Moy-Prasad filtration subgroups are generalization of congruence subgroups for $GL_n(Q_p)$ to a general $p$-adic reductive group $G(F)$. Moy-Prasad proved that any irreducible smooth representation of $G(F)$ has its restriction to a Moy-Prasad subgroup given by an irreducible representation (which we call a "Moy-Prasad type") of the successive quotient, and the type is almost unique in a precise sense. Moy-Prasad types and their generalizations then play a role in the study of $Rep(G(F))$.In this talk, under the assumption that $G$ splits over a tame extension and p>2, we present a construction which start from a Moy-Prasad type "of depth r>0" and produces a continuous homomorphism $P_F^r/P_F^{r+}$ -> $G^{\vee}$ where $P_F^r$ is the upper numbering subgroup of the wild inertia. We conjecture that this is compatible with the local Langlands correspondence, and explains that this is the case for Kaletha's construction of supercuspidal L-packets. This is a joint work in progress with Tsao-Hsien Chen and Stephen DeBacker.