Stability for boundary actions of cocompact lattices in Euclidean buildings

What the math gives to ML

The paper’s transferable mechanism is a robust symbolic coder built from nested geometric regions: each admissible transition maps the successor region strictly inside the predecessor region, so every infinite path defines a nonempty intersection and, when diameters shrink, a unique coded point. This nesting yields stability of the boundary action under sufficiently small perturbations through a semi-conjugacy rather than requiring exact trajectory matching. A neural analogue is a latent-state architecture whose transitions preserve nested uncertainty or cone regions, with an explicit inclusion/contraction regularizer and a certified perturbation margin. The key falsifiable prediction is that representation drift under parameter or input perturbations is bounded geometrically and undergoes a sharp failure when the inclusion margin vanishes.