Expected-dimension conjecture for non-increasing-width polynomial neural networks

Let $d53d=(d_0,d_1,d55fd53\dots,d_L)$ be a non-increasing sequence of widths with $d_L>1$. For each activation degree $r$, let $d4b1_{d53d,r}$ denote the associated neurovariety, and let its expected dimension be the dimension predicted by the parameter count and ambient dimension.

Non-increasing-width expected-dimension conjecture. For every $r$, the neurovariety $d4b1_{d53d,r}$ attains the expected dimension.

This predicts non-defectivity for architectures whose widths never increase toward the output. The source presents it as a conjecture contrasting with the asymptotic large-activation-degree statement; no resolution is supplied in the provided text.