Sparse Spectral Training and Inference on Euclidean and Hyperbolic Neural Networks

Jialin Zhao, Yingtao Zhang, Xinghang Li, Huaping Liu, Carlo Vittorio Cannistraci
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:77976-78002, 2025.

Abstract

The growing demands on GPU memory posed by the increasing number of neural network parameters call for training approaches that are more memory-efficient. Previous memory reduction training techniques, such as Low-Rank Adaptation (LoRA) and ReLoRA, face challenges, with LoRA being constrained by its low-rank structure, particularly during intensive tasks like pre-training, and ReLoRA suffering from saddle point issues. In this paper, we propose Sparse Spectral Training (SST) to optimize memory usage for pre-training. SST updates all singular values and selectively updates singular vectors through a multinomial sampling method weighted by the magnitude of the singular values. Furthermore, SST employs singular value decomposition to initialize and periodically reinitialize low-rank parameters, reducing distortion relative to full-rank training compared to other low-rank methods. Through comprehensive testing on both Euclidean and hyperbolic neural networks across various tasks, SST demonstrates its ability to outperform existing memory reduction training methods and is comparable to full-rank training in various cases. On LLaMA-1.3B, with only 18.7% of the parameters trainable compared to full-rank training (using a rank equivalent to 6% of the embedding dimension), SST reduces the perplexity gap between other low-rank methods and full-rank training by 97.4%. This result highlights SST as an effective parameter-efficient technique for model pre-training.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhao25ah, title = {Sparse Spectral Training and Inference on {E}uclidean and Hyperbolic Neural Networks}, author = {Zhao, Jialin and Zhang, Yingtao and Li, Xinghang and Liu, Huaping and Cannistraci, Carlo Vittorio}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {77976--78002}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhao25ah/zhao25ah.pdf}, url = {https://proceedings.mlr.press/v267/zhao25ah.html}, abstract = {The growing demands on GPU memory posed by the increasing number of neural network parameters call for training approaches that are more memory-efficient. Previous memory reduction training techniques, such as Low-Rank Adaptation (LoRA) and ReLoRA, face challenges, with LoRA being constrained by its low-rank structure, particularly during intensive tasks like pre-training, and ReLoRA suffering from saddle point issues. In this paper, we propose Sparse Spectral Training (SST) to optimize memory usage for pre-training. SST updates all singular values and selectively updates singular vectors through a multinomial sampling method weighted by the magnitude of the singular values. Furthermore, SST employs singular value decomposition to initialize and periodically reinitialize low-rank parameters, reducing distortion relative to full-rank training compared to other low-rank methods. Through comprehensive testing on both Euclidean and hyperbolic neural networks across various tasks, SST demonstrates its ability to outperform existing memory reduction training methods and is comparable to full-rank training in various cases. On LLaMA-1.3B, with only 18.7% of the parameters trainable compared to full-rank training (using a rank equivalent to 6% of the embedding dimension), SST reduces the perplexity gap between other low-rank methods and full-rank training by 97.4%. This result highlights SST as an effective parameter-efficient technique for model pre-training.} }
Endnote
%0 Conference Paper %T Sparse Spectral Training and Inference on Euclidean and Hyperbolic Neural Networks %A Jialin Zhao %A Yingtao Zhang %A Xinghang Li %A Huaping Liu %A Carlo Vittorio Cannistraci %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhao25ah %I PMLR %P 77976--78002 %U https://proceedings.mlr.press/v267/zhao25ah.html %V 267 %X The growing demands on GPU memory posed by the increasing number of neural network parameters call for training approaches that are more memory-efficient. Previous memory reduction training techniques, such as Low-Rank Adaptation (LoRA) and ReLoRA, face challenges, with LoRA being constrained by its low-rank structure, particularly during intensive tasks like pre-training, and ReLoRA suffering from saddle point issues. In this paper, we propose Sparse Spectral Training (SST) to optimize memory usage for pre-training. SST updates all singular values and selectively updates singular vectors through a multinomial sampling method weighted by the magnitude of the singular values. Furthermore, SST employs singular value decomposition to initialize and periodically reinitialize low-rank parameters, reducing distortion relative to full-rank training compared to other low-rank methods. Through comprehensive testing on both Euclidean and hyperbolic neural networks across various tasks, SST demonstrates its ability to outperform existing memory reduction training methods and is comparable to full-rank training in various cases. On LLaMA-1.3B, with only 18.7% of the parameters trainable compared to full-rank training (using a rank equivalent to 6% of the embedding dimension), SST reduces the perplexity gap between other low-rank methods and full-rank training by 97.4%. This result highlights SST as an effective parameter-efficient technique for model pre-training.
APA
Zhao, J., Zhang, Y., Li, X., Liu, H. & Cannistraci, C.V.. (2025). Sparse Spectral Training and Inference on Euclidean and Hyperbolic Neural Networks. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:77976-78002 Available from https://proceedings.mlr.press/v267/zhao25ah.html.

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