aiqbench analysis
This paper offers a rigorous theoretical framework by modeling LLM interactions as deterministic multi-tape Turing machines to precisely localize systematic reasoning failures within specific pipeline stages. By mapping components like tokenization and activations to distinct tapes, the study provides a falsifiable alternative to geometric metaphors for understanding why techniques such as chain-of-thought prompting succeed or fail. This principled error analysis complements empirical scaling laws with structural insights essential for advancing model reliability.
Understanding LLM Failures: A Multi-Tape Turing Machine Analysis of Systematic Errors in Language Model Reasoning
arXiv:2602.15868v3 Announce Type: replace 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.
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.
8 pages, 1 page appendix; v2 added Acknowledgements; v3 is 7 pages. Substantially revised exposition and claims; title changed; related work and references updated; no new empirical results
Computation and Language (cs.CL)
arXiv:2602.15868 [cs.CL]
(or arXiv:2602.15868v3 [cs.CL] for this version)
Full text under the publisher's open licence · 147 words
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