Implicit biases in multitask and continual learning from a backward error analysis perspective
This provides theoretical insights into optimization challenges in continual learning, though it appears incremental as it extends known multitask analysis to continual settings.
The paper analyzed implicit training biases in multitask and continual learning for neural networks trained with SGD using backward error analysis, deriving modified losses with three terms including a new conflict term for continual learning based on Lie brackets between task gradients.
Using backward error analysis, we compute implicit training biases in multitask and continual learning settings for neural networks trained with stochastic gradient descent. In particular, we derive modified losses that are implicitly minimized during training. They have three terms: the original loss, accounting for convergence, an implicit flatness regularization term proportional to the learning rate, and a last term, the conflict term, which can theoretically be detrimental to both convergence and implicit regularization. In multitask, the conflict term is a well-known quantity, measuring the gradient alignment between the tasks, while in continual learning the conflict term is a new quantity in deep learning optimization, although a basic tool in differential geometry: The Lie bracket between the task gradients.