Routing by Geometry: Weak-to-Strong LLM Inference with MAGE

Weak-to-strong routing reduces inference cost by escalating selected queries to a stronger language model, but effective routing requires identifying which queries are likely to benefit from escalation. We introduce Model-Adaptive Geometric Escalation (MAGE), a white-box router that probes local predictive sensitivity by applying small Gaussian perturbations to an intermediate weak-model hidden state using only forward passes. The resulting perturbation responses provide a geometric signal motivated by Fisher information complementary to output uncertainty. At its core, MAGE combines perturbation-response statistics with margin uncertainty to form a label-free default ranking for escalation. Calibration labels and predictions from both models refine this ranking to reward successful rescues and penalize harmful escalations, while reliability shrinkage limits adjustments when calibration support is weak. Across eight multiple-choice benchmarks, MAGE achieves a higher observed macro-averaged area under the accuracy–budget curve than all five adapted routing baselines on both Qwen and Llama endpoint pairs. These results highlight local predictive sensitivity as a complementary signal for balancing prediction quality and inference cost in weak-to-strong model routing.