# Scaling Laws for State Dynamics in Large Language Models

arXiv: https://arxiv.org/abs/2505.14892 · HTML: https://mlsanity.com/paper/2505.14892/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 27 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 17 of 17)

- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [World Models](https://mlsanity.com/paper/1803.10122/) (2018)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [On the Planning Abilities of Large Language Models : A Critical Investigation](https://mlsanity.com/paper/2305.15771/) (2023)
- [Fine-Tuning Enhances Existing Mechanisms: A Case Study on Entity Tracking](https://mlsanity.com/paper/2402.14811/) (2024)
- [Generalized Planning in PDDL Domains with Pretrained Large Language Models](https://mlsanity.com/paper/2305.11014/) (2023)
- [Explicit Planning Helps Language Models in Logical Reasoning](https://mlsanity.com/paper/2303.15714/) (2023)
- [Selecting the State-Representation in Reinforcement Learning](https://mlsanity.com/paper/1302.2552/) (2013)
- [Feature-Based Interpretable Reinforcement Learning based on State-Transition Models](https://mlsanity.com/paper/2105.07099/) (2021)
- [Towards a Better Understanding of Representation Dynamics under TD-learning](https://mlsanity.com/paper/2305.18491/) (2023)

## Abstract (arXiv)

Large Language Models (LLMs) are increasingly used in tasks requiring internal state tracking, yet their ability to model state transition dynamics remains poorly understood. We evaluate how well LLMs capture deterministic state dynamics across 3 domains: Box Tracking, Abstract DFA Sequences, and Complex Text Games, each formalizable as a finite-state system. Across tasks, we find that next-state prediction accuracy degrades with increasing state-space size and sparse transitions. GPT-2 XL reaches about 70% accuracy in low-complexity settings but drops below 30% when the number of boxes or states exceeds 5 or 10, respectively. In DFA tasks, Pythia-1B fails to exceed 50% accuracy when the number of states is > 10 and transitions are < 30. Through activation patching, we identify attention heads responsible for propagating state information: GPT-2 XL Layer 22 Head 20, and Pythia-1B Heads at Layers 10, 11, 12, and 14. While these heads successfully move relevant state features, action information is not reliably routed to the final token, indicating weak joint state-action reasoning. Our results suggest that state tracking in LLMs emerges from distributed interactions of next-token heads rather than explicit symbolic computation.