How catastrophic can catastrophic forgetting be in linear regression?

Jul 2, 2022



To better understand catastrophic forgetting, we study fitting an overparameterized linear model to a sequence of tasks with different input distributions. We analyze how much the model forgets the true labels of earlier tasks after training on subsequent tasks, obtaining exact expressions and bounds. We establish connections between continual learning in the linear setting and two other research areas – alternating projections and the Kaczmarz method. In specific settings, we highlight differences between forgetting and convergence to the offline solution as studied in those areas. In particular, when T tasks in d dimensions are presented cyclically for k iterations, we prove an upper bound of T^2min{1/√(k),d/k} on the forgetting. This stands in contrast to the convergence to the offline solution, which can be arbitrarily slow according to existing alternating projection results. We further show that the T^2 factor can be lifted when tasks are presented in a random ordering.


About COLT

The conference is held annually since 1988 and has become the leading conference on Learning theory by maintaining a highly selective process for submissions. It is committed in high-quality articles in all theoretical aspects of machine learning and related topics.

Store presentation

Should this presentation be stored for 1000 years?

How do we store presentations

Total of 0 viewers voted for saving the presentation to eternal vault which is 0.0%


Recommended Videos

Presentations on similar topic, category or speaker