# Proactive Routing to Interpretable Surrogates with Distribution-Free Safety Guarantees

arXiv: https://arxiv.org/abs/2603.14623 · HTML: https://mlsanity.com/paper/2603.14623/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 15 Mar 2026.

## Builds on (most cited first, 20 of 20)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [SkipNet: Learning Dynamic Routing in Convolutional Networks](https://mlsanity.com/paper/1711.09485/) (2017)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [BlockDrop: Dynamic Inference Paths in Residual Networks](https://mlsanity.com/paper/1711.08393/) (2017)
- [Conformal Arbitrage: Risk-Controlled Balancing of Competing Objectives in Language Models](https://mlsanity.com/paper/2506.00911/) (2025)
- [C3PO: Optimized Large Language Model Cascades with Probabilistic Cost Constraints for Reasoning](https://mlsanity.com/paper/2511.07396/) (2025)
- [LEC: Linear Expectation Constraints for Selection-Conditioned Risk Control in Selective Prediction and Routing Systems](https://mlsanity.com/paper/2512.01556/) (2025)

## Built on by (most cited first, 2 of 2)

- [RouteGuard: Certifying Routing Gain in LLM Multi-Agent Systems When Complementarity Is Not Enough](https://mlsanity.com/paper/2608.07583/) (2026)
- [Threshold-Aware Conformal Routing](https://mlsanity.com/paper/2610.02487/) (2026)

## Abstract (arXiv)

Model routing determines whether to use an accurate black-box model or a simpler surrogate that approximates it at lower cost or greater interpretability. In deployment settings, practitioners often wish to restrict surrogate use to inputs where its degradation relative to a reference model is controlled. We study proactive (input-based) routing, in which a lightweight gate selects the model before either runs, enabling distribution-free control of the fraction of routed inputs whose degradation exceeds a tolerance τ. The gate is trained to distinguish safe from unsafe inputs, and a routing threshold is chosen via Clopper-Pearson conformal calibration on a held-out set, guaranteeing that the routed-set violation rate is at most α with probability 1-δ. We derive a feasibility condition linking safe routing to the base safe rate π and risk budget α, along with sufficient AUC thresholds ensuring that feasible routing exists. Across 35 OpenML datasets and multiple black-box model families, gate-based conformal routing maintains controlled violation while achieving substantially higher coverage than regression conformal and naive baselines. We further show that probabilistic calibration primarily affects routing efficiency rather than distribution-free validity.