Learning on Transformers is Provable Low-Rank and Sparse: A One-layer Analysis
Document Type
Conference Proceeding
Publication Date
1-1-2024
Abstract
Efficient training and inference algorithms, such as low-rank adaption and model pruning, have shown impressive performance for learning Transformer-based large foundation models. However, due to the technical challenges of the non-convex optimization caused by the complicated architecture of Transformers, the theoretical study of why these methods can be applied to learn Transformers is mostly elusive. To the best of our knowledge, this paper shows the first theoretical analysis of the property of low-rank and sparsity of one-layer Transformers by characterizing the trained model after convergence using stochastic gradient descent. By focusing on a data model based on label-relevant and label-irrelevant patterns, we quantify that the gradient updates of trainable parameters are low-rank, which de-pends on the number of label-relevant patterns. We also analyze how model pruning affects the generalization while improving computation efficiency and conclude that proper magnitude-based pruning has a slight effect on the testing performance. We implement numerical experiments to support our findings.
Identifier
85203387061 (Scopus)
ISBN
[9798350344813]
Publication Title
Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
External Full Text Location
https://doi.org/10.1109/SAM60225.2024.10636559
e-ISSN
2151870X
Recommended Citation
Li, Hongkang; Wang, Meng; Zhang, Shuai; Liu, Sijia; and Chen, Pin Yu, "Learning on Transformers is Provable Low-Rank and Sparse: A One-layer Analysis" (2024). Faculty Publications. 891.
https://digitalcommons.njit.edu/fac_pubs/891