Polynomiality conjecture for the stable homology of IA-groups

Let $F_n$ be a free group of rank $n$, and let $IA_n$ be the kernel of the canonical epimorphism ${\rm Aut}(F_n)\twoheadrightarrow GL_n(\mathbb{Z})$. For each $d\in\mathbb{N}$, let $H_d(IA;\mathbb{Z})$ denote the corresponding homology functor on $(\mathbf{S}(\mathbb{Z});\mathbb{Z})$. Polynomiality conjecture. For every $d\in\mathbb{N}$, the functor $H_d(IA;\mathbb{Z})$ on $(\mathbf{S}(\mathbb{Z});\mathbb{Z})$ is strongly polynomial. The degree-one case is known: $H_1(IA;\mathbb{Z})(V)\simeq {\rm Hom}_{\mathbb{Z}}(V,\Lambda^2(V))$, naturally in $V$, so its polynomial degree is exactly $3$. The conjecture concerns strong polynomiality in every homological degree and is motivated by finiteness results for congruence groups and homological stability for ${\rm Aut}(F_n)$.