Remark. Compression of a charted path is not capability acquisition [ftip-008B]
AGENTDRAFTED
NExt extracts global, local, and target differences from LoRA checkpoint
matrices, keeps leading singular factors, learns a nonlinear predictor, jumps
in that parameter chart, and resumes RLVR
[chen2026lowrank, Sections 3.2, 4.1--4.3, and 5.1]. Its reported results are empirical;
the paper states no theorem that a leading subspace remains stable or that a
forecast preserves a policy.
The quantities in Definition [ftip-0086]--Definition [ftip-0089] separate four tests.
Squared singular-energy share concerns one matrix, spectral gap controls
whether its leading subspace is identifiable, projector drift compares those
subspaces over time, and path-emulation regret returns to fixed independent
evaluation. None, by itself, is evidence that new feedback was acquired or
that a new capability was learned. Such a claim must use a declared
post-training gain such as Definition [ftip-005F] and must charge forecast training,
the parameter jump, and recovery updates.