Projected incrementally scattering passive systems on closed convex sets

What the math gives to ML

The paper proves that constraining an incrementally passive dynamical system to a closed convex set preserves maximal dissipativity and contraction of the resulting semigroup. The transferable asset is a principled alternative to ad hoc hidden-state clipping: boundary-aware tangent-cone projection prevents forbidden motion while retaining a two-trajectory energy inequality. This can become a stable recurrent or continuous-depth architecture for very long sequences. The first implementation should use a dissipative residual drift, projected onto a box or ball, and test whether long-horizon sensitivity and gradient behavior improve at equal compute.