Continual learning for pre-trained vision-language models requires balancing three competing objectives: retaining pre-trained knowledge, preserving knowledge from a sequence of learned tasks, and maintaining the plasticity to acquire new knowledge. This paper presents KeepLoRA++, balancing these objectives through a unified dual-dimensional knowledge retention mechanism. We analyze knowledge distribution of Transformer architecture from both inter-layer and intra-layer perspectives. The inter-layer perspective examines how retention is distributed across layers, while the intra-layer perspective focuses on the parameter space within each layer. Our analysis reveals a structural property: general transferable knowledge is mainly encoded in the shallow layers and the principal subspace of the parameters, while task-specific adaptations are localized in the deep layers and the residual subspace. Motivated by this insight, KeepLoRA++ introduces a layer-scaled residual gradient adaptation method. New tasks are learned by restricting LoRA parameter updates to the residual subspace, combined with a shallow-to-deep layer scaling, to prevent interference with previously acquired capabilities. Specifically, the gradient of a new task is projected onto a subspace orthogonal to both the principal subspace of the pre-trained model and the dominant directions of previous task features, while simultaneously assigning smaller update magnitudes to shallow layers and larger ones to deeper layers. Our theoretical analysis and empirical evaluations confirm that KeepLoRA++ successfully balances these three competing objectives, consistently outperforming representative baselines across image classification, visual question answering, and video understanding tasks.
Many real-world applications collect data in a streaming environment, where learning tasks are encountered sequentially. This necessitates continual learning (CL) to update models online, enabling adaptation to new tasks while preserving past knowledge to prevent catastrophic forgetting. Nowadays, with the flourish of large pre-trained models (LPMs), efficiency has become increasingly critical for CL, due to their substantial computational demands and growing parameter sizes. In this paper, we introduce TreeLoRA (K-D Tree of Low-Rank Adapters), a novel approach that constructs layer-wise adapters by leveraging hierarchical gradient similarity to enable efficient CL, particularly for LPMs. To reduce the computational burden of task similarity estimation, we employ bandit techniques to develop an algorithm based on lower confidence bounds to efficiently explore the task structure. Furthermore, we use sparse gradient updates to facilitate parameter optimization, making the approach better suited for LPMs. Theoretical analysis is provided to justify the rationale behind our approach, and experiments on both vision transformers (ViTs) and large language models (LLMs) demonstrate the effectiveness and efficiency of our approach across various domains, including vision and natural language processing tasks.
Large language models generalize well to individual tasks but lack an inherent mechanism for learning them sequentially, leading to catastrophic forgetting. To mitigate this, LoRA-based continual learning methods allocate a separate low-rank adapter per task, yet existing approaches either require task identity at inference or sum all adapters indiscriminately, letting irrelevant branches distort the output. Recent gating-based solutions route inputs to the correct adapter but introduce trainable parameters that themselves need protection against forgetting. In this work, we observe that pooled token embeddings from a frozen LLM embedding layer already separate task distributions throughout the learning sequence. A Gaussian mixture model fitted on these embeddings, without any gradient-based training, is sufficient for task-agnostic adapter selection at test time. This eliminates the need for a learned gating module. On the adapter side, constraining each task's parameters to the principal subspace of the pretrained weights via SVD yields a compact latent-space parameterization. Within this subspace, orthogonal regularization directly controls inter-task interference. The resulting system, Latent-LoRA, is replay-free, requires no trainable routing component, and uses substantially fewer parameters per task. Experiments across five model scales and two established continual learning benchmarks show state-of-the-art performance with near-zero forgetting.
While orthogonal subspace methods try to mitigate task interference in Continual Learning (CL), they often suffer from energy diffusion across the basis, hindering knowledge compaction and exhausting capacity for future tasks. We observe that output feature drift induced by parameter updates is inherently low-rank, and theoretically prove that preserving parameters along the principal directions of this drift minimizes the output reconstruction error. Motivated by this, we propose \textbf{E}nergy-Concentrated and \textbf{E}nergy-Ordered \textbf{Lo}w-\textbf{R}ank \textbf{A}daptation (E2-LoRA). By explicitly ordering and concentrating knowledge into leading ranks, E2-LoRA frees capacity for subsequent tasks. Furthermore, we design a dynamic rank allocation strategy to balance stability and plasticity by jointly optimizing energy retention and model plasticity. Extensive experiments across multiple benchmarks demonstrate that E2-LoRA achieves state-of-the-art performance. Code is available at https://github.com/kiddo127/E2-LoRA.