arXiv Machine Learning By Qingsen Ma, Dianyun Wang, Jiahong Liu, Irwin King

Why Constrained Updates Still Forget: A Functional-Path Analysis of Continual SFT

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The paper investigates why constrained updates in supervised fine‑tuning (SFT) still lead to forgetting by developing a functional‑path analysis that decomposes changes in old loss into controlled direction, gradient staleness, probe mismatch, and finite‑step effects. It introduces a conditional refresh budget and identifies a restoring direction provided by informative replay, showing that the placement of constraints relative to Adam and the granularity of constraints significantly affect retention across code‑label audits. The study also explores checkpointed generation, replay schedules, and sequential‑task comparisons, demonstrating that subspace regularization, projection, and supervised replay differentially influence backward transfer and content retention.

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