Convergence and endpoint of the mechanistic readout

Determine whether the cross-seed and cross-budget variation in the RECENCY-versus-RARITY readout reflects incomplete convergence toward a common endpoint or convergence to genuinely different endpoints under the training dynamics.

Background

The terminal sign fraction of the multiplicity-inversion readout can change substantially when the cosine schedule is lengthened, even when circuit formation occurs at the same time. Some runs remain stable, whereas others drift or cross from one sign to the other after the retrieval circuit has formed.

Consequently, the reported single-budget, single-schedule map cannot establish whether the observed variation is merely the result of stopping before convergence or reflects distinct endpoints selected along an objective-indifferent direction.

References

We therefore report the map at one budget and one schedule, and cannot say how much of the cross-seed spread at 16000 steps is incomplete convergence rather than a different endpoint.

— Shortcut Before Circuit: Document Statistics Time In-Context Conflict Resolution  (2608.24460 - Liao et al., 25 Aug 2026) in Section 8, Limitations, p. 8

Whether the circuit would convert to accuracy past our budget or is a different solution we cannot say from one run.

— Shortcut Before Circuit: Document Statistics Time In-Context Conflict Resolution  (2608.24460 - Liao et al., 25 Aug 2026) in Appendix G.3, “One run acquires the circuit without solving the task,” p. 29