# Stabilizing the Dynamic Low-Rank Training

arXiv: https://arxiv.org/abs/2609.32615 · HTML: https://mlsanity.com/paper/2609.32615/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 56 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 30 of 42)

- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [DeBERTaV3: Improving DeBERTa using ELECTRA-Style Pre-Training with Gradient-Disentangled Embedding Sharing](https://mlsanity.com/paper/2111.09543/) (2021)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [The Lottery Ticket Hypothesis for Pre-trained BERT Networks](https://mlsanity.com/paper/2007.12223/) (2020)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [DepGraph: Towards Any Structural Pruning](https://mlsanity.com/paper/2301.12900/) (2023)
- [A Survey on Deep Neural Network Pruning-Taxonomy, Comparison, Analysis, and Recommendations](https://mlsanity.com/paper/2308.06767/) (2023)
- [Proving the Lottery Ticket Hypothesis: Pruning is All You Need](https://mlsanity.com/paper/2002.00585/) (2020)
- [Structured Pruning for Deep Convolutional Neural Networks: A survey](https://mlsanity.com/paper/2303.00566/) (2023)
- [A Unified Lottery Ticket Hypothesis for Graph Neural Networks](https://mlsanity.com/paper/2102.06790/) (2021)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [One ticket to win them all: generalizing lottery ticket initializations across datasets and optimizers](https://mlsanity.com/paper/1906.02773/) (2019)
- [The Lottery Tickets Hypothesis for Supervised and Self-supervised Pre-training in Computer Vision Models](https://mlsanity.com/paper/2012.06908/) (2020)
- [Optimal Lottery Tickets via SubsetSum: Logarithmic Over-Parameterization is Sufficient](https://mlsanity.com/paper/2006.07990/) (2020)
- [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)
- [LoRAPrune: Structured Pruning Meets Low-Rank Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2305.18403/) (2023)
- [Sanity Checks for Lottery Tickets: Does Your Winning Ticket Really Win the Jackpot?](https://mlsanity.com/paper/2107.00166/) (2021)
- [Low-rank lottery tickets: finding efficient low-rank neural networks via matrix differential equations](https://mlsanity.com/paper/2205.13571/) (2022)

## Abstract (arXiv)

Training neural networks directly in a low-rank parameterization is an appealing route to reducing memory, compute, and storage simultaneously during both training and inference. Dynamic low-rank training (DLRT), which confines weights to a rank-r manifold via the Galerkin projection of the gradient flow, is particularly attractive because it identifies efficient subnetworks on the fly without specialized initialization or post-factorization. However, DLRT fails to find trainable networks under high compression. In this paper, we derive the gradient flow of the best rank-r approximation and point out that the offset of DLRT comes from a curvature-coupling term which is large and thus non-negligible under aggressive compression. Guided by this analysis, we propose a stable dynamic low-rank training method, named SDLRT, which maintains a lightweight compensation buffer that reinjects the top neglected singular directions. Additionally, we introduce a negative feedback on the truncation tolerance to stabilize each layer's rank. Experimentally, SDLRT reliably finds trainable subnetworks where DLRT collapses and as a PEFT adapter on DeBERTa-v3, it achieves the best average score on SuperGLUE at only 2.8% parameter overhead over LoRA.