Stabilizing the Dynamic Low-Rank Training

Low-rank factorization is widely used to compress neural networks, but modern models are often not naturally amenable to aggressive factorization without significant accuracy loss. Existing training-time low-rank regularizers can improve compressibility, but they often require SVDs of large weight matrices, modify the model architecture (introducing additional trainable parameters), or rely on stateful cached quantities. To address these limitations, we introduce SLORR, a simple, stateless, and architecture-preserving framework for in-training low-rank regularization, instantiated with two main variants based on the Hoyer sparsity metric and the nuclear norm. SLORR directly regularizes the original weight matrices using GPU-friendly approximations for the forward and backward passes of the regularizers, for which we provide approximation guarantees. We first evaluate SLORR on ImageNet-1K across short-horizon continued training of ResNet-50, ViT-B/16, and ViT-L/16, and pretraining of ResNet-18, where SLORR induces compressibility while introducing less than 8% training overhead. We further evaluate SLORR-Hoyer in LLM pretraining at 135M and 560M scales: SLORR-trained compressed models preserve performance substantially better than unregularized models while adding less than 1% average training overhead.

Low-rank adaptation (LoRA) often underperforms full fine-tuning. We investigate this performance gap through a tangent-space lens: factorized updates are confined to the tangent space of the current low-rank factors, leaving gradient components outside this space unexploited. An analysis of ten representative LoRA variants reveals that these residual components account for most of the gradient energy and exhibit strong spectral concentration. Motivated by this finding, we propose Dynamic Tangent LoRA (DT-LoRA), which partitions a fixed rank budget into a stable branch and a dynamic branch to capture the principal residual gradient directions. We show that these directions define the optimal update of a local quadratic model under orthogonal-complement and rank constraints. Matrix-free randomized SVD recovers them without materializing the residual gradient, while controlled write-back preserves accumulated updates and stabilizes training within the allocated rank. DT-LoRA adds no trainable parameters or inference cost over LoRA. Experiments across computer vision and natural language processing tasks demonstrate consistent improvements over LoRA and its variants. Moreover, despite being a general-purpose adaptation method, DT-LoRA outperforms task-specific approaches to open-vocabulary domain generalization for semantic segmentation, achieving state-of-the-art results. Code is available at https://github.com/Snipine/DT-LoRA.

Foundation models have achieved remarkable success, yet their growing parameter counts pose significant computational and memory challenges. Low-rank factorization offers a promising route to reduce training and inference costs, but the community lacks a stable recipe for training models from scratch using exclusively low-rank weights while matching the performance of the dense model. We demonstrate that Large Language Models (LLMs) can be trained from scratch using exclusively low-rank factorized weights for all non-embedding matrices without auxiliary "full-rank" guidance required by prior methods. While native low-rank training often suffers from instability and loss spikes, we identify uncontrolled growth in the spectral norm (largest singular value) of the weight matrix update as the dominant factor. To address this, we introduce Spectron: Spectral renormalization with orthogonalization, which dynamically bounds the resultant weight updates based on the current spectral norms of the factors. Our method enables stable, end-to-end factorized training with negligible overhead. Finally, we establish compute-optimal scaling laws for natively low-rank transformers, demonstrating predictable power-law behavior and improved inference efficiency relative to dense models.