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Nearly Optimal Bounds for Cyclic Forgetting

William Swartworth · Deanna Needell · Rachel Ward · Mark Kong · Halyun Jeong

Great Hall & Hall B1+B2 (level 1) #1807
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[ Paper [ Slides [ Poster [ OpenReview
Wed 13 Dec 3 p.m. PST — 5 p.m. PST

Abstract: We provide theoretical bounds on the forgetting quantity in the continual learning setting for linear tasks, where each round of learning corresponds to projecting onto a linear subspace. For a cyclic task ordering on $T$ tasks repeated $m$ times each, we prove the best known upper bound of $O(T^2/m)$ on the forgetting. Notably, our bound holds uniformly over all choices of tasks and is independent of the ambient dimension. Our main technical contribution is a characterization of the union of all numerical ranges of products of $T$ (real or complex) projections as a sinusoidal spiral, which may be of independent interest.

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