Let $\mathbb{K}$ be a field of characteristic zero. Let $\Delta \geq 1$, $k \geq 2$, and $n \geq 2k + 1$. For a polynomial $p \in \mathbb{K}[\mathcal{X}_n]$, the following are equivalent:

1. $p$ is computed by a reduced matrix-symmetric circuit of support size $\leq k$ and support depth $\leq \Delta$.
2. $p$ is a linear combination of homomorphism polynomials $\hom_{F,n}$ for patterns $F$ with $\mathrm{fw}_\Delta(F) \leq k - 1$.

The implication from 1 to 2 is the theorem on homomorphism polynomials from symmetric circuits. For the implication from 2 to 1, one constructs a circuit for every pattern in the linear combination as in the theorem on circuits for patterns of bounded forestwidth, multiplies the output gates by the coefficients, adds an output sum gate, and rigidifies.