Correlated Errors in Language Models

Self-consistency assumes that independent samples disagree when a model is unsure, so agreement is evidence of correctness. Holding weights fixed and toggling only a reasoning mode, over five benchmarks and 74,944 samples, we show that reasoning concentrates a model's errors: the probability that two independently drawn wrong answers coincide rises in all ten dataset-scale comparisons (p = 0.00098), and in nine of nine after restricting both arms to the problems each gets wrong. Where the answer space is unbounded, reasoning cuts the distinct answers produced to 0.43-0.65 of the non-reasoning count; where it is bounded, both arms hold an identical option set and reasoning concentrates mass on it instead, which no positional prior can explain at fixed weights. The aggregate cost is smaller than the mechanism predicts, because reasoning also shrinks the set of problems where answer diversity can decide anything, in ten of ten cells and by 2.7x; normalized for available headroom, both arms convert a quarter of it in domain. Confidence weighting does not recover what is left. Across 280 method-dataset-model combinations on eight models and five benchmarks, not one beats plain majority voting after correction; weighted voting agrees with it on 98.5% of problem-method pairs and is right 56.3% of the time on the rest; and a signal's direction can invert within fixed weights, with answer log-probability predicting correctness when reasoning is off and error when it is on. A learned six-signal combination gains nothing out of domain. Confidence signals should be evaluated on decisions, not on discrimination.

Diversity is a widely observed factor in the resilient function of collective systems, yet the type of diversity that matters depends on the properties and failure modes of the system. This distinction is important for systems composed of multiple language models. Different models may be treated as independent components even when their behaviour and failures remain strongly correlated. Assessments of language-model populations using semantic similarity demonstrate limited semantic diversity, but this captures only differences in the meaning of observed outputs. We argue that a more fundamental notion of model diversity is generative-process diversity, the differences between processes capable of generating the observed outputs. Drawing from Algorithmic Information Theory, we use Normalised Compression Distance between raw model outputs, residualised against a permutation control, as a measure of inferred generative-process diversity. Across 38 language models, this measure identifies population structure missed by semantic similarity and predicts cross-task variation in chance-corrected correlated failure among model pairs across ten disjoint benchmark families, beyond semantic similarity and model-pair capability. The cross-benchmark partial rank association is $-0.216$ with a 95% interval of $[-0.309,-0.122]$, and the estimate is negative on all ten benchmarks. These results indicate that increased generative-process diversity is associated with reduced correlated failure in model pairs that is not attributable to semantic similarity or capability. Inferred generative-process diversity offers a novel and practical approach for investigating diversity of multi-model systems in safety-relevant contexts.

Panels of inexpensive LLM judges increasingly make accept-or-escalate decisions. In factuality settings, accepting a claim because several reference-free judges agree can create a hidden risk: agreement may reflect shared false-negative blind spots rather than independent evidence. We introduce JuryProbe, an empirical consensus-risk diagnostic for reference-free factuality judge panels, paired with a calibration-based routing policy. JuryProbe estimates consensus risk from a labeled calibration probe using false-negative-only (FN-only) judge correlation and false-consensus lift; when flagged high-risk, reference-free majority accepts are routed to the same judges with trusted references. On audited FEVER corruptions, reference-free panels show correlated false negatives (FN-only correlations 0.402 and 0.368; lifts 3.13x and 18.13x), while unanimous false consensus drops to zero under a trusted-reference best-case diagnostic on both minimal-pair and non-minimal-pair evidence. In flagged settings, the routed policy is by construction equivalent to grounding every reference-free majority accept (verified in 34/34 splits): improvement comes from accept-conditioned grounding, while the diagnostic determines whether to activate it. A fixed, pre-specified rule flags 8-10 of 10 splits across synthetic, benchmark-authored, and scientific families and 0 of 10 on a negative control, where standing down avoids 28% of reference acquisitions at a 0.004 increase in false accepts. False-accept reduction persists under weak BM25 retrieval at substantial coverage cost, while stale stand-down labels require periodic recalibration. JuryProbe provides no formal risk guarantee and does not establish reliable stand-down on natural panels; its supported contribution is an empirical diagnostic of high-risk panel error dependence.

Multi-Agent Debate (MAD) with Majority Voting is a dominant paradigm for improving LLM reasoning, yet its effectiveness rests on the Condorcet Jury Theorem's assumption of independent errors. Because contemporary LLMs share similar pretraining corpora, their errors are strongly correlated, causing the majority to systematically suppress correct minority opinions, a phenomenon we term Minority Truth. Through debates among three heterogeneous LLM agents on six benchmarks, we find that roughly one in four divergent cases has the minority holding the correct answer, yielding a 10-percentage-point theoretical recovery margin. We propose Minority Sentinel, a lightweight meta-classifier that extracts a multi-dimensional debate fingerprint from debate logs and trains a LightGBM model to decide when to overturn majority voting. Minority Sentinel achieves a stable Flip Precision of 81.2% with positive Net Gain across all six datasets and all 20 random seed trials, demonstrating that debate logs contain sufficient behavioral signals for a non-LLM classifier to reliably recover suppressed minorities without degrading system accuracy. The LLM-as-Judge baseline yields negative Net Gain despite higher recall, confirming that flip safety, not recovery volume, determines intervention value.

