (FOCS 2020)--established the equivalence between online learnability and globally stable PAC…
Structure in Communication Complexity and Constant-Cost Complexity Classes
Hamed Hatami, Pooya Hatami
Several theorems and conjectures in communication complexity state or speculate that the complexity of a matrix in a given communication model is controlled by a related analytic o…