Optimal Training-Time Scaling in Gradual Adaptation
cs.LG
Submitted: 2026-08-05
Updated: 2026-09-30
Comments: 24 pages, 5 figures
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
The gist: In gradual adaptation, how should the training time on each task change as the number of intermediate tasks increases? We study this question for overparameterized linear regression tasks that change
Terminology
Abstract
In gradual adaptation, how should the training time on each task change as the number of intermediate tasks increases? We study this question for overparameterized linear regression tasks that change smoothly and share a zero-loss solution. With N tasks and training time s N on each, the final learning progress converges to a continuum curve when Ns N to tau. The limiting progress is (tau) for small tau and (tau-1) for large tau, so both very short and very long training produce little progress. It follows that optimal per-task training times scale as s N= (N-1), equivalently Ns N= (1). Experiments on gradually rotated MNIST and a natural Yearbook time shift are consistent with less per-task training as the path is divided more finely.
Sources
- Test-time Adaptation in the Dynamic World with Compound Domain Knowledge Management
- From Order to Distribution: An Exact Operator Framework for Forgetting in Continual Learning
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