Beyond Embedding Transfer: Component Roles in Grokking Transfer and Stability
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Computer Science > Machine Learning
arXiv:2609.18078 (cs)
[Submitted on 16 Sep 2026]
Title:Beyond Embedding Transfer: Component Roles in Grokking Transfer and Stability
Authors:Zeyu Jia
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Abstract:Warm-start transfer can make algorithmic tasks generalize rapidly, yet it is unclear which model components provide the gain and whether that gain remains stable under continued optimization. We study cross-operator transfer on modular arithmetic and separate efficacy (early velocity) from stability (post-reach drawdown). In a scale-matched 108-run battery across 12 seed blocks (96-run 2^3 factorial plus 12-run scale control), transferring internal attention/MLP weights (B) alongside token embeddings and readout (E+U) improves early accuracy by 5.46 pp (Holm p=0.0039) and cuts confirmation latency by 558 steps (Holm p=0.0088). While readout plus internal-block transfer satisfies the pre-specified +/-500-step latency equivalence criterion in 1-layer models (TOST p=0.0011, though Full is faster in 11/12 paired seeds), a prospective 2-layer replication confirms the internal-block advantage (12/12 seeds, +704.67 integral units, p=4.88x10^-4) while revealing an architectural boundary: omitting donor embeddings falls 4475.6 units below Full, outside the +/-250-unit margin. Continued target training frequently triggers severe post-grokking relapse. Freezing transferred representation carriers (E, U) nearly eliminates offline relapse (19.40% -> 0.07%, Holm p=0.005859). Online validation-triggered gating slashes True Max Drawdown from 22.06% to 0.60% on 2a+b (p=0.000488), with prospective confirmations extending protection across affine, nonlinear quadratic, and 2-layer targets (10.94-23.47 pp reductions), distinguishing continual stabilization from static early stopping. In non-abelian S_5, unshielded transfer surges transiently (95.4% peak), but a prospective shielding cohort yields no confirmed benefit (+0.15 +/- 1.14 pp). These results establish a component-level dissociation between transfer acceleration and trajectory stability, and expose the empirical boundaries of parameter shielding.
| Comments: | 15 pages, 5 figures, conference preprint |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.18078 [cs.LG] |
| (or arXiv:2609.18078v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.18078
arXiv-issued DOI via DataCite (pending registration)
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