Unifying Two Types of Scaling Laws from the Perspective of Conditional Kolmogorov Complexity
This work provides a theoretical unification for scaling laws in AI, which is incremental as it builds on existing proposals without introducing new empirical results.
The paper tackles the problem of unifying two types of scaling laws in large language models by analyzing training and inference processes from the perspective of conditional Kolmogorov complexity, finding that both laws improve approximation of this complexity by increasing execution steps of a Turing machine.
In 2020, OpenAI proposed the first type of Scaling Laws, describing the relationships between model loss and the scale of parameters, data, and training computation. In 2024, OpenAI proposed the second type of Scaling Laws, describing the relationship between model inference performance and inference computation. In this paper, we analyze LLMs training and inference processes from the perspective of lossless compression using conditional Kolmogorov complexity, and unify these two types of Scaling Laws. We find that both types of Scaling Laws improve approximation of conditional Kolmogorov complexity by increasing execution steps of Turing machine. The first type of Scaling Laws increases execution steps by increasing number of model parameters. The second type of Scaling Laws increases execution steps by increasing the number of intermediate tokens.