# SLTrain: a sparse plus low-rank approach for parameter and memory efficient pretraining

arXiv: https://arxiv.org/abs/2406.02214 · HTML: https://mlsanity.com/paper/2406.02214/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 59 references that are in the map.
- First posted on arXiv 4 Jun 2024.

## Builds on (most cited first, 30 of 44)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [Parameter-Efficient Transfer Learning with Diff Pruning](https://mlsanity.com/paper/2012.07463/) (2020)
- [Training Neural Networks with Fixed Sparse Masks](https://mlsanity.com/paper/2111.09839/) (2021)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [Composable Sparse Fine-Tuning for Cross-Lingual Transfer](https://mlsanity.com/paper/2110.07560/) (2021)
- [Full Parameter Fine-tuning for Large Language Models with Limited Resources](https://mlsanity.com/paper/2306.09782/) (2023)
- [Scatterbrain: Unifying Sparse and Low-rank Attention Approximation](https://mlsanity.com/paper/2110.15343/) (2021)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [Sparse Low-rank Adaptation of Pre-trained Language Models](https://mlsanity.com/paper/2311.11696/) (2023)
- [Chain of LoRA: Efficient Fine-tuning of Language Models via Residual Learning](https://mlsanity.com/paper/2401.04151/) (2024)

## Built on by (most cited first, 30 of 45)

- [A Survey on LoRA of Large Language Models](https://mlsanity.com/paper/2407.11046/) (2024)
- [CoLA: Compute-Efficient Pre-Training of LLMs via Low-Rank Activation](https://mlsanity.com/paper/2502.10940/) (2025)
- [CompAct: Compressed Activations for Memory-Efficient LLM Training](https://mlsanity.com/paper/2410.15352/) (2024)
- [Memory-Efficient LLM Pretraining via Minimalist Optimizer Design](https://mlsanity.com/paper/2506.16659/) (2025)
- [Greedy Low-Rank Gradient Compression for Distributed Learning with Convergence Guarantees](https://mlsanity.com/paper/2507.08784/) (2025)
- [LOST: Low-rank and Sparse Pre-training for Large Language Models](https://mlsanity.com/paper/2508.02668/) (2025)
- [Reparameterized LLM Training via Orthogonal Equivalence Transformation](https://mlsanity.com/paper/2506.08001/) (2025)
- [Breaking the Frozen Subspace: Importance Sampling for Low-Rank Optimization in LLM Pretraining](https://mlsanity.com/paper/2502.05790/) (2025)
- [CR-Net: Scaling Parameter-Efficient Training with Cross-Layer Low-Rank Structure](https://mlsanity.com/paper/2509.18993/) (2025)
- [TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Training](https://mlsanity.com/paper/2501.02379/) (2025)
- [CE-LoRA: Computation-Efficient LoRA Fine-Tuning for Language Models](https://mlsanity.com/paper/2502.01378/) (2025)
- [LaX: Boosting Low-Rank Training of Foundation Models via Latent Crossing](https://mlsanity.com/paper/2505.21732/) (2025)
- [TEON: Tensorized Orthonormalization Beyond Layer-Wise Muon for Large Language Model Pre-Training](https://mlsanity.com/paper/2601.23261/) (2026)
- [MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-training](https://mlsanity.com/paper/2602.21545/) (2026)
- [ElaLoRA: Elastic & Learnable Low-Rank Adaptation for Efficient Model Fine-Tuning](https://mlsanity.com/paper/2504.00254/) (2025)
- [Scalable Parameter and Memory Efficient Pretraining for LLM: Recent Algorithmic Advances and Benchmarking](https://mlsanity.com/paper/2505.22922/) (2025)
- [POET-X: Memory-efficient LLM Training by Scaling Orthogonal Transformation](https://mlsanity.com/paper/2603.05500/) (2026)
- [Cut Less, Fold More: Model Compression through the Lens of Projection Geometry](https://mlsanity.com/paper/2602.18116/) (2026)
- [Full-Rank No More: Low-Rank Weight Training for Modern Speech Recognition Models](https://mlsanity.com/paper/2410.07771/) (2024)
- [3BASiL: An Algorithmic Framework for Sparse plus Low-Rank Compression of LLMs](https://mlsanity.com/paper/2603.01376/) (2026)
- [Low-Rank Adaptation Redux for Large Models](https://mlsanity.com/paper/2604.21905/) (2026)
- [QKV Projections Require a Fraction of Their Memory](https://mlsanity.com/paper/2506.02939/) (2025)
- [Sparse corruption in low-rank matrix inference: the PCA benchmark](https://mlsanity.com/paper/2511.11927/) (2025)
- [BOOST: BOttleneck-Optimized Scalable Training Framework for Low-Rank Large Language Models](https://mlsanity.com/paper/2512.12131/) (2025)
- [Taming Momentum: Rethinking Optimizer States Through Low-Rank Approximation](https://mlsanity.com/paper/2602.24283/) (2026)
- [Sparsity Outperforms Low-Rank Projections in Few-Shot Adaptation](https://mlsanity.com/paper/2504.12436/) (2025)
- [ParaVul: A Parallel Large Language Model and Retrieval-Augmented Framework for Smart Contract Vulnerability Detection](https://mlsanity.com/paper/2510.17919/) (2025)
- [EcoSpa: Efficient Transformer Training with Coupled Sparsity](https://mlsanity.com/paper/2511.11641/) (2025)
- [SALAAD: Sparse And Low-Rank Adaptation via ADMM for Large Language Model Inference](https://mlsanity.com/paper/2602.00942/) (2026)
- [Structural Correspondence and Universal Approximation in Diagonal plus Low-Rank Neural Networks](https://mlsanity.com/paper/2605.05659/) (2026)

## Abstract (arXiv)

Large language models (LLMs) have shown impressive capabilities across various tasks. However, training LLMs from scratch requires significant computational power and extensive memory capacity. Recent studies have explored low-rank structures on weights for efficient fine-tuning in terms of parameters and memory, either through low-rank adaptation or factorization. While effective for fine-tuning, low-rank structures are generally less suitable for pretraining because they restrict parameters to a low-dimensional subspace. In this work, we propose to parameterize the weights as a sum of low-rank and sparse matrices for pretraining, which we call SLTrain. The low-rank component is learned via matrix factorization, while for the sparse component, we employ a simple strategy of uniformly selecting the sparsity support at random and learning only the non-zero entries with the fixed support. While being simple, the random fixed-support sparse learning strategy significantly enhances pretraining when combined with low-rank learning. Our results show that SLTrain adds minimal extra parameters and memory costs compared to pretraining with low-rank parameterization, yet achieves substantially better performance, which is comparable to full-rank training. Remarkably, when combined with quantization and per-layer updates, SLTrain can reduce memory requirements by up to 73% when pretraining the LLaMA 7B model.