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arXiv · 2509.07909

Uncovering Scaling Laws for Large Language Models via Inverse Problems

Arun Verma·Zhaoxuan Wu·Zijian Zhou·Xiaoqiang Lin·Zhiliang Chen·Rachael Hwee Ling Sim·Rui Qiao·Jingtan Wang·Nhung Bui·Xinyuan Niu·Wenyang Hu·Gregory Kang Ruey Lau·Zi-Yu Khoo·Zitong Zhao·Xinyi Xu·Apivich Hemachandra·See-Kiong Ng·Bryan Kian Hsiang Low
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Abstract

Large Language Models (LLMs) are large-scale pretrained models that have achieved remarkable success across diverse domains. These successes have been driven by unprecedented complexity and scale in both data and computations. However, due to the high costs of training such models, brute-force trial-and-error approaches to improve LLMs are not feasible. Inspired by the success of inverse problems in uncovering fundamental scientific laws, this position paper advocates that inverse problems can also efficiently uncover scaling laws that guide the building of LLMs to achieve the desirable performance with significantly better cost-effectiveness.

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Arun Verma, Zhaoxuan Wu, Zijian Zhou, Xiaoqiang Lin, Zhiliang Chen, Rachael Hwee Ling Sim, Rui Qiao, Jingtan Wang, Nhung Bui, Xinyuan Niu, Wenyang Hu, Gregory Kang Ruey Lau, Zi-Yu Khoo, Zitong Zhao, Xinyi Xu, Apivich Hemachandra, See-Kiong Ng, Bryan Kian Hsiang Low. 2025-09-09. Uncovering Scaling Laws for Large Language Models via Inverse Problems. https://arxiv.org/abs/2509.07909

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