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.
Sharing context between LLMs in a multi-model system requires the receiving model to prefill the shared prefix because KV caches are model-specific. Recent closed-form cross-model KV transfer, hereafter Full-Head Mapping, avoids this replay by fitting a training-free affine mapper from source to target caches. However, its full-head design maps each target KV head from every source KV head in the selected layers, making transfer quality sensitive to architectural differences and causing mapper storage and application cost to grow with layer support. To this end, we introduce CacheBridge, which co-designs architecture-indexed mapper support, attention-aligned calibration, and bounded mapper construction while retaining a closed-form affine interface for online deployment. CacheBridge restricts each target head to a matched source head, weights reconstruction errors by causal attention sensitivity, and uses a fused GPU kernel to construct weighted sufficient statistics without materializing full observation tensors. Across three transfer directions, CacheBridge recovers the two Ministral 3 transfer directions where Full-Head Mapping loses substantial accuracy while preserving 99.83\% mean target retention on Qwen3. On Qwen3 $14\mathrm{B}\to32\mathrm{B}$, it reduces mapper storage by $8\times$, accelerates application by up to $3.0\times$, matches \fullhead with one tenth of the calibration data, and reduces 500-sequence construction from 92.63 to 8.63 seconds ($10.7\times$).
Multi-model LLM systems such as routing, voting, cascades, fusion, and mixture-of-agents are used to beat single-model accuracy. We show that their gain is capped by a quantity the field rarely reports. For any policy whose output is one member model answer, accuracy cannot exceed one minus beta, where beta is the rate at which every model is wrong on the same query. In contrast, the usual diagnostic, average pairwise error correlation rho, cannot identify beta: error laws with identical marginals and pairwise correlations can have different all-wrong rates. A Clopper-Pearson bound on beta gives a finite-sample certificate on the largest gain any router, vote, or cascade could deliver before training a router. Across 67 models from 21 providers, a tetrachoric-calibrated single-factor model still underprices the all-wrong tail: on open-ended mathematics, observed beta is 0.052 versus 0.023 under the full 67-model Gaussian copula, about 2.5 times underpricing, with 90 percent CI 1.7 to 3.4 and k equals 17. The effect recurs on execution-graded code, where beta is 0.079. Re-asking the same GPQA-Diamond questions in free-response rather than multiple-choice form reopens the tail, with beta 0.127 and a five-judge panel with kappa 0.73 to 0.92, locating co-failure in answer format rather than subject. At matched quality, low-rho heterogeneous ensembles beat high-rho Self-MoA, but on checkable tasks in our pool, combining models rarely beats the single best model without a strong query-level routing signal. Gains come from models failing on different questions, not from adding more models.