Removal-Only Actuation in Age-Structured Branching Populations: Fundamental Limits of Equilibrium Placement

What the math gives to ML

The paper gives a sharp authority limit for removal-only controllers in age-structured branching systems. Adding an age-dependent killing rate changes extinction and survival conditioning, but leaves the reproduction-driven transmission barrier \(\Lambda\) invariant; the best achievable decay rate is only \(\Lambda+\nu^{\star}\), with residual gap \(|\nu^{\star}|\) caused by multi-offspring reproduction. A transferable neural analogue is a dynamically gated branching or residual network in which gates may remove active paths or units but cannot modify their reproduction or connectivity law. This predicts when pruning, dropout, or early exits cannot improve propagation stability, and when the architecture must change its expansion operator instead.