# ERRORQUAKE: Heavy-Tailed Error Severity Distributions in Open-Weight Large Language Models

arXiv: https://arxiv.org/abs/2606.05170 · HTML: https://mlsanity.com/paper/2606.05170/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Builds on (most cited first, 17 of 17)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [FaithDial: A Faithful Benchmark for Information-Seeking Dialogue](https://mlsanity.com/paper/2204.10757/) (2022)
- [MedHallu: A Comprehensive Benchmark for Detecting Medical Hallucinations in Large Language Models](https://mlsanity.com/paper/2502.14302/) (2025)
- [Lost in Transcription, Found in Distribution Shift: Demystifying Hallucination in Speech Foundation Models](https://mlsanity.com/paper/2502.12414/) (2025)
- [Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications](https://mlsanity.com/paper/2001.10488/) (2020)
- [MedHEval: Benchmarking Hallucinations and Mitigation Strategies in Medical Large Vision-Language Models](https://mlsanity.com/paper/2503.02157/) (2025)
- [Towards a Systematic Evaluation of Hallucinations in Large-Vision Language Models](https://mlsanity.com/paper/2412.20622/) (2024)
- [Overview of the ClinIQLink 2025 Shared Task on Medical Question-Answering](https://mlsanity.com/paper/2506.21597/) (2025)

## Abstract (arXiv)

At matched accuracy, open-weight LLMs differ substantially in the shape of their error severity distribution -- a difference invisible to the scalar error rate. Hallucination benchmarks report a single error count and treat all errors as equivalent, yet a wrong date and a fabricated court ruling differ by orders of magnitude. We introduce Errorquake-10k, a 10,000-query benchmark scoring each response on a continuous 0-4 severity scale across 8 domains and 5 difficulty tiers, and we fit per-model severity distributions for 21 open-weight models. For each model we estimate a severity distribution index (b, the Gutenberg-Richter upper-tail slope) with 95% bootstrap confidence intervals. Headline: across the 210 model pairs, 85 have disjoint 95% b confidence intervals at matched accuracy (|Delta epsilon| < 0.05) on human-consensus scoring, e.g. deepseek-v3.2 vs. ministral-14b at epsilon = 0.586 and Delta b = 0.47. A 519-item three-rater human validation study confirms measurement reliability (ICC(2,k=3) = 0.85), validates the LLM-judge ranking (rho = 0.89), and confirms the dense-model scaling correlation on human data (rho_s = -0.86). We prove a Non-Reducibility Theorem showing that severity profile and error rate are informationally non-redundant (I(b; model | epsilon) = 1.56 bits; 64.5% of cross-model b variance is unexplained by epsilon). A severity mechanism taxonomy (kappa = 0.83) reveals that error type shifts categorically with severity: low-severity errors are retrievals (71%); high-severity errors are fabrications (39%) -- and this composition differs by model size (p < 0.0001). Severity distribution should be reported alongside accuracy; it carries discriminative information that the error rate cannot.