5 problems

Let $r$ be the activation power, let $L$ be the depth, and fix input and output widths $d_0$ and $d_L$. For an architecture $\mathbf{d}=(d_0,d_1,\dots,d_L)$, call it minimal fillin…

Unimodality conjecture. Every minimal width vector whose architecture is filling is unimodal: there exists $i\in\{0,1,d55fd53dots,L\}$ such that $(d_0,d55fd53dots,d_i)$ is weakly i…

Asymptotic expected-dimension conjecture. There exists a threshold $d53fdd53f(d53d)$ such that, whenever $r>d53f$, the neurovariety $d4b1_{d53d,r}$ attains the expected dimension.

Let $d$, $k$, and $s$ be integers, and let $p_1,\ldots,p_k\in\mathbb{R}[x_1,\ldots,x_d]$ be homogeneous polynomials of the same degree $s$, with no two linearly dependent. Proposit…

Fix an activation degree $r$, a depth $h$, and input and output widths $d_0$ and $d_h$. Let $\bm d=(d_0,d_1,\ldots,d_h)$ be a minimal filling architecture. Unimodality conjecture.…