Potentials of homotopy cyclic $\text{AI}$-algebras

For a cyclic $\text{AI}$-algebra, a potential recording the structure constants can be defined. We define an analogous potential for a homotopy cyclic $\text{AI}$-algebra and prove its properties. On the other hand, we find another different potential for a homotopy cyclic $\text{AI}$-algebra, which is related to the algebraic analogue of generalized holonomy map of Abbaspour, Tradler and Zeinalian.