Low-rank pre-training methods converge to geometrically and spectrally distinct basins and show diverging activations compared to full-rank training at 60M-350M scales.
Lost: Low-rank and sparse pre-training for large language models
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
While large language models (LLMs) have achieved remarkable performance across a wide range of tasks, their massive scale incurs prohibitive computational and memory costs for pre-training from scratch. Recent studies have investigated the use of low-rank parameterization as a means of reducing model size and training cost. In this context, sparsity is often employed as a complementary technique to recover important information lost in low-rank compression by capturing salient features in the residual space. However, existing approaches typically combine low-rank and sparse components in a simplistic or ad hoc manner, often resulting in undesirable performance degradation compared to full-rank training. In this paper, we propose \textbf{LO}w-rank and \textbf{S}parse pre-\textbf{T}raining (\textbf{LOST}) for LLMs, a novel method that ingeniously integrates low-rank and sparse structures to enable effective training of LLMs from scratch under strict efficiency constraints. LOST applies singular value decomposition to weight matrices, preserving the dominant low-rank components, while allocating the remaining singular values to construct channel-wise sparse components to complement the expressiveness of low-rank training. We evaluate LOST on LLM pretraining ranging from 60M to 7B parameters. Our experiments show that LOST achieves competitive or superior performance compared to full-rank models, while significantly reducing both memory and compute overhead. Moreover, Code is available at \href{https://github.com/JiaxiLi1/LOST-Low-rank-and-Sparse-Training-for-Large-Language-Models}{LOST Repo}
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cs.LG 6representative citing papers
A stateless, SVD-free regularizer approximates polar factors to induce low-rank weight structure during training, enabling better post-training compression of vision models and LLMs at under 8% overhead.
SCT pre-trains LLMs by keeping weights as compact SVD factors with Stiefel QR retraction, delivering up to 199x memory reduction per layer and allowing 70B-parameter training on a Steam Deck.
BOOST delivers 1.46-2.27x end-to-end speedups for low-rank bottleneck LLMs by redesigning tensor parallelism around the bottleneck structure plus supporting optimizations.
CR-Net uses cross-layer low-rank residuals in a dual-path network plus specialized recomputation to outperform prior low-rank methods on 60M-7B model pre-training while using less compute and memory.
An overview revisits LoRA variants by categorizing advances in architectural design, efficient optimization, and applications while linking them to classical signal processing tools for principled fine-tuning.
citing papers explorer
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Beyond Perplexity: A Geometric and Spectral Study of Low-Rank Pre-Training
Low-rank pre-training methods converge to geometrically and spectrally distinct basins and show diverging activations compared to full-rank training at 60M-350M scales.
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SLORR: Simple and Efficient In-Training Low-Rank Regularization
A stateless, SVD-free regularizer approximates polar factors to induce low-rank weight structure during training, enabling better post-training compression of vision models and LLMs at under 8% overhead.
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Spectral Compact Training: Pre-Training Large Language Models via Permanent Truncated SVD and Stiefel QR Retraction
SCT pre-trains LLMs by keeping weights as compact SVD factors with Stiefel QR retraction, delivering up to 199x memory reduction per layer and allowing 70B-parameter training on a Steam Deck.
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BOOST: BOttleneck-Optimized Scalable Training Framework for Low-Rank Large Language Models
BOOST delivers 1.46-2.27x end-to-end speedups for low-rank bottleneck LLMs by redesigning tensor parallelism around the bottleneck structure plus supporting optimizations.
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CR-Net: Scaling Parameter-Efficient Training with Cross-Layer Low-Rank Structure
CR-Net uses cross-layer low-rank residuals in a dual-path network plus specialized recomputation to outperform prior low-rank methods on 60M-7B model pre-training while using less compute and memory.
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Low-Rank Adaptation Redux for Large Models
An overview revisits LoRA variants by categorizing advances in architectural design, efficient optimization, and applications while linking them to classical signal processing tools for principled fine-tuning.