Some intuition for why cooperative systems "look 1-dimensional" and 2-cooperative systems "look 2-dimensional"

What the math gives to ML

The paper provides a nonstandard dimensional-collapse mechanism: uniform 2-positivity makes the second exterior-power variational cocycle contractive in Hilbert's projective metric, so transported 2-planes align toward a lower-dimensional direction or surface. The transferable asset is a cone condition on the additive compound Jacobian together with a finite-window strict-positivity condition that yields an explicit projective contraction rate. A neural ODE or recurrent model can be trained with a wedge-power Jacobian regularizer, predicting measurable alignment of tangent planes and improved long-horizon stability when the contraction condition is satisfied.