# Efficient Pre-Training of LLMs through Truncated SVD Representations

arXiv: https://arxiv.org/abs/2605.28573 · HTML: https://mlsanity.com/paper/2605.28573/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 40 references that are in the map.
- First posted on arXiv 27 May 2026.

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

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Documenting Large Webtext Corpora: A Case Study on the Colossal Clean Crawled Corpus](https://mlsanity.com/paper/2104.08758/) (2021)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networks](https://mlsanity.com/paper/1709.06079/) (2017)
- [Can We Gain More from Orthogonality Regularizations in Training Deep CNNs?](https://mlsanity.com/paper/1810.09102/) (2018)
- [Initialization and Regularization of Factorized Neural Layers](https://mlsanity.com/paper/2105.01029/) (2021)
- [Learning Low-rank Deep Neural Networks via Singular Vector Orthogonality Regularization and Singular Value Sparsification](https://mlsanity.com/paper/2004.09031/) (2020)
- [SLTrain: a sparse plus low-rank approach for parameter and memory efficient pretraining](https://mlsanity.com/paper/2406.02214/) (2024)
- [Exploring Low Rank Training of Deep Neural Networks](https://mlsanity.com/paper/2209.13569/) (2022)
- [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)
- [StelLA: Subspace Learning in Low-rank Adaptation using Stiefel Manifold](https://mlsanity.com/paper/2510.01938/) (2025)
- [Robust low-rank training via approximate orthonormal constraints](https://mlsanity.com/paper/2306.01485/) (2023)
- [ELRT: Efficient Low-Rank Training for Compact Convolutional Neural Networks](https://mlsanity.com/paper/2401.10341/) (2024)
- [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)
- [Investigating Low-Rank Training in Transformer Language Models: Efficiency and Scaling Analysis](https://mlsanity.com/paper/2407.09835/) (2024)
- [POET-X: Memory-efficient LLM Training by Scaling Orthogonal Transformation](https://mlsanity.com/paper/2603.05500/) (2026)
- [Full-Rank No More: Low-Rank Weight Training for Modern Speech Recognition Models](https://mlsanity.com/paper/2410.07771/) (2024)

## Abstract (arXiv)

LLM pretraining is extremely costly; therefore, parameter-efficient LLM architectures have recently emerged as a compelling research direction. One such promising approach is to represent the parameters as orthonormal low-rank weight matrices. However, maintaining orthonormality during training is computationally expensive, making it impractical. This paper presents the TSVD (Truncated Singular Value Decomposition) framework which efficiently maintains orthonormality through QR decomposition and caching. Furthermore, a spectral energy heuristic is introduced to select the rank of the resulting low-rank weight matrices. Empirical evaluations across model sizes show that TSVD matches or outperforms full-parameter baselines at a fraction of the compute cost. TSVD thus provides a scalable, computationally efficient foundation for LLM pretraining.