Unlocking the Theory Behind Scaling 1-Bit Neural Networks

• URL: http://arxiv.org/abs/2411.01663v1
• Date: Sun, 03 Nov 2024 19:18:57 GMT
• Title: Unlocking the Theory Behind Scaling 1-Bit Neural Networks
• Authors: Majid Daliri, Zhao Song, Chiwun Yang,
• Abstract summary: 1-bit Large Language Models (LLMs) have emerged, showcasing an impressive combination of efficiency and performance that rivals traditional LLMs. We present the first theoretical result that rigorously establishes a Scaling Law for 1-bit Neural Networks. Our findings underscore the promising potential of scaling 1-bit neural networks, suggesting that int1 could become the standard in future neural network precision.
• Score: 7.578147116161996
• License:
• Abstract: 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.

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