@article{spectralcompacttrainingpretraininglargel, title = {Spectral Compact Training: Pre-Training Large Language Models via Permanent Truncated SVD and Stiefel QR Retraction}, author = {Björn Roman Kohlberger}, year = {2026}, eprint = {2604.00733}, archivePrefix = {arXiv}, url = {https://arxiv.org/abs/2604.00733}, }