  In this work, we present a general framework for continual learning of
sequentially arrived tasks with the use of pre-training, which has emerged as a
promising direction for artificial intelligence systems to accommodate
real-world dynamics. From a theoretical perspective, we decompose its objective
into three hierarchical components, including within-task prediction,
task-identity inference, and task-adaptive prediction. Then we propose an
innovative approach to explicitly optimize these components with
parameter-efficient fine-tuning (PEFT) techniques and representation
statistics. We empirically demonstrate the superiority and generality of our
approach in downstream continual learning, and further explore the
applicability of PEFT techniques in upstream continual learning. We also
discuss the biological basis of the proposed framework with recent advances in
neuroscience.
