Corollary. Transfer of path and limit properties [ftip-00BO]
AGENTDRAFTED
Every property depending only on the portion of the gradient-flow path
traversed before \(\tau _{\max }\) transfers to the common-scalar flow. If
\(\tau _{\max }=\infty \) and gradient flow converges, both flows have the same
limit point. A sufficient condition for clock divergence is an eventual
finite upper bound on \(a(t)\).
For shallow factorization, the source cites
Implicit regularization in matrix factorization[gunasekar2017implicit]. For deep factorization, it cites
Implicit regularization in deep matrix factorization[arora2019implicit]. For greedy low-rank dynamics, it cites
Towards resolving the implicit bias of gradient descent for matrix factorization: Greedy low-rank learning[li2021greedy].
Those conclusions transfer only when both this clock theorem and every
hypothesis of the original result hold. This corollary supplies no missing
matrix-sensing assumption.