LLM-as-a-judge panels aggregate votes from multiple models, with the expectation that diverse models yield more reliable evaluations. We develop a framework to measure the true informational value of such panels and quantify how far their reliability falls short of the independent-voting ideal. Testing a panel of 9 frontier LLMs from 7 model families on three natural language inference datasets (each with 100 human annotations per item), we find that the 9 judges effectively provide only about 2 independent votes' worth of information. Roughly three-quarters of the panel's nominal independence is lost because the models make the same mistakes on the same items. The consequences are stark: the panel's actual accuracy falls 8-22 percentage points short of what independent voting would achieve, and the best single judge matches or outperforms the full panel across all conditions. Neither adding more judges nor using smarter aggregation algorithms helps -- established methods close at most 11% of this gap, even with access to the correct answers. We quantify these findings using the Kish effective sample size (n_eff) and a Condorcet null model, and show the deficit is robust across prompt variants, temperatures, chain-of-thought reasoning, and a pairwise preference task (RewardBench). The bottleneck is correlated judges, not the aggregation algorithm, implying that scaling up panels cannot substitute for genuinely independent evaluation.

The rapid growth of the large language model (LLM) ecosystem raises a critical question: are seemingly diverse models truly independent? Shared pretraining data, distillation, and alignment pipelines can induce hidden behavioral dependencies, or latent entanglement, that undermine multi-model systems such as LLM-as-a-judge pipelines and ensemble verification, which implicitly assume independent signals. In practice, this manifests as correlated reasoning patterns and synchronized failures, where apparent agreement reflects shared error modes rather than independent validation. To address this, we develop a statistical framework for auditing behavioral entanglement among black-box LLMs. Our approach introduces a multi-resolution hierarchy that characterizes the joint failure manifold through two information-theoretic metrics: (i) a Difficulty-Weighted Behavioral Entanglement Index (BEI), which amplifies synchronized failures on easy tasks, and (ii) a Cumulative Information Gain (CIG) metric, which captures directional alignment in erroneous responses. Through experiments on 18 LLMs from six model families, we identify statistically significant behavioral entanglement. Such behavioral dependence is associated with judge over-endorsement bias on a disjoint MMLU-Pro evaluation set (rho = 0.508 for BEI and rho = 0.520 for CIG; p < 0.01). The association further transfers to the MATH-500 benchmark (rho = 0.441 for BEI and rho = 0.457 for CIG; p < 0.05), providing cross-benchmark evidence that the identified dependency structure generalizes beyond the data and response format used for its estimation. Finally, we demonstrate a practical use case of entanglement through de-entangled verifier ensemble reweighting, achieving 3.5 and 2.6 percentage-point gains in accuracy and precision, respectively, over majority voting.

When large language models (LLMs) are consulted as forecasting tools, the independence of individual errors -- the foundation of collective intelligence -- may collapse. We test three conditions necessary for this "epistemic monoculture" to emerge. In Study 1, we show that GPT-4o, Claude, and Gemini exhibit highly correlated forecasting errors on 568 resolved binary prediction questions (mean pairwise error correlation r = 0.77, p < 0.001; r = 0.78 excluding likely-leaked questions), despite being developed independently by different organizations. In Study 2, we test whether this correlated bias has propagated into human crowd forecasts, using a within-question design that tracks community prediction shifts across the ChatGPT launch boundary (November 2022). We find that community forecasts move in the direction predicted by LLMs (r = 0.20, p = 0.007), but this shift is fully explained by rational updating toward ground truth. In Study 3, we examine whether the category-level pattern of human forecasting errors increasingly resembles the LLM bias fingerprint. We find the opposite: pre-ChatGPT human biases already strongly resembled the LLM pattern (r = 0.87), while post-ChatGPT the resemblance weakened (r = -0.28). Together, these findings reveal an epistemic monoculture that is built but not yet activated: three nominally independent AI systems share the same failure modes, amplifying precisely the biases humans already hold.

Pass@k and other methods of scaling inference compute can improve language model performance in domains with external verifiers, including mathematics and code, where incorrect candidates can be filtered reliably. This raises a natural question: can we similarly scale compute to elicit gains in truthfulness for domains without convenient verification? We show that across five benchmarks and models, surprisingly, it cannot. Even at 25x the inference cost of naive sampling, polling-style aggregation yields no consistent accuracy gains over single-sample baselines and often amplifies shared misconceptions. We find that under uncertainty, models are better at predicting what other models will say within model ensembles than at identifying what is true, revealing a separation between social prediction and truth verification. Across models and benchmarks, aggregation fails to provide a robust truth signal because language model errors are strongly correlated. The source of correlation goes beyond any individual benchmark: we show that even when conditioned on out of distribution random strings and asked to produce pseudo-random outputs, different models produce correlated outputs. Confidence-based weighting provides no benefit because self-reported confidence fails to reliably distinguish correct from incorrect answers. These results delineate a boundary for inference-time scaling: in verified domains, additional samples provide more candidates for a verifier to filter; in unverified domains, additional samples merely reinforce shared misconceptions.