Predictable performance is suboptimal, and what it means for model routing
Guanhua Zhang and Moritz Hardt (Max Planck Institute for Intelligent Systems, Tubingen AI Center) prove that a separate predictor of whether a model will answer correctly can beat the model's own self-confidence only when the model is suboptimal or the predictor adds substantial capacity.
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Transfer result. Any predictor that beats a model's self-confidence can be used, through recalibration, to reduce that model's log loss by exactly the same amount.
Bound. Accounting for the predictor's extra parameters, its advantage is bounded by the model's suboptimality plus the gain from those parameters. The same bound limits how many extra weak-model errors a two-model cascade can catch compared with confidence routing.
Experiments. Across 16 language models and four benchmarks, predictors have a larger advantage over self-confidence on more suboptimal models, and the advantage shrinks after finetuning.
Implication for routing. Predictor-based routing beats confidence-based routing mainly for weak models, so improving the model can remove the need for a separate router. When self-confidence is unavailable, recovering it is already a source of predictor value.
Abstract
Large language models (LLMs) differ in capabilities and costs, motivating routing methods that adaptively choose a model for each query. These methods rely on performance prediction: given a query, estimate whether a model will answer it correctly. Most routing methods train separate predictors of candidate models' performance to guide model selection. Our work shows that performance prediction only beats a simple baseline when the candidate model is suboptimal on the task or the performance predictor adds significant capacity relative to the candidate model. Specifically, we take a model's self-confidence, the probability it assigns to its chosen answer, as a baseline and study how much a performance predictor can improve on it. First, we show that any performance predictor that outperforms a model's self-confidence can be used to improve the model's loss: the predictor's advantage transfers exactly in log loss through recalibration. Second, accounting for the predictor's additional parameters, we bound its advantage by the model's suboptimality plus the gain from those parameters. Third, we extend our theoretical results to two-model cascades, which route queries to a more capable model when the first model is predicted to fail. Experiments with 16 language models on four benchmarks show that predictors gain a larger advantage over self-confidence on more suboptimal models. This advantage shrinks as models improve through finetuning. Cascading exhibits the same two patterns: predictor-based routing offers larger gains over confidence-based routing for more suboptimal models, and these gains diminish after finetuning.