Lina Yao | Search arXiv

arXiv2026

Take Only What You Need: Rank Minimization as an Implicit Forgetting Regularizer in Continual Learning

The central tension in continual learning (CL) is the trade-off between plasticity (acquiring new knowledge) and stability (retaining prior knowledge). We study how a pre-trained backbone can be continually updated to absorb new knowledge while preserving existing capabilities, via capacity control: regulating the effective rank of each parameter update, a per-step quantity directly controllable inside a LoRA update. A controlled probe of LoRA rank and placement across modules and tasks reveals a consistent trade-off, with a moderate-rank sweet spot that varies by placement and task, leaving no universally optimal fixed rank; a formal bound shows forgetting grows with rank. Building on these findings, we propose Continual Dynamic Rank-Selective LoRA (CoDyRA), which jointly trains each LoRA update with rank minimization via sparsity-promoting regularization on per-component importance weights. The supervised objective drives plasticity; rank minimization regularizes forgetting. We show that rank minimization serves as an implicit forgetting regularizer in the CL regime, protecting general capability and prior-task knowledge simultaneously by controlling forgetting against the current model state. Across MTIL, X-TAIL, and TRACE (CLIP, LLaMA, Gemma), CoDyRA outperforms prior CL methods on new knowledge learning and forgetting, achieving a strong plasticity-stability balance. Project page: https://artificer-ai-lab.github.io/CoDyRA.

cs.CV↗

arXiv2026

One Rate Is Not Enough: Adaptive Anisotropic Learning Rates for LoRA Fine-Tuning

Low-rank adaptation (LoRA) has become the standard for parameter-efficient fine-tuning of large language models. Most LoRA variants follow a uniform-LR convention, applying a single global learning rate across every rank-one component of every adapter. We show that this convention overlooks substantial within-module heterogeneity, where the rank-one components of a LoRA adapter update at highly uneven rates and low-velocity modules converge to concentrated singular spectra that underutilize the nominal rank budget. To address this, we propose an adaptive anisotropic learning-rate model that assigns each rank-one component its own effective learning rate, computed online from training-time signals and mean-normalized per module to preserve the global LR budget. AnLR-LoRA instantiates this model with two signals available during AdamW optimization, namely function-space velocity and Adam SNR, as a lightweight scheme with no extra trainable parameters. Across commonsense reasoning, natural language generation and visual instruction-tuning benchmarks, AnLR-LoRA consistently improves over LoRA while encouraging broader use of rank capacity, with gains that remain robust across a wide range of global learning rates and transfer cleanly to other LoRA variants.

cs.LG↗