Example. A sign-invariant checkpoint-trajectory forecast [ftip-006B]
Example. A sign-invariant checkpoint-trajectory forecast [ftip-006B]
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.