# MPD2-Router: Mask-aware Multi-expert Prior-regularized Dual-head Deferral Router in Glaucoma Screening and Diagnosis

arXiv: https://arxiv.org/abs/2605.08024 · HTML: https://mlsanity.com/paper/2605.08024/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 37 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 19 of 19)

- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [ViM: Out-Of-Distribution with Virtual-logit Matching](https://mlsanity.com/paper/2203.10807/) (2022)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Consistent Estimators for Learning to Defer to an Expert](https://mlsanity.com/paper/2006.01862/) (2020)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [REFUGE Challenge: A Unified Framework for Evaluating Automated Methods for Glaucoma Assessment from Fundus Photographs](https://mlsanity.com/paper/1910.03667/) (2019)
- [The Algorithmic Automation Problem: Prediction, Triage, and Human Effort](https://mlsanity.com/paper/1903.12220/) (2019)
- [Differentiable Learning Under Triage](https://mlsanity.com/paper/2103.08902/) (2021)
- [Towards Unbiased and Accurate Deferral to Multiple Experts](https://mlsanity.com/paper/2102.13004/) (2021)
- [Calibrated Learning to Defer with One-vs-All Classifiers](https://mlsanity.com/paper/2202.03673/) (2022)
- [Grader variability and the importance of reference standards for evaluating machine learning models for diabetic retinopathy](https://mlsanity.com/paper/1710.01711/) (2017)
- [Forming Effective Human-AI Teams: Building Machine Learning Models that Complement the Capabilities of Multiple Experts](https://mlsanity.com/paper/2206.07948/) (2022)
- [Principled Approaches for Learning to Defer with Multiple Experts](https://mlsanity.com/paper/2310.14774/) (2023)
- [Learning to Defer to a Population: A Meta-Learning Approach](https://mlsanity.com/paper/2403.02683/) (2024)
- [In Defense of Softmax Parametrization for Calibrated and Consistent Learning to Defer](https://mlsanity.com/paper/2311.01106/) (2023)
- [Cost-Sensitive Learning to Defer to Multiple Experts with Workload Constraints](https://mlsanity.com/paper/2403.06906/) (2024)

## Abstract (arXiv)

Learning-to-defer (L2D) can make glaucoma screening safer by routing difficult/uncertain cases to humans, yet standard formulations overlook expert availability, heterogeneous readers behavior, workload imbalance, asymmetric diagnostic harm, case difficulty from morphology and deployment shift. We introduce MPD2-Router, a mask-aware multi-expert deferral framework that recasts ophthalmic triage as constrained human--AI routing: whether to defer and to which available expert. It couples a dual-head deferral/allocation policy with mask-aware Gumbel--sigmoid gating that strictly enforces per-sample availability, and fuses uncertainty, morphology, image-quality, and OOD signals. Training uses an asymmetric cost-sensitive objective with an augmented-Lagrangian deferral budget, a group-specific distribution prior, and a rank-majorization JS regularizer that jointly prevent expert collapse without forcing uniform allocation. Across three cross-national glaucoma cohorts (REFUGE, CHAKSU, ORIGA) with a frozen REFUGE-trained backbone, MPD2-Router substantially lowers clinical cost and improves MCC over AI-only at a moderate deferral rate. It is Pareto-optimal in F1--MCC--cost, robust under cross-domain shift, and yields balanced expert utilization.