Can Sparse Spectral Training Make AI More Accessible?

Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Abstract and 1. Introduction Related Work Low Rank Adaptation 3.1 LoRA and 3.2 Limitation of LoRA 3.3 ReLoRA* Sparse Spectral Training 4.1 Preliminaries and 4.2 Gradient Update of U, VT with Σ 4.3 Why SVD Initialization is Important 4.4 SST Balances Exploitation and Exploration 4.5 Memory-Efficient Implementation for SST and 4.6 Sparsity of SST Experiments 5.1 Machine Translation 5.2 Natural Language Generation 5.3 Hyperbolic Graph Neural Networks Conclusion and Discussion Broader Impacts and References Related Work Related Work Related Work Related Work Low Rank Adaptation 3.1 LoRA and 3.2 Limitation of LoRA 3.3 ReLoRA* Low Rank Adaptation Low Rank Adaptation 3.1 LoRA and 3.2 Limitation of LoRA 3.1 LoRA and 3.2 Limitation of LoRA 3.3 ReLoRA* 3.3 ReLoRA* Sparse Spectral Training 4.1 Preliminaries and 4.2 Gradient Update of U, VT with Σ 4.3 Why SVD Initialization is Important 4.4 SST Balances Exploitation and Exploration 4.5 Memory-Efficient Implementation for SST and 4.6 Sparsity of SST Sparse Spectral Training Sparse Spectral Training 4.1 Preliminaries and 4.2 Gradient Update of U, VT with Σ 4.1 Preliminaries and 4.2 Gradient Update of U, VT with Σ 4.3 Why SVD Initialization is Important 4.3 Why SVD Initialization is Important 4.4 SST Balances Exploitation and Exploration 4.4 SST Balances Exploitation and Exploration 4.5 Memory-Efficient Implementation for SST and 4.6 Sparsity of SST 4.5 Memory-Efficient Implementation for SST and 4.6 Sparsity of SST Experiments 5.1 Machine Translation 5.2 Natural Language Generation 5.3 Hyperbolic Graph Neural Networks Experiments Experiments Experiments 5.1 Machine Translation 5.1 Machine Translation 5.2 Natural Language Generation 5.2 Natural Language Generation 5.3 Hyperbolic Graph Neural Networks 5.3 Hyperbolic Graph Neural Networks Conclusion and Discussion Conclusion and Discussion Conclusion and Discussion Conclusion and Discussion Broader Impacts and References Broader Impacts and References Broader Impacts and References Broader Impacts and References Supplementary Information Supplementary Information A. Algorithm of Sparse Spectral Training A. Algorithm of Sparse Spectral Training B. Proof of Gradient of Sparse Spectral Layer B. Proof of Gradient of Sparse Spectral Layer C. Proof of Decomposition of Gradient of Weight C. Proof of Decomposition of Gradient of Weight D. Proof of Advantage of Enhanced Gradient over Default Gradient D. Proof of Advantage of Enhanced Gradient over Default Gradient E. Proof of Zero Distortion with SVD Initialization E. Proof of Zero Distortion with SVD Initialization F. Experiment Details F. Experiment Details G. Singular Value Pruning G. Singular Value Pruning H. Evaluating SST and GaLore: Complementary Approaches to Memory Efficiency H. Evaluating SST and GaLore: Complementary Approaches to Memory Efficiency I. Ablation Study I. Ablation Study 6 Conclusion and Discussion In this work, Sparse Spectral Training (SST) has demonstrated its efficacy as a resource-efficient training methodology that closely approximates the performance of full-rank training across diverse architectures, tasks and embedding geometries. SST introduces a noval approach by updating all singular values and selectively adjusting the singular vectors of network weights, optimizing resource utilization while closely mirroring the performance of full-rank training. Moreover, some areas that need further explorations are: (1) Investigating faster convergence approaches that avoid optimizer state reset (2) Extending the application of SST to the embeddings of large language models (LLMs). 7 Broader Impacts This research enhances the memory efficiency of training large language models (LLMs), which contributes positively by reducing the environmental impact and making LLM training accessible to researchers with limited resources. 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Authors: (1) Jialin Zhao, Center for Complex Network Intelligence (CCNI), Tsinghua Laboratory of Brain and Intelligence (THBI) and Department of Computer Science; (2) Yingtao Zhang, Center for Complex Network Intelligence (CCNI), Tsinghua Laboratory of Brain and Intelligence (THBI) and Department of Computer Science; (3) Xinghang Li, Department of Computer Science; (4) Huaping Liu, Department of Computer Science; (5) Carlo Vittorio Cannistraci, Center for Complex Network Intelligence (CCNI), Tsinghua Laboratory of Brain and Intelligence (THBI), Department of Computer Science, and Department of Biomedical Engineering Tsinghua University, Beijing, China. Authors: Authors: (1) Jialin Zhao, Center for Complex Network Intelligence (CCNI), Tsinghua Laboratory of Brain and Intelligence (THBI) and Department of Computer Science; (2) Yingtao Zhang, Center for Complex Network Intelligence (CCNI), Tsinghua Laboratory of Brain and Intelligence (THBI) and Department of Computer Science; (3) Xinghang Li, Department of Computer Science; (4) Huaping Liu, Department of Computer Science; (5) Carlo Vittorio Cannistraci, Center for Complex Network Intelligence (CCNI), Tsinghua Laboratory of Brain and Intelligence (THBI), Department of Computer Science, and Department of Biomedical Engineering Tsinghua University, Beijing, China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv available on arxiv