Predicting LLM Hallucination Risk from Entity Frequency via Rate-Distortion Theory

TMLR Paper8200 Authors

Abstract: Large language models struggle with factual hallucinations, and mitigating them typically requires executing the model to assess uncertainty. We introduce a query-dependent rate--distortion framework showing that factual accuracy follows a predictable, sigmoidal ``knowledge cliff'' governed by training exposure. Below a critical frequency $f_{\mathrm{crit}}$, the model lacks the representational budget to reliably retrieve facts; above this threshold, accuracy increases precipitously. We present five core findings based on this framework. First, mapping this frequency response yields an accurate, zero-compute risk score; we formally prove that this pre-inference metric achieves $>99\%$ of the theoretical upper bound for any frequency-only predictor. Second, this cliff is heterogeneous, with $f_{\mathrm{crit}}$ varying by up to $76\times$ depending on the query's relation type. Integrating these structural metadata creates a classifier that outperforms the LLM's own post-inference confidence scores in the rare-entity tail. Third, we establish a sample-complexity bound demonstrating that the calibration data required to locate this cliff under Zipfian sampling is independent of its location. Fourth, we isolate the effect of model scale using the Qwen2.5-Instruct family (0.5B--14B, trained on a fixed corpus), revealing a power-law relationship ($f_{\mathrm{crit}} \propto P^{-0.52}$) where a $10\times$ parameter increase yields reliable recall for entities only $\sim 3.3\times$ less frequent. Finally, we show that these metadata-driven signals establish a superior budget--utility frontier for retrieval routing. By demonstrating that reliability is largely determined by query properties prior to generation, this work enables highly efficient, pre-hoc triage for retrieval-augmented systems.

Submission Type: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=OBb7pMS9ph

Changes Since Last Submission:

Dear Editors,

This is a resubmission of https://openreview.net/forum?id=OBb7pMS9ph Our previous submission was administratively desk-rejected due to formatting errors (the inclusion of layout-altering packages such as caption and enumitem, and an empty author macro that broke the tmlr.sty header generation). We have removed all forbidden packages and ensured strict compliance with the unmodified tmlr.sty template. No changes have been made to the scientific content or methodology.

Thank you for your consideration,

Assigned Action Editor: ~Jian_Kang1

Submission Number: 8200