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

We report a striking statistical regularity in frontier LLM outputs that enables a CPU-only scoring primitive running at 2.6 microseconds per token, with estimated latency up to 100,000$\times$ (five orders of magnitude) below existing sampling-based detectors. Across six contemporary models from five independent vendors, two generation sizes, and five held-out domains, token rank-frequency distributions converge to the same two-parameter Mandelbrot ranking distribution, with 34 of 36 model-by-domain fits exceeding $R^{2} = 0.94$ and 35 of 36 favoring Mandelbrot over Zipf by AIC. The shared family does not collapse the models into statistical duplicates. Fitted Mandelbrot parameters remain cleanly separable between models: the cross-model spread in $q$ (1.63 to 3.69) exceeds its per-model bootstrap standard deviation (0.03 to 0.10) by more than an order of magnitude, yielding tens of standard deviations of separation per few thousand output tokens. Two capabilities follow. First, statistical model fingerprinting: text from a vendor-delivered LLM can be tested against its claimed model family without cryptographic watermarks or access to model internals, supporting provenance verification and silent-substitution audits. Second, a model-agnostic reference distribution for black-box output assessment, from which we derive a single-pass scoring primitive that composes with model log probabilities when available and degrades to a rank-only mode usable on closed APIs. Pilot results on FRANK, TruthfulQA, and HaluEval map where the primitive helps (lexical anomalies, unsupported entities) and where it structurally cannot (reasoning errors in domain-appropriate vocabulary). We position the primitive as a first-pass triage layer in compound evaluation stacks, not as a replacement for sampling-based or source-conditioned verifiers.

How much do large language models actually hallucinate when answering questions grounded in provided documents? Despite the critical importance of this question for enterprise AI deployments, reliable measurement has been hampered by benchmarks that rely on static datasets vulnerable to contamination, LLM-based judges with documented biases, or evaluation scales too small for statistical confidence. We address this gap using RIKER, a ground-truth-first evaluation methodology that enables deterministic scoring without human annotation. Across 35 open-weight models, three context lengths (32K, 128K, and 200K tokens), four temperature settings, and three hardware platforms (NVIDIA H200, AMD MI300X, and Intel Gaudi 3), we conducted over 172 billion tokens of evaluation - an order of magnitude beyond prior work. Our findings reveal that: (1) even the best-performing models fabricate answers at a non-trivial rate - 1.19% at best at 32K, with top-tier models at 5 - 7% - and fabrication rises steeply with context length, nearly tripling at 128K and exceeding 10% for all models at 200K; (2) model selection dominates all other factors, with overall accuracy spanning a 72-percentage-point range and model family predicting fabrication resistance better than model size; (3) temperature effects are nuanced - T=0.0 yields the best overall accuracy in roughly 60% of cases, but higher temperatures reduce fabrication for the majority of models and dramatically reduce coherence loss (infinite generation loops), which can reach 48x higher rates at T=0.0 versus T=1.0; (4) grounding ability and fabrication resistance are distinct capabilities - models that excel at finding facts may still fabricate facts that do not exist; and (5) results are consistent across hardware platforms, confirming that deployment decisions need not be hardware-dependent.

Existing benchmarks typically report accuracy for a single model on a single run. This systematically understates real-world LLM capabilities, particularly under heterogeneous data distributions: (i) different models get different questions correct according to their specializations, and (ii) given a budget, multiple generations can be sampled and selectively retained. To quantify this gap, we introduce the Capability Frontier: a Pareto frontier over a set of models that characterizes the best achievable performance at each cost level under optimal selection across models and generations (i.e., via an oracle). Our construction corrects for two opposing biases: underestimation from single-model evaluation and overestimation from taking maxima over noisy samples. We study 21 LLMs across 16 widely used benchmarks spanning coding, reasoning, medicine, factuality, instruction following, and agentic tasks, comparing Capability Frontier performance at matched cost to each benchmark's top-performing model. Correcting for single-model evaluation yields a 54% error rate reduction; additionally correcting for single runs yields an 82% improvement, with SOTA accuracy matched at 85% cost reduction. Complementing these empirical results, we use controlled probabilistic simulations to show that higher query topic entropy produces a near-monotonic increase in the performance gap between oracle routing and the best single model. Our findings suggest collective LLM capabilities are substantially underestimated, with implications for evaluation and deployment in data-heterogeneous, multi-domain settings.