Conjecture on extension of zero-pattern results to arbitrary sample size

Consider linear neural networks trained on $m$ data points. The results referred to as Proposition

$$, Theorem$$

, Corollary

$$, and Corollary$$

are observed computationally to hold when $m=2$. Extension conjecture. These results should hold for every $m$. The conjecture extends the results established in the section from a single data point to arbitrary sample size; the source provides computational evidence for $m=2$ but no proof or resolution for general $m$.