# When LLMs Stop Following Steps: A Diagnostic Study of Procedural Execution in Language Models

arXiv: https://arxiv.org/abs/2605.00817 · HTML: https://mlsanity.com/paper/2605.00817/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 39 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 27 of 27)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [Towards AI-Complete Question Answering: A Set of Prerequisite Toy Tasks](https://mlsanity.com/paper/1502.05698/) (2015)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [ToolSandbox: A Stateful, Conversational, Interactive Evaluation Benchmark for LLM Tool Use Capabilities](https://mlsanity.com/paper/2408.04682/) (2024)
- [Measuring Compositional Generalization: A Comprehensive Method on Realistic Data](https://mlsanity.com/paper/1912.09713/) (2019)
- [Compositionality decomposed: how do neural networks generalise?](https://mlsanity.com/paper/1908.08351/) (2019)
- [COGS: A Compositional Generalization Challenge Based on Semantic Interpretation](https://mlsanity.com/paper/2010.05465/) (2020)
- [What Algorithms can Transformers Learn? A Study in Length Generalization](https://mlsanity.com/paper/2310.16028/) (2023)
- [Thinking Like Transformers](https://mlsanity.com/paper/2106.06981/) (2021)
- [Implicit Representations of Meaning in Neural Language Models](https://mlsanity.com/paper/2106.00737/) (2021)
- [CLUTRR: A Diagnostic Benchmark for Inductive Reasoning from Text](https://mlsanity.com/paper/1908.06177/) (2019)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [Teaching Algorithmic Reasoning via In-context Learning](https://mlsanity.com/paper/2211.09066/) (2022)
- [Neural Algorithmic Reasoning](https://mlsanity.com/paper/2105.02761/) (2021)
- [Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad](https://mlsanity.com/paper/2503.21934/) (2025)
- [Generalization on the Unseen, Logic Reasoning and Degree Curriculum](https://mlsanity.com/paper/2301.13105/) (2023)
- [Tracking State Changes in Procedural Text: A Challenge Dataset and Models for Process Paragraph Comprehension](https://mlsanity.com/paper/1805.06975/) (2018)
- [Sample, Scrutinize and Scale: Effective Inference-Time Search by Scaling Verification](https://mlsanity.com/paper/2502.01839/) (2025)
- [Reasoning about Actions and State Changes by Injecting Commonsense Knowledge](https://mlsanity.com/paper/1808.10012/) (2018)
- [Principled Understanding of Generalization for Generative Transformer Models in Arithmetic Reasoning Tasks](https://mlsanity.com/paper/2407.17963/) (2024)
- [GroundCocoa: A Benchmark for Evaluating Compositional & Conditional Reasoning in Language Models](https://mlsanity.com/paper/2404.04237/) (2024)

## Abstract (arXiv)

Large language models (LLMs) often achieve strong performance on reasoning benchmarks, but final-answer accuracy alone does not show whether they faithfully execute the procedure specified in a prompt. We introduce a controlled diagnostic benchmark for arithmetic procedural execution, where models are given a step-wise arithmetic procedure and two numeric inputs, and must return the final computed value. Complexity is varied through procedure length and look-back dependencies over intermediate variables. Average first-answer accuracy drops from 63% on 5-step procedures to 20% on 95-step procedures. Generation-level analysis shows that failures often involve missing answers, premature answers, self-correction after an initial error and under-executed traces. These findings reveal a consistent decline in execution performance as arithmetic procedural complexity increases.