# SLORR: Simple and Efficient In-Training Low-Rank Regularization

arXiv: https://arxiv.org/abs/2607.08754 · HTML: https://mlsanity.com/paper/2607.08754/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 56 references that are in the map.
- First posted on arXiv 9 Jul 2026.

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm](https://mlsanity.com/paper/2505.16932/) (2025)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [Initialization and Regularization of Factorized Neural Layers](https://mlsanity.com/paper/2105.01029/) (2021)
- [DeepHoyer: Learning Sparser Neural Network with Differentiable Scale-Invariant Sparsity Measures](https://mlsanity.com/paper/1908.09979/) (2019)
- [Learning Low-rank Deep Neural Networks via Singular Vector Orthogonality Regularization and Singular Value Sparsification](https://mlsanity.com/paper/2004.09031/) (2020)
- [Dobi-SVD: Differentiable SVD for LLM Compression and Some New Perspectives](https://mlsanity.com/paper/2502.02723/) (2025)
- [Compression-aware Training of Deep Networks](https://mlsanity.com/paper/1711.02638/) (2017)
- [SLTrain: a sparse plus low-rank approach for parameter and memory efficient pretraining](https://mlsanity.com/paper/2406.02214/) (2024)
- [Compressing Neural Networks: Towards Determining the Optimal Layer-wise Decomposition](https://mlsanity.com/paper/2107.11442/) (2021)
- [TRP: Trained Rank Pruning for Efficient Deep Neural Networks](https://mlsanity.com/paper/2004.14566/) (2020)
- [Exploring Low Rank Training of Deep Neural Networks](https://mlsanity.com/paper/2209.13569/) (2022)
- [From Low Rank Gradient Subspace Stabilization to Low-Rank Weights: Observations, Theories, and Applications](https://mlsanity.com/paper/2407.11239/) (2024)
- [Compression-aware Training of Neural Networks using Frank-Wolfe](https://mlsanity.com/paper/2205.11921/) (2022)
- [Domain Generalization via Nuclear Norm Regularization](https://mlsanity.com/paper/2303.07527/) (2023)
- [LOST: Low-rank and Sparse Pre-training for Large Language Models](https://mlsanity.com/paper/2508.02668/) (2025)
- [Trace norm regularization and faster inference for embedded speech recognition RNNs](https://mlsanity.com/paper/1710.09026/) (2017)

## Built on by (most cited first, 1 of 1)

- [Spectral Weight Decay: Inducing Low-Rank Structure in Neural Network Weights](https://mlsanity.com/paper/2610.11730/) (2026)

## Abstract (arXiv)

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.