Stabilizing Native Low-Rank LLM Pretraining
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Abstract (arXiv)
Foundation models have achieved remarkable success, yet their growing parameter counts pose significant computational and memory challenges. Low-rank factorization offers a promising route to reduce training and inference costs, but the community lacks a stable recipe for training models from scratch using exclusively low-rank weights while matching the performance of the dense model. We demonstrate that Large Language Models (LLMs) can be trained from scratch using exclusively low-rank factorized weights for all non-embedding matrices without auxiliary "full-rank" guidance required by prior methods. While native low-rank training often suffers from instability and loss spikes, we identify uncontrolled growth in the spectral norm (largest singular value) of the weight matrix update as the dominant factor. To address this, we introduce Spectron: Spectral renormalization with orthogonalization, which dynamically bounds the resultant weight updates based on the current spectral norms of the factors. Our method enables stable, end-to-end factorized training with negligible overhead. Finally, we establish compute-optimal scaling laws for natively low-rank transformers, demonstrating predictable power-law behavior and improved inference efficiency relative to dense models.
Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 48 of its 63 references that are in the map. First posted on arXiv 12 Feb 2026.
Builds on
48 of 63 references.
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Built on by
Citing papers per year: 2026: 6.
6 papers.
- 2026Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifoldscited by 6
- 2026LoRA-Muon: Spectral Steepest Descent on the Low-Rank Manifoldcited by 3
- 2026PoLoRA: A Preconditioned Orthogonalized LoRA Optimizercited by 2
- 2026SOAP, Muon, and Beyond: Pushing LLM Pretraining Scalescited by 1
- 2026Learned Subspace Compression for Communication-Efficient Pipeline Parallelismcited by 0
- 2026Approximate Muon with low-rank adapterscited by 0
- 2026Approximate Muon with low-rank adapters14 Aug 2026
- 2026PoLoRA: A Preconditioned Orthogonalized LoRA Optimizer20 Jul 2026
- 2026SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales13 Jul 2026
- 2026LoRA-Muon: Spectral Steepest Descent on the Low-Rank Manifold11 Jun 2026
- 2026Learned Subspace Compression for Communication-Efficient Pipeline Parallelism3 Jun 2026
- 2026Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds10 May 2026