Local to Global: Learning Dynamics and Effect of Initialization for Transformers
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909232201203712 |
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| author | Makkuva, Ashok Vardhan Bondaschi, Marco Ekbote, Chanakya Girish, Adway Nagle, Alliot Kim, Hyeji Gastpar, Michael |
| author_facet | Makkuva, Ashok Vardhan Bondaschi, Marco Ekbote, Chanakya Girish, Adway Nagle, Alliot Kim, Hyeji Gastpar, Michael |
| contents | In recent years, transformer-based models have revolutionized deep learning, particularly in sequence modeling. To better understand this phenomenon, there is a growing interest in using Markov input processes to study transformers. However, our current understanding in this regard remains limited with many fundamental questions about how transformers learn Markov chains still unanswered. In this paper, we address this by focusing on first-order Markov chains and single-layer transformers, providing a comprehensive characterization of the learning dynamics in this context. Specifically, we prove that transformer parameters trained on next-token prediction loss can either converge to global or local minima, contingent on the initialization and the Markovian data properties, and we characterize the precise conditions under which this occurs. To the best of our knowledge, this is the first result of its kind highlighting the role of initialization. We further demonstrate that our theoretical findings are corroborated by empirical evidence. Based on these insights, we provide guidelines for the initialization of transformer parameters and demonstrate their effectiveness. Finally, we outline several open problems in this arena. Code is available at: https://github.com/Bond1995/Markov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03072 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local to Global: Learning Dynamics and Effect of Initialization for Transformers Makkuva, Ashok Vardhan Bondaschi, Marco Ekbote, Chanakya Girish, Adway Nagle, Alliot Kim, Hyeji Gastpar, Michael Machine Learning Information Theory In recent years, transformer-based models have revolutionized deep learning, particularly in sequence modeling. To better understand this phenomenon, there is a growing interest in using Markov input processes to study transformers. However, our current understanding in this regard remains limited with many fundamental questions about how transformers learn Markov chains still unanswered. In this paper, we address this by focusing on first-order Markov chains and single-layer transformers, providing a comprehensive characterization of the learning dynamics in this context. Specifically, we prove that transformer parameters trained on next-token prediction loss can either converge to global or local minima, contingent on the initialization and the Markovian data properties, and we characterize the precise conditions under which this occurs. To the best of our knowledge, this is the first result of its kind highlighting the role of initialization. We further demonstrate that our theoretical findings are corroborated by empirical evidence. Based on these insights, we provide guidelines for the initialization of transformer parameters and demonstrate their effectiveness. Finally, we outline several open problems in this arena. Code is available at: https://github.com/Bond1995/Markov. |
| title | Local to Global: Learning Dynamics and Effect of Initialization for Transformers |
| topic | Machine Learning Information Theory |
| url | https://arxiv.org/abs/2406.03072 |