The Factor Conjecture for arithmetic circuit complexity

Let $\mathbb{F}$ be a field of characteristic zero, let $f\in\mathbb{F}[x_1,\ldots,x_n]$, and let $g$ be a factor of $f$. Write $L(h)$ for the size of the smallest arithmetic circuit computing $h$ from the variables and arbitrary constants in $\mathbb{F}$.

Factor Conjecture. One has

$$L(g)\leq\operatorname{poly}(L(f)+\deg(g)).$$

This is a central question in algebraic complexity theory. It is known for approximate complexity, and the source explains that a possible failure in the exact setting could only arise when $g$ occurs with exponentially large multiplicity.