Unlock the Theory behind Scaling 1-bit Neural Networks

Majid Daliri, Zhao Song, Chiwun Yang
Conference on Parsimony and Learning, PMLR 280:545-598, 2025.

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 in 1-bit Neural Networks*. This paper presents 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v280-daliri25a, title = {Unlock the Theory behind Scaling 1-bit Neural Networks}, author = {Daliri, Majid and Song, Zhao and Yang, Chiwun}, booktitle = {Conference on Parsimony and Learning}, pages = {545--598}, year = {2025}, editor = {Chen, Beidi and Liu, Shijia and Pilanci, Mert and Su, Weijie and Sulam, Jeremias and Wang, Yuxiang and Zhu, Zhihui}, volume = {280}, series = {Proceedings of Machine Learning Research}, month = {24--27 Mar}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v280/main/assets/daliri25a/daliri25a.pdf}, url = {https://proceedings.mlr.press/v280/daliri25a.html}, 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 in 1-bit Neural Networks*. This paper presents 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.} }
Endnote
%0 Conference Paper %T Unlock the Theory behind Scaling 1-bit Neural Networks %A Majid Daliri %A Zhao Song %A Chiwun Yang %B Conference on Parsimony and Learning %C Proceedings of Machine Learning Research %D 2025 %E Beidi Chen %E Shijia Liu %E Mert Pilanci %E Weijie Su %E Jeremias Sulam %E Yuxiang Wang %E Zhihui Zhu %F pmlr-v280-daliri25a %I PMLR %P 545--598 %U https://proceedings.mlr.press/v280/daliri25a.html %V 280 %X 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 in 1-bit Neural Networks*. This paper presents 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.
APA
Daliri, M., Song, Z. & Yang, C.. (2025). Unlock the Theory behind Scaling 1-bit Neural Networks. Conference on Parsimony and Learning, in Proceedings of Machine Learning Research 280:545-598 Available from https://proceedings.mlr.press/v280/daliri25a.html.

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