Retreat and widen

The cone moves toward the origin and widens, admitting unrelated points while its positive-only entailment loss stays zero.

Inside cone ● P · match × N · unrelated

Move toward origin

Farther out · narrowNear origin · wide

Unrelated points inside 0 / 3 Entailment loss 0.000 Cone opening

Show equation

α (r) = 0.7 \arcsin (\min (\frac{0.2}{\sinh (\underset{r}{1.000}) + ε}, 1 - ε)) \approx 6.9 °

Radius r ↓ → half-opening α ↑, until the cap.

r: distance from origin · α: half the cone opening · ε: tiny numerical safeguard