# Unifying Two Types of Scaling Laws from the Perspective of Conditional Kolmogorov Complexity

arXiv: https://arxiv.org/abs/2501.06802 · HTML: https://mlsanity.com/paper/2501.06802/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 34 references that are in the map.
- First posted on arXiv 12 Jan 2025.

## Builds on (most cited first, 6 of 6)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [Language Modeling Is Compression](https://mlsanity.com/paper/2309.10668/) (2023)
- [How Powerful are Decoder-Only Transformer Neural Models?](https://mlsanity.com/paper/2305.17026/) (2023)

## Built on by (most cited first, 2 of 2)

- [Large Language Models as Computable Approximations to Solomonoff Induction](https://mlsanity.com/paper/2505.15784/) (2025)
- [Towards Alignment-Centric Paradigm: A Survey of Instruction Tuning in Large Language Models](https://mlsanity.com/paper/2508.17184/) (2025)

## Abstract (arXiv)

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.