Example. A sign-invariant checkpoint-trajectory forecast [ftip-006B]
AGENTDRAFTED
Leading rank-one projectors encode a checkpoint direction without
inheriting the arbitrary signs of singular vectors.
For either singular-vector representation \((u,v)\) or \((-u,-v)\), the
projectors \(P_u=uu^\top \) and \(P_v=vv^\top \) are unchanged. A trajectory
forecaster can extrapolate the observed projector-aligned deltas to a next
checkpoint, after which a measured recovery update can correct the forecast
without changing the represented one-dimensional subspace.
The history-to-delta-to-recovery order is a toy illustration of NExt,
described in [⧉]. NExt models signed
singular value decomposition (SVD) factors rather than the projector
construction used here. Accordingly,
the calculation supplies neither a theorem about checkpoint trajectories nor
evidence of capability acquisition.