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This study reveals a fundamental limitation in LLMs where error accumulation follows a super-linear, double-exponential law rather than simple independent decay, causing accuracy to collapse sharply after a specific sequence length. The authors demonstrate that per-step errors are not independent but interact through dense couplings, challenging standard assumptions about model reliability on repetitive deterministic tasks. These findings provide critical insight into the structural constraints of current generative models when performing long-chain reasoning or multi-step operations.
A Quantitative Study of Sustained Focus in Large Language Models via Repetitive Deterministic Prediction Tasks
arXiv:2511.00763v3 Announce Type: replace Abstract: We investigate the performance of large language models (LLMs) on repetitive deterministic prediction tasks and study how the sequence accuracy rate (SAR) scales with output length. Each such task involves the repetition of the same operation $N$ times. Examples of such tasks include letter replacement in letter strings following a given rule, integer addition, and multiplication of string operators in many-body quantum mechanics. If the LLM performs the task by a simple repetition algorithm, the success rate would follow an exponential decay with sequence length. In contrast, our experiments on leading LLMs reveal a crossover that is sharper than exponential: $-\log\mathrm{SAR}$ grows super-linearly with $N$, and accuracy collapses around a characteristic length $N_*$, the accuracy cliff that separates reliable from unreliable generation. The hypothesis of independent per-step errors is rejected for every model and task we studied. The crossover is well described by a double-exponential accumulation law, $\mathrm{SAR}=\exp(-\beta_0 N\alpha^{N-1})$, whose crossover scale $N_*$ does not depend on the functional form chosen to fit it. To interpret this behaviour we introduce a minimal effective model in which step-correctness variables interact through dense random couplings and compete with an external field set by the prompt. Solved by direct enumeration, the model reproduces the super-linear error accumulation and the accuracy cliff qualitatively, and it assigns to each model--task pair two interpretable parameters, an intrinsic error rate and an error-accumulation factor.
Abstract:We investigate the performance of large language models (LLMs) on repetitive deterministic prediction tasks and study how the sequence accuracy rate (SAR) scales with output length. Each such task involves the repetition of the same operation $N$ times. Examples of such tasks include letter replacement in letter strings following a given rule, integer addition, and multiplication of string operators in many-body quantum mechanics. If the LLM performs the task by a simple repetition algorithm, the success rate would follow an exponential decay with sequence length. In contrast, our experiments on leading LLMs reveal a crossover that is sharper than exponential: $-\log\mathrm{SAR}$ grows super-linearly with $N$, and accuracy collapses around a characteristic length $N_*$, the accuracy cliff that separates reliable from unreliable generation. The hypothesis of independent per-step errors is rejected for every model and task we studied. The crossover is well described by a double-exponential accumulation law, $\mathrm{SAR}=\exp(-\beta_0 N\alpha^{N-1})$, whose crossover scale $N_*$ does not depend on the functional form chosen to fit it. To interpret this behaviour we introduce a minimal effective model in which step-correctness variables interact through dense random couplings and compete with an external field set by the prompt. Solved by direct enumeration, the model reproduces the super-linear error accumulation and the accuracy cliff qualitatively, and it assigns to each model--task pair two interpretable parameters, an intrinsic error rate and an error-accumulation factor.
Artificial Intelligence (cs.AI)
arXiv:2511.00763 [cs.AI]
(or arXiv:2511.00763v3 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2511.00763 Focus to learn more arXiv-issued DOI via DataCite
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