When is Routing Meaningful? Diversity and Robustness in Language Model Societies
Authors: Fantine Huot, Michael Kaisers, Mirella Lapata
Organizations: Google DeepMind
Abstract
Routing policies for multi-model systems are evaluated almost exclusively on task accuracy and inference cost. We argue that two properties, orthogonal to performance, determine whether routing is meaningful. First, the society of actors must be behaviourally differentiated: if all actors respond identically, routing is vacuous. Second, the routing policy must be stable: surface-form variants of a query should be assigned to the same actor. High task accuracy is compatible with violating both properties, since a router can operate over a redundant society or assign queries inconsistently, preventing specialisation regardless of performance. We adapt Hierarchic Social Entropy (HSE) to language-model societies and introduce a perturbation-based robustness metric to diagnose these failure modes. Applied to EmbedLLM and RouterBench, we find that HSE exhibits strong diminishing returns, suggesting that a curated subset of fewer than ten agents recovers most available diversity in a large pool -- a practical coreset heuristic for society design. We further find that KNN routers gain accuracy from specialist societies but collapse in robustness under perturbation, while prompted routing remains stable across all perturbation types -- illustrating that accuracy and meaningfulness can sharply diverge.
LLM routing has become a popular approach to improve the cost-quality trade-off of LLM services by dynamically selecting a model for each query. Recent work has explored a broad range of routing methods, including clustering-based routers, learned classifiers, pairwise ranking, and confidence-based approaches. Our extensive study of 21 routing methods across five benchmarks reveals a consistent phenomenon that we call the routing plateau: many methods, including kNN, achieve very similar accuracy and converge to a narrow performance range that remains far below the oracle router. Our investigation shows that the plateau is largely caused by a predictability bottleneck: current routers mainly learn global averaged model-performance trends rather than fine-grained query-specific routing signals. As a result, they solve overlapping easy queries but collectively fail on hard queries that require instance-specific routing decisions. We further study how to move beyond the plateau and find that larger training datasets, stronger encoders, and end-to-end fine-tuning can further improve routing accuracy. These findings characterize the common limits of current routing methods and provide insights and actionable directions for the community to build more effective routing systems.
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.
Oracle routing measures how much a pool of language models could gain from per-query selection, but the diagnostic has two flaws: testing against a best fixed model selected on the same examples invalidates paired inference, and a full-information oracle sees outcomes no deployable router observes. We separate three estimands (outcome-oracle opportunity, the Bayes-optimal gain from a declared pre-answer signal, and the held-out gain of a learned router) and prove selection-valid confidence intervals that survive choosing the best fixed model or the best member of a router family, a signal-information sandwich, and a (1−1/e) greedy guarantee for building compact pools from submodular complementary coverage. On eight checkpoints from six families over four benchmarks, selection-valid intervals certify a population oracle gap of 9.7--30.7 points on every task, yet the strongest deployable prompt router recovers only 7.5--14.4% of it, and the simultaneous interval for the best of eleven tested policies has lower limit zero throughout. The realizable share of oracle opportunity is small and certifiable: strong routers beat the best fixed model, and most of the gap remains.
Ibne Farabi Shihab, Abu Sa-Adat Mohamed Moon-Im Al Ahsan, Md Najmus Swaqeeb