# Sparse Spectral Training and Inference on Euclidean and Hyperbolic Neural Networks

arXiv: https://arxiv.org/abs/2405.15481 · HTML: https://mlsanity.com/paper/2405.15481/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 66 references that are in the map.
- First posted on arXiv 24 May 2024.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [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)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [GPT Understands, Too](https://mlsanity.com/paper/2103.10385/) (2021)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [A Corpus and Evaluation Framework for Deeper Understanding of Commonsense Stories](https://mlsanity.com/paper/1604.01696/) (2016)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [OpenNMT: Open-source Toolkit for Neural Machine Translation](https://mlsanity.com/paper/1709.03815/) (2017)
- [Multi30K: Multilingual English-German Image Descriptions](https://mlsanity.com/paper/1605.00459/) (2016)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)

## Built on by (most cited first, 4 of 4)

- [Hyperbolic Large Language Models](https://mlsanity.com/paper/2509.05757/) (2025)
- [Stabilizing Native Low-Rank LLM Pretraining](https://mlsanity.com/paper/2602.12429/) (2026)
- [SwitchLoRA: Switched Low-Rank Adaptation Can Learn Full-Rank Information](https://mlsanity.com/paper/2406.06564/) (2024)
- [Reuse or Relearn? A Spectral View of Earth Observation Foundation Models](https://mlsanity.com/paper/2609.32756/) (2026)

## Abstract (arXiv)

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.