Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision

ArXi:2605.18820v1 Announce Type: cross Superposition allows Transformers to reason in depth, carrying an entire reasoning frontier in parallel through a bounded-depth forward pass instead of unrolling serial chain-of-thought tokens. While Zhu hand-crafted an equal-weight breadth-first frontier in a single residual stream for graph reachability, it remained open whether gradient descent could ever find this target amidst permutation-symmetric saddles. We close this gap on Reachability-by-Superposition over Erd\H{o}s-R\'enyi graphs by isolating architectural and supervisional contributions.