Diplomacyisacomplex environment, where training requires significant time. The action is an allocation of the player's coins across the fields: the player decides how manyof itsccoins to put in each of the fields, choosing c1,c2,...,cf where Pf Finally, Blotto is a single-turn (i.e.

Weconsider Diplomacy,a7-player board game designed toaccentuate dilemmas resulting from many-agent interactions.

A fundamental procedure in the analysis of massive datasets is the construction of similarity graphs. Such graphs play a key role for many downstream tasks, including clustering, classification, graph learning, and nearest neighbor search.

Asoneofthe most successful models, EGNN [1] leverages a simple scalarization technique to perform equivariant message passing over only Cartesian vectors (i.e., 1stdegree steerable vectors), enjoying greater efficiency and efficacy compared to equivariant GNNs using higher-degree steerable vectors.