Unlocking the Theory Behind Scaling 1-Bit Neural Networks
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| author | Daliri, Majid Song, Zhao Yang, Chiwun |
| author_facet | Daliri, Majid Song, Zhao Yang, Chiwun |
| contents | Recently, 1-bit Large Language Models (LLMs) have emerged, showcasing an impressive combination of efficiency and performance that rivals traditional LLMs. Research by Wang et al. (2023); Ma et al. (2024) indicates that the performance of these 1-bit LLMs progressively improves as the number of parameters increases, hinting at the potential existence of a Scaling Law for 1-bit Neural Networks. In this paper, we present the first theoretical result that rigorously establishes this scaling law for 1-bit models. We prove that, despite the constraint of weights restricted to $\{-1, +1\}$, the dynamics of model training inevitably align with kernel behavior as the network width grows. This theoretical breakthrough guarantees convergence of the 1-bit model to an arbitrarily small loss as width increases. Furthermore, we introduce the concept of the generalization difference, defined as the gap between the outputs of 1-bit networks and their full-precision counterparts, and demonstrate that this difference maintains a negligible level as network width scales. Building on the work of Kaplan et al. (2020), we conclude by examining how the training loss scales as a power-law function of the model size, dataset size, and computational resources utilized for training. Our findings underscore the promising potential of scaling 1-bit neural networks, suggesting that int1 could become the standard in future neural network precision. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01663 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unlocking the Theory Behind Scaling 1-Bit Neural Networks Daliri, Majid Song, Zhao Yang, Chiwun Machine Learning Artificial Intelligence Computational Complexity Computation and Language Recently, 1-bit Large Language Models (LLMs) have emerged, showcasing an impressive combination of efficiency and performance that rivals traditional LLMs. Research by Wang et al. (2023); Ma et al. (2024) indicates that the performance of these 1-bit LLMs progressively improves as the number of parameters increases, hinting at the potential existence of a Scaling Law for 1-bit Neural Networks. In this paper, we present the first theoretical result that rigorously establishes this scaling law for 1-bit models. We prove that, despite the constraint of weights restricted to $\{-1, +1\}$, the dynamics of model training inevitably align with kernel behavior as the network width grows. This theoretical breakthrough guarantees convergence of the 1-bit model to an arbitrarily small loss as width increases. Furthermore, we introduce the concept of the generalization difference, defined as the gap between the outputs of 1-bit networks and their full-precision counterparts, and demonstrate that this difference maintains a negligible level as network width scales. Building on the work of Kaplan et al. (2020), we conclude by examining how the training loss scales as a power-law function of the model size, dataset size, and computational resources utilized for training. Our findings underscore the promising potential of scaling 1-bit neural networks, suggesting that int1 could become the standard in future neural network precision. |
| title | Unlocking the Theory Behind Scaling 1-Bit Neural Networks |
| topic | Machine Learning Artificial Intelligence Computational Complexity Computation and Language |
| url | https://arxiv.org/abs/2411.01663 |