  In this paper we introduce entropy-stability and F-stability for
homothetically shrinking Yang-Mills solitons, employing entropy and second
variation of $\mathcal{F}$-functional respectively. For a homothetically
shrinking soliton which does not descend, we prove that entropy-stability
implies F-stability. These stabilities have connections with the study of
Type-I singularities of the Yang-Mills flow. Two byproducts are also included:
We show that the Yang-Mills flow in dimension four cannot develop a Type-I
singularity; and we obtain a gap theorem for homothetically shrinking solitons.
