# Understanding LLM Failures: A Multi-Tape Turing Machine Analysis of Systematic Errors in Language Model Reasoning

arXiv: https://arxiv.org/abs/2602.15868 · HTML: https://mlsanity.com/paper/2602.15868/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Neural Turing Machines](https://mlsanity.com/paper/1410.5401/) (2014)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [Theoretical Limitations of Self-Attention in Neural Sequence Models](https://mlsanity.com/paper/1906.06755/) (2019)
- [Transformers Learn Shortcuts to Automata](https://mlsanity.com/paper/2210.10749/) (2022)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Byte Pair Encoding is Suboptimal for Language Model Pretraining](https://mlsanity.com/paper/2004.03720/) (2020)
- [Thinking Like Transformers](https://mlsanity.com/paper/2106.06981/) (2021)
- [What Formal Languages Can Transformers Express? A Survey](https://mlsanity.com/paper/2311.00208/) (2023)
- [Self-Attention Networks Can Process Bounded Hierarchical Languages](https://mlsanity.com/paper/2105.11115/) (2021)
- [Verbalized Sampling: How to Mitigate Mode Collapse and Unlock LLM Diversity](https://mlsanity.com/paper/2510.01171/) (2025)
- [Why Do Large Language Models (LLMs) Struggle to Count Letters?](https://mlsanity.com/paper/2412.18626/) (2024)
- [Large Linguistic Models: Investigating LLMs' metalinguistic abilities](https://mlsanity.com/paper/2305.00948/) (2023)
- [Autoregressive Large Language Models are Computationally Universal](https://mlsanity.com/paper/2410.03170/) (2024)

## Abstract (arXiv)

Large language models (LLMs) exhibit failure modes on seemingly trivial tasks. We propose a formalisation of LLM interaction using a deterministic multi-tape Turing machine, where each tape represents a distinct component: input characters, tokens, vocabulary, model parameters, activations, probability distributions, and output text. The model enables precise localisation of failure modes to specific pipeline stages, revealing, e.g., how tokenisation obscures character-level structure needed for counting tasks. The model clarifies why techniques like chain-of-thought prompting help, by externalising computation on the output tape, while also revealing their fundamental limitations. This approach provides a rigorous, falsifiable alternative to geometric metaphors and complements empirical scaling laws with principled error analysis.