5 papers
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…
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…
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…
Game-theoretic variants of splitting number
Jorge Antonio Cruz Chapital, Tatsuya Goto, Yusuke Hayashi +1
We consider combining the definition of a cardinal invariant and the notion of an infinite game. We focus on the splitting number since the corresponding cardinal in…
Collective Predictive Coding as Model of Science: Formalizing Scientific Activities Towards Generative Science
Tadahiro Taniguchi, Shiro Takagi, Jun Otsuka +2
This paper proposes a new conceptual framework called Collective Predictive Coding as a Model of Science (CPC-MS) to formalize and understand scientific activities. Building on the…