Limits of Reliability and Scaling in Language Models

arXiv:2607.14112v2 Announce Type: replace Abstract: Large language models (LLMs) are trained and evaluated as though perfect reliability is achievable for any task given sufficient scale. We show that this assumption is information-theoretically unjustified. Every generative task has a reliability ceiling that no model can exceed, determined by how much output uncertainty is resolvable from observable context. The gap decomposes into a resolvable component closable with additional context and a subjective component inherent to task ambiguity. Autoregressive generation further degrades this ceiling at a rate governed by the task's dependency kernel, which quantifies inter-token correlations in the output. From these two primitives, we derive a first-principles scaling law where LLM performance is bottlenecked by the scarcer resource: training data or model capacity. This law recovers the Chinchilla scaling law as a special case and provides a structural account of when scaling improves reliability. Beyond scaling, our framework unifies diverse practical phenomena, such as the benefits of retrieval-augmentation and the spectral mechanics of catastrophic forgetting. Our work formalizes the resource-complexity tradeoffs that govern model performance across domains, offering a unified theory of performance limits in generative language models.

Abstract:Large language models (LLMs) are trained and evaluated as though perfect reliability is achievable for any task given sufficient scale. We show that this assumption is information-theoretically unjustified. Every generative task has a reliability ceiling that no model can exceed, determined by how much output uncertainty is resolvable from observable context. The gap decomposes into a resolvable component closable with additional context and a subjective component inherent to task ambiguity. Autoregressive generation further degrades this ceiling at a rate governed by the task's dependency kernel, which quantifies inter-token correlations in the output. From these two primitives, we derive a first-principles scaling law where LLM performance is bottlenecked by the scarcer resource: training data or model capacity. This law recovers the Chinchilla scaling law as a special case and provides a structural account of when scaling improves reliability. Beyond scaling, our framework unifies diverse practical phenomena, such as the benefits of retrieval-augmentation and the spectral mechanics of catastrophic forgetting. Our work formalizes the resource-complexity tradeoffs that govern model performance across domains, offering a unified theory of performance limits in generative language models.

Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Information Theory (cs.IT)

arXiv:2607.14112 [cs.CL]

(or arXiv:2607.14112v2 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2607.14112 Focus to learn more arXiv-issued DOI via DataCite

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Limits of Reliability and Scaling in Language Models

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