3 papers
math.LO2025
Stationary list colorings
Yusuke Hayashi
Komjath studied the list chromatic number of infinite graphs and introduced the notion of restricted list chromatic number. For a graph and a cardinal , we say tha…
math.LO2025
Dominating numbers at singular cardinals
Yusuke Hayashi
We study the generalized dominating number at a singular cardinal of cofinality . We show two lower bounds: in ZFC, $\mathrm{cf}([μ]^κ,\subseteq) \leq \math…
cs.AI2025
Universal AI maximizes Variational Empowerment
Yusuke Hayashi, Koichi Takahashi
This paper presents a theoretical framework unifying AIXI -- a model of universal AI -- with variational empowerment as an intrinsic drive for exploration. We build on the existing…