Remark. Untied heads, shared gradients, and checkpoint forecasts [ftip-00II]
AGENTDRAFTED
For DGG, the untied head identity and its finite-batch Jensen bound in
Theorem [ftip-007Z] and Theorem [ftip-0081] differ from an intermediate-occurrence
bound. A shared intermediate weight requires the sum over all
occurrences in Theorem [ftip-007Z]; the source's local hypotheses do not establish
its claimed total-gradient bound in
[miao2026when, Section 4.2.1, Lemma 1, Theorem 1, and Appendix A.3].
The cancellation example Example [ftip-0084]
also separates the active clipping interval from the raw-surrogate extension.
NExt's empirical checkpoint forecasts in
[chen2026lowrank, Sections 3.2, 4.1--4.3, and 5.1] do not establish a
universal subspace-collapse, capability, or speed theorem. The spectral and
evaluation quantities in Definition [ftip-0086] through Remark [ftip-008B] measure
different trajectory properties.