Sign-Rank, Index, and List Replicability: Connections and Separations
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, lower bounds on sign-rank are notoriously difficult to come by. Two recent approaches to the problem establish lower bounds on sign-rank by measures that are easier to analyze: the $\mathbb{Z}_2$-index and the list replicability number. We order these measures, showing that the $\mathbb{Z}_2$-index is upper-bounded by a linear function of the list replicability number. As a main consequence, we obtain a strong separation between sign-rank and $\mathbb{Z}_2$-index, thereby resolving a question of Frick, Hosseini, a...
| Authors | Ari Blondal, Hamed Hatami, Pooya Hatami et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 June 2026 |
| Last updated at source | 21 July 2026 |
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