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

TL;DR

This paper introduces a formal multi-tape Turing machine model to analyze systematic errors in large language models, clarifying failure modes and the impact of techniques like chain-of-thought prompting.

Contribution

It provides a novel formal framework for localizing LLM failures to specific pipeline stages, offering insights beyond empirical observations.

Findings

Tokenization can obscure character-level information needed for counting tasks.

Chain-of-thought prompting externalizes computation but has fundamental limitations.

The model offers a rigorous, falsifiable approach to understanding LLM errors.

Abstract

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.