CODE-CL: Conceptor-Based Gradient Projection for Deep Continual Learning

Continual learning (CL) - the ability to progressively acquire and integrate new concepts - is essential to intelligent systems to adapt to dynamic environments. However, deep neural networks struggle with catastrophic forgetting (CF) when learning tasks sequentially, as training for new tasks often overwrites previously learned knowledge. To address this, recent approaches constrain updates to orthogonal subspaces using gradient projection, effectively preserving important gradient directions for previous tasks. While effective in reducing forgetting, these approaches inadvertently hinder forward knowledge transfer (FWT), particularly when tasks are highly correlated. In this work, we propose Conceptor-based gradient projection for Deep Continual Learning (CODE-CL), a novel method that leverages conceptor matrix representations, a form of regularized reconstruction, to adaptively handle highly correlated tasks. CODE-CL mitigates CF by projecting gradients onto pseudo-orthogonal subspaces of previous task feature spaces while simultaneously promoting FWT. It achieves this by learning a linear combination of shared basis directions, allowing efficient balance between stability and plasticity and transfer of knowledge between overlapping input feature representations. Extensive experiments on continual learning benchmarks validate CODE-CL's efficacy, demonstrating superior performance, reduced forgetting, and improved FWT as compared to state-of-the-art methods. ${ }^{1}$