# Language models fail at extended rule following

arXiv: https://arxiv.org/abs/2605.02028 · HTML: https://mlsanity.com/paper/2605.02028/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 166 references that are in the map.
- First posted on arXiv 3 May 2026.

## Builds on (most cited first, 10 of 10)

- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systems](https://mlsanity.com/paper/2505.11831/) (2025)
- [Transformers represent belief state geometry in their residual stream](https://mlsanity.com/paper/2405.15943/) (2024)
- [LongGenBench: Benchmarking Long-Form Generation in Long Context LLMs](https://mlsanity.com/paper/2409.02076/) (2024)
- [On the Impacts of Contexts on Repository-Level Code Generation](https://mlsanity.com/paper/2406.11927/) (2024)

## Built on by (most cited first, 1 of 1)

- [Beyond Retrieval: Evidence Access and Event Aggregation in Agent Memory](https://mlsanity.com/paper/2610.19474/) (2026)

## Abstract (arXiv)

Large language models are highly capable of answering difficult questions by retrieving, recombining, and attending to information in long contexts. For agentic tasks, an additional capability is required: the preservation of an exact state while repeatedly applying rules. We find that this reliability is absent across language models. To demonstrate, we query 126 leading model variants with the task of counting a long string of repeated characters, and we find they all cannot accurately count above a model-dependent, syntax-sensitive counting capacity threshold. Failures are abrupt and persist even with increasing model size, inference time computation, and external tool. Mechanistic probing indicates that models use a finite number of internal states to mimic counting as a rule and fail once these states are exhausted. Furthermore, such states are the basis for performing complex tasks beyond counting. These results indicate that fundamentally new model architectures are required for autonomous agents to achieve truly reliable rule following capabilities.