Continual learning (CL) algorithms strive to acquire new knowledge while preserving prior information. However, this stability-plasticity trade-off remains a central challenge. This paper introduces a framework that dissects this trade-off, offering valuable insights into CL algorithms. The Readout-Decomposition of Activation Change (RDAC) framework first addresses the stability-plasticity dilemma and its relation to catastrophic forgetting. It relates learning-induced activation changes in the range of prior readouts to the degree of stability and changes in the null space to the degree of plasticity. In deep non-linear networks tackling split-CIFAR-110 tasks, the framework clarifies the stability-plasticity trade-offs of the popular regularization algorithms Synaptic intelligence (SI), Elastic-weight consolidation (EWC), and learning without Forgetting (LwF), and replay-based algorithms Gradient episodic memory (GEM), and data replay. GEM and data replay preserved stability and plasticity, while SI, EWC, and LwF traded off plasticity for stability. The inability of the regularization algorithms to maintain plasticity was linked to them restricting the change of activations in the null space of the prior readout. Additionally, for one-hidden-layer linear neural networks, we derived a gradient decomposition algorithm to restrict activation change only in the range of the prior readouts, to maintain high stability while not further sacrificing plasticity. Results demonstrate that the algorithm maintained stability without significant plasticity loss. The RDAC framework informs the behavior of existing CL algorithms and paves the way for novel CL approaches. Finally, it sheds light on the connection between learning-induced activation/representation changes and the stability-plasticity dilemma, also offering insights into representational drift in biological systems.

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