RASP: Read-All, Sparse-Plasticity Continual Learning in a Stationary-Size LoRA

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 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 historical-and-current Gram matrix, and a novelty complement extracted via generalized Rayleigh whitening followed by orthogonal complement projection. After single-task training, BISECT folds both blocks back into the frozen backbone using a closed-form precision gate that scales each rank-1 invariant atom by its current-to-joint Rayleigh ratio while preserving novelty atoms at unit gain. Across eight incremental settings on ImageNet-R, ImageNet-A, CIFAR-100, CUB-200, and DomainNet, BISECT outperforms prompt, adapter, and LoRA baselines with zero extra inference parameters or FLOPs, and remains complementary to sparse analytic expansion.

LoRA-based continual learning methods mitigate catastrophic forgetting through various mechanisms, yet nearly all complement these with small learning rates as a heuristic to restrict gradient scaling magnitude. Such fixed heuristics lack theoretical guidance on how the strength of this restriction should evolve as tasks accumulate. We reveal that even under directional constraints such as nullspace projection, finite-precision updates inevitably leak into the subspace of accumulated prior knowledge along multiple directions. While small learning rates attenuate such leakage, they cannot prevent the accumulated forgetting from intensifying as the effective rank of historical knowledge grows. We show that the optimal magnitude restriction should adaptively increase with this effective rank to balance stability and plasticity, i.e., preservation of previous knowledge and acquisition of new task information. Under an anisotropic leakage model, we derive a pacing law $s^*=\sqrt{R/c}$ that characterizes the optimal scaling of gradient steps, i.e., the magnitude restriction itself, where $R$ is the effective rank of past updates. Based on this insight, we propose PaLoRA, which compresses historical knowledge via adaptive SVD truncation, projects gradients onto the nullspace of prior tasks, and applies rank-aware adaptive pacing. Experiments demonstrate consistent improvements over prior methods, with particularly strong performance in long-horizon settings, achieving substantial gains of 4% accuracy on challenging 50-task ImageNet-A and ImageNet-R benchmarks.

Robotic and edge intelligence systems operate in dynamic environments where data arrives continuously, requiring models to adapt while preserving previously learned knowledge under strict memory and energy constraints. While parameter-efficient fine-tuning has shown promise for continual learning with vision transformers, conventional architectures rely on dense computation and remain costly for real-world deployment. Sparse event-based vision transformers provide energy-efficient event-driven computation, yet their continual learning capabilities remain largely unexplored. We here introduce sLoTh, a parameter-efficient continual learning framework for pretrained sparse event-based (spiking) vision transformers. sLoTh freezes the backbone and restricts plasticity to scalable-efficient low-rank attention updates (seLoRA) and shared neuronal threshold modulation, enabling adaptation without replay buffers by updating less than 1% of model parameters. Experiments across CIFAR-100, Tiny-ImageNet, ImageNet-100, and ImageNet-R with up to 100 tasks demonstrate competitive rehearsal-free performance in class-incremental learning and online continual learning, while enabling approximately 6.5x lower energy consumption than conventional dense vision transformers.