BISECT: Bilevel Spectral Decomposition for Low-Rank Continual Learning

Tom Saliencro, Wen-Hsuan Liu, Rohan Desai, Amara Okonkwo, Maya Lindqvist

Exemplar-free continual learning on pre-trained Vision Transformers increasingly relies on Low-Rank Adaptation (LoRA), yet prevailing methods govern the low-rank update space through strict subspace isolation. By projecting each incoming task into the approximate null space of historical token activations, isolation-based learners equate any cross-task feature overlap with catastrophic interference. We show that this orthogonality premise induces a structural bottleneck we term \emph{spectral starvation}: when down-projection bases are locked before task optimization, the gradient norm reaching the trainable up-projection is upper-bounded by the energy of current-task features captured by the chosen basis. Because natural visual tasks share low- and mid-level covariance structure, historical null tails contain barely $5.5\%$ of incoming task variance, starving new-class plasticity while blocking positive consolidation along shared directions. We propose BISECT (Bilevel Spectral Decomposition), a continual LoRA framework that partitions a fixed rank-$r$ budget into two orthogonal functional blocks: an invariant carrier spanned by the dominant modes of the joint…