Weak admissibility of exponentially twisted cohomology associated with some nondegenerate functions

In this article, we study the filtered $\mathrm{\Phi }$-modules canonically attached to the exponentially twisted cohomology associated with some nondegenerate functions. Inspired by $p$-adic Hodge theory, we conjecture that those filtered $\mathrm{\Phi }$-modules are weakly admissible. We show that this expectation is correct under some assumptions using the theory of Adolphson and Sperber.