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, is introduced.
Abstract
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) has become a de facto standard for parameter-efficient fine-tuning (PEFT), yet its performance is highly sensitive to initialization due to the information bottleneck imposed by low-rank decomposition. Existing approaches attempt to construct high-quality LoRA initializations by exploiting principal components of pretrained weights, activations, or gradients. However, these methods do not directly account for the training dynamics of the full-rank model. In this paper, we propose Training-aware Low-Rank Adaptation Initialization (TaRA), a method that initializes LoRA such that the gradients induced by the low-rank factors closely approximate the gradient of the corresponding full-rank weight matrix. Derived from a mathematical formulation, TaRA improves gradient fidelity at the start of training while introducing negligible computational overhead. Across diverse and challenging fine-tuning tasks, TaRA consistently outperforms prior state-of-the-art methods, establishing a simple, robust, and scalable solution for effective LoRA initialization.
Modern natural language systems rely on large language models, whose sheer size makes full fine-tuning costly in computation, graphics processing unit (GPU) memory, and storage. Low-rank adaptation (LoRA) sidesteps most of that cost. It keeps the pre-trained weights frozen and captures each task-specific change as the product of two smaller matrices, so adapting a model reduces to a low-rank decomposition. This review covers LoRA and its main variants and pays particular attention to the linear algebra behind them. It first explains why the low intrinsic dimension of fine-tuning makes low-rank updates effective, then compares the major variants: quantized LoRA (QLoRA), quantization-aware LoRA (QA-LoRA), adaptive low-rank adaptation (AdaLoRA), sparse low-rank adaptation (SoRA), and weight-decomposed low-rank adaptation (DoRA). Across published studies, these methods come close to full fine-tuning accuracy while updating well under one percent of a model's parameters in some settings. For reference, LoRA cuts the trainable parameter count of Generative Pre-trained Transformer 3 (GPT-3) by four orders of magnitude, and QLoRA brings a 65-billion-parameter model within the memory of one 48 GB card. Open problems remain in choosing the rank, comparing results across studies, limiting quantization loss, and combining multiple adapters without interference. Ultimately, an established piece of linear algebra, approximating high-dimensional objects in low-dimensional subspaces, is what keeps the adaptation of very large models affordable.
Shi-Cheng Wei· Theoretical and Natural Scie...· 0 citations
Structured pruning of large language models (LLMs) offers hardware-efficient compression, yet existing methods require calibration data, gradient computation, or large auxiliary policy networks at pruning time. LILA (\emph{Latent-Informed Layer Analysis}) scores neuron importance via the Kolmogorov--Smirnov (KS) distance between empirical singular value distributions of the full and neuron-ablated feed-forward network (FFN) weight matrix, providing a closed-form spectral rule requiring no training, calibration data, or auxiliary network. Without any fine-tuning, LILA surpasses PruneNet (45M-parameter RL policy) by 1.57~pp in zero-shot accuracy on LLaMA-2-7B at 25\% sparsity, and outperforms WikiText-2-calibrated SliceGPT by up to 6.0~pp across all sparsity levels, while preserving the original architecture. After one epoch of LoRA recovery fine-tuning, LILA achieves highly competitive performance, matching the heavily calibrated SliceGPT baseline to within a 0.48~pp margin across LLaMA-2-7B and Phi-2, despite using zero calibration data. A Neural Tangent Kernel analysis confirms a 22$\times$ reduction in functional distortion versus random pruning, providing theoretical grounding for the spectral importance criterion. Finally, extending LILA to dynamically allocate sparsity budgets via KS-scores yields state-of-the-art generative preservation at moderate compression, while uncovering fundamental single-layer architectural bottlenecks at higher compression regimes.
Sankar Behera, Dhruv Singh, Anshika Agnihotri et al.· 0 citations
A training-free framework, BAL-ANCER, which achieves global budget allocation for mixed-precision quantization and low-rank correction through information-guided subspace matrices, allowing a principled greedy allocator to distribute compression bits and ranks across the entire model.
Model compression is key to mitigate deployment challenges of ever growing machine learning models. In this area of research, singular value decomposition (SVD)-based compression offers a compelling trade-off between computational efficiency and model accuracy. Fisher-weighted SVD in particular provides principled, loss-aware compression. However, we find that improving the fidelity of Fisher approximation used in the compression is poorly predictive of post-compression accuracy for Vision Transformers (ViTs). Motivated by this observation, we propose FACTS, a structured Fisher Approximation tailored to Compressing ViTs with Fisher-weighted SVD, which enforces token-local aggregation while preserving within-token activation-gradient dependence. Additionally, we introduce a fast Constrained Rank Search (CoRS), that optimizes layer-wise rank allocation while adhering to a fixed floating point operation (FLOP) constraint. Extensive experiments across ViTs and hybrid architectures demonstrate that FACTS consistently improves accuracy-efficiency trade-offs without requiring finetuning. Notably, it outperforms the strongest SVD baseline by up to +5.8 percentage points (p.p.) Top-1 on Swin-B, with further gains driven by our search method. Code is available at https://github.com/MoritzTho/FACTS.
Moritz Thoma, Maximilian Groezinger, Maximilian Forstenh\"ausler et al.· 0 citations
Prohibitive computational and environmental costs impede the scalable deployment of Large Language Models (LLMs). Traditional compression techniques (sparsity, quantization, low-rank approximations) are typically applied in isolation, and each hits an accuracy-efficiency wall. This thesis proposes the"Compression Trinity,"a unified framework that applies the three pillars jointly: sparsity to reduce computation, quantization to minimize memory bandwidth, and low-rank approximations to recover accuracy. To accelerate pretraining, we apply the Trinity to the optimizer and model architecture. MKOR approximates curvature via block-diagonal sparsity and low-rank inversion, maintaining numerical stability for quantized states; it reduces curvature update complexity from $O(d^3)$ to $O(d^2)$ and accelerates convergence by up to 1.85x over KFAC. SLoPe accelerates training by up to 1.25x via a double-pruned backward pass for N:M sparsity, using low-rank"lazy"adapters in the final 1% of training to recover accuracy. For post-training compression, OPTIMA stabilizes static masks in a zero-training regime by formulating weight reconstruction as globally optimal column-wise quadratic programs, improving zero-shot accuracy by up to 3.97%. Given a fine-tuning budget, PATCH breaks the ceiling of static masks by learning a dynamic hybrid sparsity ratio between 0% and 50%, yielding up to 1.38x speedups. Finally, SLiM realizes the full Compression Trinity in one shot, using mathematically derived low-rank adapters to recover information lost to quantization and sparsity, improving accuracy by up to 5.66% over state-of-the-art methods and outperforming uncompressed dense models at equal parameter budgets by 0.6%. Together, these results show that jointly applying the Compression Trinity is essential for efficient, scalable, high-performance LLMs.
Mohammad Mozaffari· 0 citations
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